IEEE Transactions on Signal Processing

Published by Institute of Electrical and Electronics Engineers
Online ISSN: 1053-587X
Publications
Q-Q plots for ECG features, for the Sitting and Standing & Fidgeting activities for subjects J2 and E2, validating the Gaussian models employed to develop the optimal allocation.  
Percentage of the total 42 sessions that employ the indexed features, using the SU metric.  
Article
The optimal allocation of samples for physical activity detection in a wireless body area network for health-monitoring is considered. The number of biometric samples collected at the mobile device fusion center, from both device-internal and external Bluetooth heterogeneous sensors, is optimized to minimize the transmission power for a fixed number of samples, and to meet a performance requirement defined using the probability of misclassification between multiple hypotheses. A filter-based feature selection method determines an optimal feature set for classification, and a correlated Gaussian model is considered. Using experimental data from overweight adolescent subjects, it is found that allocating a greater proportion of samples to sensors which better discriminate between certain activity levels can result in either a lower probability of error or energy-savings ranging from 18% to 22%, in comparison to equal allocation of samples. The current activity of the subjects and the performance requirements do not significantly affect the optimal allocation, but employing personalized models results in improved energy-efficiency. As the number of samples is an integer, an exhaustive search to determine the optimal allocation is typical, but computationally expensive. To this end, an alternate, continuous-valued vector optimization is derived which yields approximately optimal allocations and can be implemented on the mobile fusion center due to its significantly lower complexity.
 
Article
This paper addresses the problem of approximating smooth bivariate functions from the samples of their partial derivatives. The approximation is carried out under the assumption that the subspace to which the functions to be recovered are supposed to belong, possesses an approximant in the form of a principal shift-invariant (PSI) subspace. Subsequently, the desired approximation is found as the element of the PSI subspace that fits the data the best in the (2)-sense. In order to alleviate the ill-posedness of the process of finding such a solution, we take advantage of the discrete nature of the problem under consideration. The proposed approach allows the explicit construction of a projection operator which maps the measured derivatives into a stable and unique approximation of the corresponding function. Moreover, the paper develops the concept of discrete PSI subspaces, which may be of relevance for several practical settings where one is given samples of a function instead of its continuously defined values. As a final point, the application of the proposed method to the problem of phase unwrapping in homomorphic deconvolution is described.
 
Article
Iterative image reconstruction can dramatically improve the image quality in X-ray computed tomography (CT), but the computation involves iterative steps of 3D forward- and back-projection, which impedes routine clinical use. To accelerate forward-projection, we analyze the CT geometry to identify the intrinsic parallelism and data access sequence for a highly parallel hardware architecture. To improve the efficiency of this architecture, we propose a water-filling buffer to remove pipeline stalls, and an out-of-order sectored processing to reduce the off-chip memory access by up to three orders of magnitude. We make a floating-point to fixed-point conversion based on numerical simulations and demonstrate comparable image quality at a much lower implementation cost. As a proof of concept, a 5-stage fully pipelined, 55-way parallel separable-footprint forward-projector is prototyped on a Xilinx Virtex-5 FPGA for a throughput of 925.8 million voxel projections/s at 200 MHz clock frequency, 4.6 times higher than an optimized 16-threaded program running on an 8-core 2.8-GHz CPU. A similar architecture can be applied to back-projection for a complete iterative image reconstruction system. The proposed algorithm and architecture can also be applied to hardware platforms such as graphics processing unit and digital signal processor to achieve significant accelerations.
 
Article
The positron emission tomography (PET) imaging technique enables the measurement of receptor distribution or neurotransmitter release in the living brain and the changes of the distribution with time and thus allows quantification of binding sites as well as the affinity of a radioligand. However, quantification of receptor binding studies obtained with PET is complicated by tissue heterogeneity in the sampling image elements (i.e., voxels, pixels). This effect is caused by a limited spatial resolution of the PET scanner. Spatial heterogeneity is often essential in understanding the underlying receptor binding process. Tracer kinetic modeling also often requires an intrusive collection of arterial blood samples. In this paper, we propose a likelihood-based framework in the voxel domain for quantitative imaging with or without the blood sampling of the input function. Radioligand kinetic parameters are estimated together with the input function. The parameters are initialized by a subspace-based algorithm and further refined by an iterative likelihood-based estimation procedure. The performance of the proposed scheme is examined by simulations. The results show that the proposed scheme provides reliable estimation of factor time-activity curves (TACs) and the underlying parametric images. A good match is noted between the result of the proposed approach and that of the Logan plot. Real brain PET data are also examined, and good performance is observed in determining the TACs and the underlying factor images.
 
Inferring the circle network using SG and SCSG with cross validation from n = 150 time samples. Black lines and numbers illustrate true connections and the percentage of 30 trials in which they are correctly identified. Red dotted lines and text identify the most common false connection and percentage of occurrence over 30 trials.  
Article
This paper addresses the problem of inferring sparse causal networks modeled by multivariate autoregressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score" ψ. In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that ψ < 1. The false connection score is also demonstrated to be a useful metric of recovery in nonasymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.
 
