# IEEE Transactions on Signal Processing

Published by Institute of Electrical and Electronics Engineers

Online ISSN: 1053-587X

Published by Institute of Electrical and Electronics Engineers

Online ISSN: 1053-587X

Publications

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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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

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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

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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.

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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.

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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.

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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

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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%.

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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

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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

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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.

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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

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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.

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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

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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.

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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)

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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.

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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

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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

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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.

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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

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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.

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Article

The recipients of the 2006 Best Paper Awards are presented.

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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

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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.

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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

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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

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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

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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

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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

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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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Article

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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Article

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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Article

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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Article

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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Article

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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Article

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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Article

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

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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.

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