Article
We present a constructive algorithm for the design of real lapped equal-norm tight frame transforms. These transforms can be efficiently implemented through filter banks and have recently been proposed as a redundant counterpart to lapped orthogonal transforms, as well as an infinite-dimensional counterpart to harmonic tight frames. The proposed construction consists of two parts: First, we design a large class of new real lapped orthogonal transforms derived from submatrices of the discrete Fourier transform. Then, we seed these to obtain real lapped tight frame transforms corresponding to tight, equal-norm frames. We identify those frames that are maximally robust to erasures, and show that our construction leads to a large class of new lapped orthogonal transforms as well as new lapped tight frame transforms.
 
Article
Synchronization is crucial to wireless sensor networks. Recently a pulse-coupled synchronization strategy that emulates biological pulse-coupled agents has been used to achieve this goal. We propose to optimize the phase response function such that synchronization rate is maximized. Since the synchronization rate is increased independently of transmission power, energy consumption is reduced, hence extending the life of battery-powered sensor networks. Comparison with existing phase response functions confirms the effectiveness of the method.
 
Article
Synchronization is crucial to wireless sensor networks due to their decentralized structure. We propose an energy-efficient pulse-coupled synchronization strategy to achieve this goal. The basic idea is to reduce idle listening by intentionally introducing a large refractory period in the sensors' cooperation. The large refractory period greatly reduces idle listening in each oscillation period, and is analytically proven to have no influence on the time to synchronization. Hence, it significantly reduces the total energy consumption in a synchronization process. A topology control approach tailored for pulse-coupled synchronization is given to guarantee a k-edge strongly connected interaction topology, which is tolerant to communication-link failures. The topology control approach is totally decentralized and needs no information exchange among sensors, and it is applicable to dynamic network topologies as well. This facilitates a completely decentralized implementation of the synchronization strategy. The strategy is applicable to mobile sensor networks, too. QualNet case studies confirm the effectiveness of the synchronization strategy.
 
Article
Pulse-coupled synchronization is attracting increased attention in the sensor network community. Yet its properties have not been fully investigated. Using statistical analysis, we prove analytically that by controlling the number of connections at each node, synchronization can be guaranteed for generally pulse-coupled oscillators even in the presence of a refractory period. The approach does not require the initial phases to reside in half an oscillation cycle, which improves existing results. We also find that a refractory period can be strategically included to reduce idle listening at nearly no sacrifice to the synchronization probability. Given that reduced idle listening leads to higher energy efficiency in the synchronization process, the strategically added refractory period makes the synchronization scheme appealing to cheap sensor nodes, where energy is a precious system resource. We also analyzed the pulse-coupled synchronization in the presence of unreliable communication links and obtained similar results. QualNet experimental results are given to confirm the effectiveness of the theoretical predictions.
 
Article
A novel Empirical Mode Decomposition (EMD) algorithm, called 2T-EMD, for both mono- and multivariate signals is proposed in this paper. It differs from the other approaches by its computational lightness and its algorithmic simplicity. The method is essentially based on a redefinition of the signal mean envelope, computed thanks to new characteristic points, which offers the possibility to decompose multivariate signals without any projection. The scope of application of the novel algorithm is specified, and a comparison of the 2T-EMD technique with classical methods is performed on various simulated mono- and multivariate signals. The monovariate behaviour of the proposed method on noisy signals is then validated by decomposing a fractional Gaussian noise and an application to real life EEG data is finally presented.
 
Article
In this paper, we develop a comprehensive framework for optimal perturbation control of dynamic networks. The aim of the perturbation is to drive the network away from an undesirable steady-state distribution and to force it to converge towards a desired steady-state distribution. The proposed framework does not make any assumptions about the topology of the initial network, and is thus applicable to general-topology networks. We define the optimal perturbation control as the minimum-energy perturbation measured in terms of the Frobenius-norm between the initial and perturbed probability transition matrices of the dynamic network. We subsequently demonstrate that there exists at most one optimal perturbation that forces the network into the desirable steady-state distribution. In the event where the optimal perturbation does not exist, we construct a family of suboptimal perturbations, and show that the suboptimal perturbation can be used to approximate the optimal limiting distribution arbitrarily closely. Moreover, we investigate the robustness of the optimal perturbation control to errors in the probability transition matrix, and demonstrate that the proposed optimal perturbation control is robust to data and inference errors in the probability transition matrix of the initial network. Finally, we apply the proposed optimal perturbation control method to the Human melanoma gene regulatory network in order to force the network from an initial steady-state distribution associated with melanoma and into a desirable steady-state distribution corresponding to a benign cell.
 
Article
A method for time-frequency signal analysis is presented. The proposed method belongs to the general class of smoothed pseudo Wigner distributions. It is derived from the analysis of the Wigner distribution defined in the frequency domain. This method provides some substantial advantages over the Wigner distribution. The well-known cross term effects are reduced or completely removed. The oversampling of signal is not necessary. In addition, the computation time can be significantly shorter. The results are demonstrated on two numerical examples with frequency modulated signals
 
Article
Scale, like frequency, is a physical characteristic of a signal. To measure the scale content of a signal, the signal must be appropriately transformed. A theory for joint time-scale energy density functions is presented, and a method for generating such functions for any signal is given. Examples for synthetic signals and real data are presented. The theory and method can be extended to arbitrary joint densities of any variables, for example, frequency and scale
 
Article
This paper presents a hardware implementation of a sound localization algorithm that localizes a single sound source by using the information gathered by two separated microphones. This is achieved through estimating the time delay of arrival (TDOA) of sound at the two microphones. We have used a TDOA algorithm known as the "phase transform" to minimize the effects of reverberations and noise from the environment. Simplifications to the chosen TDOA algorithm were made in order to replace complex operations, such as the cosine function, with less expensive ones, such as iterative additions. The custom digital signal processor implementing this algorithm was designed in a 0.18-μm CMOS process and tested successfully. The test chip is capable of localizing the direction of a sound source within 2.2° of accuracy, utilizing approximately 30 mW of power and 6.25 mm<sup>2</sup> of silicon area.
 
Article
In this correspondence, we add a condition in Theorem 1 and some explanations in the proof of Theorem 2 in IEEE Transactions on Signal Processing , vol. 54, no. 3, pp. 1041–1053, March 2006.
 
Article
In the above titled paper (ibid., vol. 56, no. 1, pp. 256-265, Jan 08), Sebery et al. claimed that even though the dual-polarized transmission channel cannot be considered as described by means if a single quaternionic gain, the maximum-likelihood (ML) decoding rule can be decoupled for orthogonal space-time-polarization block codes (OSTPBCs) derived from quaternion orthogonal designs (QODs) [1, Sec. IV]. Regretfully, a correction is necessary, and we will show that decoupled decoding using the method presented therein is only optimal for codes derived from certain QODs, not from arbitrary QODs as previously suggested.
 
(a) A synthetic time series consisting of a low frequency signal for the £rst half, a middle frequency signal for the second half, and a high frequency burst at t=20. The function is h[0 : 63] = cos(2πt * 6.0/128.0), h[63 : 127] = cos(2πt * 25.0/128.0), h[20 : 30] = h[20 : 30] + 0.5 * cos(2πt * 52.0/128.0). (b) The amplitude of the S transform of the time series of Fig 1(a). Note the good frequency resolution for the f = 6/128 signal, as well as the good time resolution of the f = 52/128 signal. (c) The Short Time Fourier transform (STFT) of the time series in Fig 1(a) using a £xed gaussian window of standard deviation = 8 units. The high frequency burst is smoothed out because of the poor time resolution of the STFT. (d) Same as Fig 1(c) except that the window is a boxcar of length = 20 units . 
(a) A synthetic time series consisting of two cross chirps and two high frequency bursts. The time series is: h[0 : 255] = cos(2π(10 + t/7) * t/256) + cos(2π(256/2.8 − t/6.0) * t/256) h[114 : 122] = h[114 : 122] + cos(2πt * 0.42) h[134 : 142] = h[134 : 142] + cos(2πt * 0.42) (b) The amplitude of the S transform of the time series in Fig 2(a). The two chirps, as well as both high frequency bursts, are seen. (c) The amplitude of the STFT (with a Gaussian window) of the time series in Fig 2(a). Both chirps are detected, but the two high frequency bursts are not detected. (d) The amplitude of the Wigner distribution of the time series in Fig 2(a). Both chirps are detected with very good resolution in both time and frequency. The two high frequency bursts are not detected. 
Article
The S transform, which is introduced in the present correspondence, is an extension of the ideas of the continuous wavelet transform (CWT) and is based on a moving and scalable localizing Gaussian window. It is shown to have some desirable characteristics that are absent in the continuous wavelet transform. The S transform is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. These advantages of the S transform are due to the fact that the modulating sinusoids are fixed with respect to the time axis, whereas the localizing scalable Gaussian window dilates and translates
 
Article
This paper presents a novel hybrid encoding method for encoding of low-density parity-check (LDPC) codes. The design approach is applied to design 10-Gigabit Ethernet transceivers over copper cables. For a specified encoding speed, the proposed method requires substantially lower complexity in terms of area and storage. Furthermore, this method is generic and can be adapted easily for other LDPC codes. One major advantage of this design is that it does not require column swapping and it maintains compatibility with optimized LDPC decoders. For a 10-Gigabit Ethernet transceiver which is compliant with the IEEE 802.3 an standard, the proposed sequential (5-Parallel) hybrid architecture has the following implementation properties: critical path: (log<sub>2</sub>(324) + 1)T<sub>xor</sub> + T<sub>and</sub>, number of XOR gates: 11 056, number of and gates: 1620, and ROM storage: 104 976 bits (which can be minimized to 52 488 bits using additional hardware). This method achieves comparable critical path, and requires 74% gate area, 10% ROM storage as compared with a similar 10-Gigabit sequential (5-parallel) LDPC encoder design using only the G matrix multiplication method. Additionally the proposed method accesses fewer bits per cycle than the G matrix method which reduces power consumption by about 82%.
 
Coefficient vector update for L = 1: Position 1 w w w(k). Position 2 w w w (k + 1), first step toward w w w-(k + 1) and w w w(k + 1).
Excess of MSE for N = 10 as a function of .  
Excess of MSE for N = 63 as a function of .  
Excess of MSE for colored input signals.  
Article
Normalized least mean squares algorithms for FIR adaptive filtering with or without the reuse of past information are known to converge often faster than the conventional least mean squares (LMS) algorithm. This correspondence analyzes an LMS-like algorithm: the binormalized data-reusing least mean squares (BNDR-LMS) algorithm. This algorithm, which corresponds to the affine projection algorithm for the case of two projections, compares favorably with other normalized LMS-like algorithms when the input signal is correlated. Convergence analyses in the mean and in the mean-squared are presented, and a closed-form formula for the mean squared error is provided for white input signals as well as its extension to the case of a colored input signal. A simple model for the input-signal vector that imparts simplicity and tractability to the analysis of second-order statistics is fully described. The methodology is readily applicable to other adaptation algorithms of difficult analysis. Simulation results validate the analysis and ensuing assumptions
 
Article
Proposes two methods for designing partially adaptive beamformers that satisfy a performance specification over a set of likely interference scenarios. Both methods choose the adaptation space in a sequential fashion; the dimension is increased one by one until the performance specification is attained. In the multilevel point design method, each dimension of the adaptation space is chosen to give optimum performance at a single interference scenario. The constrained minimization design method chooses each dimension of the adaptation space to exactly satisfy the performance specification at a single interference scenario while approximately minimizing the average interference output power over neighboring scenarios. Simulations indicate that both methods result in better performance than existing methods while using fewer degrees of freedom
 
Article
A novel comparative analysis of the benefits brought by different degrees of linearization to offset the modulation fidelity (MF) and spectrum regrowth impairments caused by solid-state power amplifier (SSPA) nonlinearity, as measured by error vector magnitude (EVM) and adjacent channel power ratio (ACPR) performance for TIA/EIA Universal Wireless Communication standard UWC-136 signals, are quantified. New results are presented showing the benefits of even modest levels of linearization but also that such benefits may be easily eroded at a receiver by the adjacent channel interference (ACI) in certain circumstances. An equation expressing the incremental MF deterioration experienced by a wanted channel (WC) signal, at its receiver, due to ACI arising from signals in the immediate upper and lower frequency channels, and as a function of adjacent channel (AC) to WC power differential, where signals are subject to different degrees of linearization, is presented. Typical SSPA characteristic values for the equation constants in the cases of one and two immediate AC signals are derived from simulation results. Interesting new results and conclusions relevant to the drafting of harmonious ACPR-EVM specifications and on the advisability of the inclusion of linearization schemes in transmitters, in the context of the UWC-136 system, are presented.
 
Article
The analysis in an earlier paper (see Trans. Acoust. Speech and Signal Processing, vol.37, no.9, p.1397-405, 1989) is improved by correcting an error in the derivation of the system equation. After the correction, the system equation is modified, and thus, so are the related analytical results
 
Article
This paper proposes a novel content-based image watermarking method based on invariant regions of an image. The invariant regions are self-adaptive image patches that deform with geometric transformations. Three different invariant-region detection methods based on the scale-space representation of an image were considered for watermarking. At each invariant region, the watermark is embedded after geometric normalization according to the shape of the region. By binding watermarking with invariant regions, resilience against geometric transformations can be readily obtained. Experimental results show that the proposed method is robust against various image processing steps, including geometric transformations, cropping, filtering, and JPEG compression.
 
Article
It is shown that it is possible to replace the real-numbered elements of a discrete cosine transform (DCT) matrix with integers and still maintain the structure, i.e., relative magnitudes and orthogonality, among the matrix elements. The result is an integer cosine transform (ICT). Thirteen ICTs have been found, and some of them have performance comparable to the DCT. The main advantage of the ICT lies in having only integer values, which in two cases can be represented perfectly by 6-bit numbers, thus providing a potential reduction in the computational complexity
 
Article
An efficient method for the realization of the paired algorithm for calculation of the one-dimensional (1-D) discrete Fourier transform (DFT), by simplifying the signal-flow graph of the transform, is described. The signal-flow graph is modified by separating the calculation for real and imaginary parts of all inputs and outputs in the signal-flow graph and using properties of the transform. The examples for calculation of the eight- and 16-point DFTs are considered in detail. The calculation of the 16-point DFT of real data requires 12 real multiplications and 58 additions. Two multiplications and 20 additions are used for the eight-point DFT.
 
Article
A code tree generated by a stochastically populated innovations tree with a backward adaptive gain and backward adaptive synthesis filters is considered. The synthesis configuration uses a cascade of two all-pole filters: a pitch (long time delay) filter followed by a formant (short time delay) filter. Both filters are updated using backward adaptation. The formant predictor is updated using an adaptive lattice algorithm. The multipath ( M , L ) search algorithm is used to encode the speech. A frequency-weighted error measure is used to reduce the perceptual loudness of the quantization noise. The addition of the pitch filter gives 2-10-dB increase in segSNR (segmental signal-to-noise ratio) in the voiced segments. Subjective testing has shown that the coder attains a subjective quality equivalent to 7 b/sample log-PCM (pulse code modulation) with an encoding delay of eight samples (1 ms with an 8-kHz sampling rate)
 
Article
The paper "Method of Flow Graph Simplification for the 16-Point Discrete Fourier Transform" by Grigoryan and Bhamidipati presents a "paired transform" fast Fourier transform (FFT) algorithm that is claimed to perform the size-8 and size-16 complex-data discrete Fourier transform (DFT) with 44 and 140 arithmetic operations, respectively. If true, this count would be less than the 56 and 168 operations achieved in the best pre-existing (split-radix) methods. Grigoryan and Bhamidipati's count of real additions is erroneous, however, and this comment shows that their algorithm actually has arithmetic complexity identical to that of standard split-radix algorithms.
 
Article
A novel general methodology is introduced for the computer-aided reconstruction of the magnificent wall paintings of the Greek island Thera (Santorini), which were painted in the middle of the second millennium BC. These wall paintings have been excavated in fragments, and as a result, their reconstruction is a painstaking and a time-consuming process. Therefore, in order to facilitate and expedite this process, a proper system has been developed based on the introduced methodology. According to this methodology, each fragment is photographed, its picture is introduced to the computer, its contour is obtained, and, subsequently, all of the fragments contours are compared in a manner proposed herein. Both the system and the methodology presented here extract the maximum possible information from the contour shape of fragments of an arbitrary initially unbroken plane object to point out possible fragment matching. This methodology has been applied to two excavated fragmented wall paintings consisting of 262 fragments with full success, but most important, it has been used to reconstruct, for the first time, unpublished parts of wall paintings from a set of 936 fragments
 
Block diagram for the proposed time-frequency distribution method.
Cross-term reduction of the WVD by using the CWD, the spectrogram, the proposed time-frequency representation, and a smoothed pseudo-Wigner-Ville distribution. (a)-(g) Contour plots (L = 32).
In Fig. 4(a)-(d), the WVD, spectrogram, GWVD, and CWD are shown, whereas the proposed TFD with WVD's and GWVD's are shown in Fig. 4(e)-(f), respectively. As we can see, the energy concentration for the proposed distribution is higher, and the presence of artifacts is lower than in the other distributions. Furthermore, the proposed TFD with GWVD's provides a higher concentration than with the use of WVD's [cf. Fig. 4(e)-(f)]. Example 3-Signal Reconstruction: We illustrate an example of signal reconstruction by using a linearly frequency-modulated signal that has normalized frequency (with respect to the sampling frequency) increasing linearly with time from 0.1 to 0.2. The number of filters used is L = 16, and the parameters used for the pulse p(t) are = 0.5 and = 1.1. The corresponding value of gives small variations of p(t) with respect to the frequency. In Fig. 5(a)-(c), the true signal and the reconstructed signals are presented. Comparing Fig. 5(b) and (c) with Fig. 5(a), an improvement in reconstruction has
Signal reconstruction from the time-frequency plane. (a)-(c) True signal (dashed-dot line) and the corresponding reconstructed signals (solid line) from (a) WVD, (b) T (t; f ), and (c) T (t; f ) 3 b(t; f ), respectively.
Article
We present a new method for time-frequency representation, which combines a filter bank and the Wigner-Ville distribution (WVD). The filter bank decomposes a multicomponent signal into a number of single component signals before the WVD is applied. Cross-terms as well as noise are reduced significantly, whereas high time-frequency concentration is attained. Properties of the proposed time-frequency distribution (TFD) are investigated, and the requirements for the filter bank to fulfil these are given. The ability of the proposed non-Cohen's (1995) class TFD to reduce cross-terms as well as noise as well as its ability to approximately reconstruct signals are illustrated by examples. The results are compared with those from the WVD, the Choi-Williams (1989) distribution (CWD), and spectrogram
 
Article
This paper introduces an approximately shift invariant redundant dyadic wavelet transform - the phaselet transform - that includes the popular dual-tree complex wavelet transform of Kingsbury (see Phil. R. Soc. London A, Sept. 1999) as a special case. The main idea is to use a finite set of wavelets that are related to each other in a special way - and hence called phaselets - to achieve approximate shift-redundancy; the bigger the set, the better the approximation. A sufficient condition on the associated scaling filters to achieve this is that they are fractional shifts of each other. Algorithms for the design of phaselets with a fixed number vanishing moments is presented - building on the work of Selesnick (see IEEE Trans. Signal Processing) for the design of wavelet pairs for Kingsbury's dual-tree complex wavelet transform. Construction of two-dimensional (2-D) directional bases from tensor products of one-dimensional (1-D) phaselets is also described. Phaselets as a new approach to redundant wavelet transforms and their construction are both novel and should be interesting to the reader, independent of the approximate shift invariance property that this paper argues they possess.
 
Article
Memory issues pose the most critical problem in designing a high-performance JPEG 2000 architecture. The tile memory occupies more than 50% area in conventional JPEG 2000 designs. To solve this problem, we propose a stripe pipeline scheduling. It well matches the throughputs and dataflows of the discrete wavelet transform and the embedded block coding to minimize the data lifetime between the two modules. As a result of the scheduling, the overall memory requirements of the proposed architecture can be reduced to only 8.5% compared with conventional architectures. This effectively reduces the hardware cost of the entire system by more than 45%. Besides reducing the cost, we also propose a two-symbol arithmetic encoder architecture to increase the throughput. By use of this technique, the proposed architecture can achieve 124 MS/s at 124 MHz, which is the highest specification in the literature. Therefore, the proposed architecture is not only low cost but also high speed
 
Article
Each year in spring, the IEEE Signal Processing Society, at the International Conference on Acoustics, Speech, and Signal Processing (ICASSP), presents its annual awards. Several of these awards are related to Best Papers, and although this is not a rule, several of these papers have appeared in IEEE TRANSACTIONS ON SIGNAL PROCESSING. In this editorial, we are pleased to announce the articles receiving 2005 awards. For the 2006 awards, readers are encouraged to nominate candidate papers before September 1, 2006 to the Editor-in-Chief. Nominations will be judged by the relevant Society Technical Committees before being forwarded to the Awards Board.
 
Article
The recipients of the 2006 Best Paper Awards are presented.
 
Article
A generalized Gaussian model for correlated signal sources is introduced. The probability density function of a first-order autoregressive process driven by generalized Gaussian white noise is approximated by a generalized Gaussian probability density function. The interdependence between the correlation coefficient and the shape parameter of the first-order autoregressive process and the shape parameter of the driving noise is investigated. Application of the proposed method for modeling of probability density functions of transform and subband coefficients is considered
 
Article
In the manifold learning problem, one seeks to discover a smooth low dimensional surface, i.e., a manifold embedded in a higher dimensional linear vector space, based on a set of measured sample points on the surface. In this paper, we consider the closely related problem of estimating the manifold's intrinsic dimension and the intrinsic entropy of the sample points. Specifically, we view the sample points as realizations of an unknown multivariate density supported on an unknown smooth manifold. We introduce a novel geometric approach based on entropic graph methods. Although the theory presented applies to this general class of graphs, we focus on the geodesic-minimal-spanning-tree (GMST) to obtaining asymptotically consistent estimates of the manifold dimension and the Re´nyi α-entropy of the sample density on the manifold. The GMST approach is striking in its simplicity and does not require reconstruction of the manifold or estimation of the multivariate density of the samples. The GMST method simply constructs a minimal spanning tree (MST) sequence using a geodesic edge matrix and uses the overall lengths of the MSTs to simultaneously estimate manifold dimension and entropy. We illustrate the GMST approach on standard synthetic manifolds as well as on real data sets consisting of images of faces.
 
Article
The increased popularity of multimedia applications places a great demand on efficient data storage and transmission techniques. Network communication, especially over a wireless network, can easily be intercepted and must be protected from eavesdroppers. Unfortunately, encryption and decryption are slow, and it is often difficult, if not impossible, to carry out real-time secure image and video communication and processing. Methods have been proposed to combine compression and encryption together to reduce the overall processing time, but they are either insecure or too computationally intensive. We propose a novel solution called partial encryption, in which a secure encryption algorithm is used to encrypt only part of the compressed data. Partial encryption is applied to several image and video compression algorithms in this paper. Only 13-27% of the output from quadtree compression algorithms is encrypted for typical images, and less than 2% is encrypted for 512×512 images compressed by the set partitioning in hierarchical trees (SPIHT) algorithm. The results are similar for video compression, resulting in a significant reduction in encryption and decryption time. The proposed partial encryption schemes are fast, secure, and do not reduce the compression performance of the underlying compression algorithm
 
Article
We investigate the convergence properties of the forgetting factor RLS algorithm in a stationary data environment. Using the settling time as our performance measure, we show that the algorithm exhibits a variable performance that depends on the particular combination of the initialization and noise level. Specifically when the observation noise level is low (high SNR) RLS, when initialized with a matrix of small norm, it has an exceptionally fast convergence. Convergence speed decreases as we increase the norm of the initialization matrix. In a medium SNR environment, the optimum convergence speed of the algorithm is reduced as compared with the previous case; however, RLS becomes more insensitive to initialization. Finally, in a low SNR environment, we show that it is preferable to initialize the algorithm with a matrix of large norm
 
Article
The author proposes bit-reversal unscrambling algorithms based on representing array indices as elements in GF(2<sup>b</sup>). These elements are sequenced through by counters implemented with integer shifts and bitwise exclusive-OR. A very simple algorithm, developed by applying these counters in a structure similar to the Gold-Rader algorithm, is shown to be less complex and significantly faster than the Gold-Rader (1969) algorithm. A second algorithm, constructed by using counters in GF(2<sup>b</sup>) to adapt an algorithm proposed by Evans (1987), eliminates the lookup tables required by the Evans algorithm while maintaining its speed advantages
 
Article
A decimation-in-frequency vector split-radix algorithm is proposed to decompose an N × N 2D discrete Hartley transform (DHT) into one ( N /2)×( N /2) DHT and twelve ( N /4) DHTs. The proposed algorithm possesses the in-place property and needs no matrix transpose. Its computational structure is very regular and is simpler than those of all existing nonseparable 2D DHTs
 
Article
The realization of 2-D digital filters based on the lower-upper triangular decomposition of the coefficient matrix is investigated. A numerical method based on the QA decomposition, which has some important characteristics, is proposed for reaching the LU structure. The coefficients in the final LU structure have values favorable to fixed-point arithmetic implementation. Furthermore, the QR structure can be used for the realization and possesses good numerical characteristics in terms of the approximate decomposition scheme. The symmetry in the impulse response coefficient matrix of an octagonally symmetric 2-D FIR filter is utilized to reduce the computational effort spent in the decomposition and the total number of multipliers in the final realization structure
 
Article
In this paper, a general class of split-radix fast Fourier transform (FFT) algorithms for computing the length-2<sup>m</sup> DFT is proposed by introducing a new recursive approach coupled with an efficient method for combining the twiddle factors. This enables the development of higher split-radix FFT algorithms from lower split-radix FFT algorithms without any increase in the arithmetic complexity. Specifically, an arbitrary radix-2/2<sup>s</sup> FFT algorithm for any value of s, 4les sles m, is proposed and its arithmetic complexity analyzed. It is shown that the number of arithmetic operations (multiplications plus additions) required by the proposed radix-2/2<sup>s</sup> FFT algorithm is independent of s and is (2m-3)2<sup>m+1</sup>+8 regardless of whether a complex multiplication is carried out using four multiplications and two additions or three multiplications and three additions. This paper thus provides a variety of choices and ways for computing the length-2<sup>m</sup> DFT with the same arithmetic complexity.
 
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We show under reasonable assumptions that an M-sensor linear-conjugate-linear (LCL) processor can separate up to 2M conjugate-symmetric signals, including the cases in which up to M of the signals each share the same direction of arrival as each of M other signals. Numerical evaluations illustrate ways in which the performance of the M-sensor LCL processor is superior to that of a conventional 2M-sensor linear processor when 2M conjugate-symmetric signals are received
 
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An intrinsic property, wherein the set of numbers formed using the magnitudes of a basis vector's elements is the same for all basis vectors in a length-2<sup>m</sup> type-III discrete sine transform (DST) and discrete cosine transform (DCT), is proved. We also show that the set of numbers formed using the magnitudes of any basis vector's elements in a length-2<sup>m</sup> type-III DST is the same as that in a length-2<sup>m</sup> type-III DCT. The same characteristics exist for the length-2<sup>m</sup> type-IV DST and DCT. A new combinational VLSI architecture that is only composed of adders for implementing the length-2<sup>m</sup> type-III DST or DCT (DST-III/DCT-III) using the intrinsic property and the permuted difference coefficient (PDC) algorithm is developed. The advantages of this new architecture are high structural regularity, very high speed, and suitability for VLSI realization. The other advanced sequential structure, which is composed of registers, multiplexers, and an accumulator, is also proposed to give a much lower complexity than the combinational structure. This new sequential structure is very suitable for chip-level, microprocessor-based, or VLSI realization. The quantization error that exhibits the effect of the internal finite word-length representations of the input and the coefficient is also analyzed. It is shown that if the length of data sequence is quadrupled, then to maintain the same signal to noise ratio, one additional bit must be added to represent both the input and the coefficient. It is also shown that the roundoff error of the coefficients is less sensitive than that of the inputs
 
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The problem of determining the maximum number of narrowband signals whose parameters can be estimated with a linear array of M equally spaced sensors is examined. While this number previously has been taken to be M -1 when the signals are mutually uncorrelated, it is shown how to estimate directions and amplitudes for as many as 2 M -1 signals. This over twofold increase is accomplished by retaining snapshot-to-snapshot phase information usually lost in algorithms based on spatial correlation matrices. The approach uses length 2 M real signal vectors rather than the usual M complex vectors. It is shown that 2 M of these real vectors are linearly independent with probability one, and, thus, in the presence of additive white noise, the parameters of 2 M -1 signals can be estimated. An algorithm for determining directions and amplitudes is presented. Because of the algorithm's computational complexity, its application is limited to small M and low time-bandwidth products
 
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This article presents an improved split-radix algorithm that can flexibly compute the discrete Hartley transforms (DHT) of length-q*2<sup>m</sup> where q is an odd integer. Comparisons with previously reported algorithms show that savings on the number of arithmetic operations can be made. Furthermore, a wider range of choices on different DHT lengths is naturally provided
 
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The eigenstructure based characterization of M-channel finite impulse response perfect reconstruction (FIR PR) filterbanks in a previous paper by the authors is extended here to the linear-phase case. Some results relating to linear-phase filterbanks is derived by finding appropriate restrictions on the eigenstructure of the analysis polyphase matrix. Consequently, a complete and minimal characterization for such filterbanks with all analysis length 2M and any synthesis length is developed. Parameterization and design examples are also presented.
 
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Based on an algorithm derived from the new Chinese remainder theorem I, we present three new residue-to-binary converters for the residue number system (2<sup>n</sup>-1, 2<sup>n</sup>, 2<sup>n</sup>+1) designed using 2n-bit or n-bit adders with improvements on speed, area, or dynamic range compared with various previous converters. The 2n-bit adder based converter is faster and requires about half the hardware required by previous methods. For n-bit adder-based implementations, one new converter is twice as fast as the previous method using a similar amount of hardware, whereas another new converter achieves improvement in either speed, area, or dynamic range compared with previous converters
 
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From the beginning of the 1980s, many second-order (SO) high-resolution direction-finding methods, such as the MUSIC method (or 2-MUSIC), have been developed mainly to process efficiently the multisource environments. Despite of their great interests, these methods suffer from serious drawbacks such as a weak robustness to both modeling errors and the presence of a strong colored background noise whose spatial coherence is unknown, poor performance in the presence of several poorly angularly separated sources from a limited duration observation and a maximum of N-1 sources to be processed from an array of N sensors. Mainly to overcome these limitations and in particular to increase both the resolution and the number of sources to be processed from an array of N sensors, fourth-order (FO) high-resolution direction-finding methods have been developed, from the end of the 1980s, to process non-Gaussian sources, omnipresent in radio communications, among which the 4-MUSIC method is the most popular. To increase even more the resolution, the robustness to modeling errors, and the number of sources to be processed from a given array of sensors, and thus to minimize the number of sensors in operational contexts, we propose in this paper an extension of the MUSIC method to an arbitrary even order 2q (qges1), giving rise to the 2q-MUSIC methods. The performance analysis of these new methods show off new important results for direction-finding applications and in particular the best performances, with respect to 2-MUSIC and 4-MUSIC, of 2q-MUSIC methods with q>2, despite their higher variance, when some resolution is required
 
Article
This paper investigates two-dimensional (2D) 2 oversampled DFT modulated filter banks and 2D critically sampled modified DFT (MDFT) modulated filter banks as well as their design. The structure and perfect reconstruction (PR) condition of 2D 2× oversampled DFT modulated filter banks are presented in terms of the polyphase decompositions of prototype filters (PFs). In the double-prototype case, the part solutions of the PR condition are parameterized by imposing the 2D two-channel lifting structure on each pair of the polyphase components of analysis and synthesis PFs. Based on the parametric structure, the analysis and synthesis PFs are separately designed by constrained quadratic programs. The obtained filter banks are of structurally PR. Moreover, 2D critically sampled MDFT modulated filter banks are proposed. It is proved that 2D critically sampled PR MDFT modulated filter banks can be rebuilt from 2D 2 oversampled PR DFT modulated filter banks when the decimation matrices satisfy a permissible condition and the analysis and synthesis PFs are identical and symmetric with respect to the origin. A numerical algorithm is given to design 2D critically sampled PR MDFT modulated filter banks and the obtained filter banks are of numerically PR.
 
Top-cited authors
G.B. Giannakis
  • University of Minnesota Twin Cities
Petre Peter Stoica
  • Uppsala University
Yonina Eldar
  • Weizmann Institute of Science
Michael Elad
  • Technion - Israel Institute of Technology
Simon Maskell
  • University of Liverpool