[Show abstract][Hide abstract] ABSTRACT: Reconstruction algorithms for Optical Diffuse Tomography (ODT) rely heavily on fast and accurate forward models. Arbitrary geometries and boundary conditions need to be handled rigorously since they are the only input to the inverse problem. From this perspective, Finite Element Methods (FEM) are good candidates to implement a forward model. However, these methods require to mesh the domain of interest, which is impractical on a routine basis. The other downside of the FEM is that the basis functions are often not compatible with the ones used for solving the inverse problem, which typically have less degrees of freedom. In this work, we tackle the 2D problem, and propose a forward model that uses a mesh-free discretization based on linear B-Splines. It combines the advantages of the FEM, while offering a fast and much simpler way of handling complex geometries. Another motivation for this work is that the underlying B-spline model is equally suitable for the subsequent reconstruction part of the process (solving the inverse problem). In particular, it is compatible with wavelets and multiresolution-type signal representations.
Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008
[Show abstract][Hide abstract] ABSTRACT: New phase-shifting techniques have recently been proposed to suppress the complex-conjugate ambiguity in frequency- domain optical-coherence tomography. A phase shift is introduced, in an elegant fashion, by incorporating a small beam offset at the scanning mirror. The tomogram is then computed by using a combination of Hilbert and Fourier transforms. This is a marked deviation from the conventional approaches, wherein each A-scan is reconstructed independently of the others. In this paper, we formulate the problem in a signal processing framework and provide theoretical proofs for maximal and partial suppression of complex-conjugate ambiguity. To supplement the theoretical derivations, we provide experimental results on in vivo measurements of a human finger nail.
Biomedical Imaging: From Nano to Macro, 2008. ISBI 2008. 5th IEEE International Symposium on; 06/2008
[Show abstract][Hide abstract] ABSTRACT: We construct parametric active contours (snakes) for outlining cells in histology images. These snakes are defined in terms of cubic B-spline basis functions. We use a steerable ridge detector for obtaining a reliable map of the cell boundaries. Using the contour informa-tion, we compute a distance map and specify it as one of the snake energies. To ensure smooth contours, we also introduce a regularization term that favors smooth contours. A convex combination of the two cost func-tions results in smooth contours that lock onto edges ef-ficiently and consistently. Experimental results on real histology images show that the snake algorithm is robust to imperfections in the images such as broken edges.
[Show abstract][Hide abstract] ABSTRACT: Recently, we proposed a noniterative cepstral technique for exact signal recovery in frequency-domain optical-coherence tomography. In this paper, we address the influence of measurement noise on the performance of the method. We derive analytical expressions for the bias and variance of the tomogram under a small noise approximation, and show that our technique yields unbiased and consistent estimators, which have a variance that is proportional to that of the noise and inversely proportional to the data size. We present simulation results to confirm the theoretical derivations. We also derive approximate Cramer-Rao bounds (CRBs) on the achievable accuracy of reconstruction.
Acoustics, Speech and Signal Processing, 2008. ICASSP 2008. IEEE International Conference on; 01/2008 · 4.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We introduce a simple and cheap method for phase-shifting Fourier domain optical coherence tomography (FDOCT) that does not need additional devices and can easily be implemented. A small beam offset at the fast beam-scanning mirror introduces a causal phase shift, which can be used for B-scan-based complex image reconstruction. We derive the conditions for optimal conjugate suppression and demonstrate the method on human skin in vivo for spectrometer-based FDOCT operating at 1300 nm employing a handheld scanner.
[Show abstract][Hide abstract] ABSTRACT: We address the problem of exact signal recovery in frequency-dom ain optical-coherence tomography (FDOCT). The standard technique for tomogram reconstruction is the inverse Fourier transform. How ever, the inverse Fourier transform is known to yield autocorrelation artifacts which interfere with the desired signal. We propose a new transformation for computing an artifact-free tomogram from inten sity measurements. Our technique relies on the fact that, in the FDOCT measurements, the intensity of the total signal reflected from the object is smaller than that of the reference arm. Our technique is noniterative, nonlinear, and it leads to an exact solution in the absence of noise. The reconstructed signal is free from autocorrelation artifacts. We present results on synthesized data as well as on experimental FDOCT measurements of the retina of the eye.
[Show abstract][Hide abstract] ABSTRACT: Frequency domain optical coherence tomography (FDOCT) is a new technique that is well-suited for fast imaging of biological specimens, as well as non-biological objects. The measurements are in the frequency domain, and the objective is to retrieve an artifact-free spatial domain description of the specimen. In this paper, we develop a new technique for model-based retrieval of spatial domain data from the frequency domain data. We use a piecewise-constant model for the refractive index profile that is suitable for multi-layered specimens. We show that the estimation of the layered structure parameters can be mapped into a harmonic retrieval problem, which enables us to use high-resolution spectrum estimation techniques. The new technique that we propose is efficient and requires few measurements. We also analyze the effect of additive measurement noise on the algorithm performance. The experimental results show that the technique gives highly accurate parameter estimates. For example, at 25 dB signal-to-noise ratio, the mean square error in the position estimate is about 0.01 % of the actual value.
Acoustics, Speech and Signal Processing, 2007. ICASSP 2007. IEEE International Conference on; 05/2007 · 4.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We address the problem of exact signal recovery in frequency do- main optical coherence tomography (FDOCT) systems. Our tech- nique relies on the fact that, in a spectral interferometry setup, the in- tensity of the total signal reflected from the object is smaller than that of the reference arm. We develop a novel algorithm to compute the reflected signal amplitude from the interferometric measurements. Our technique is non-iterative, non-linear and it leads to an exact so- lution in the absence of noise. The reconstructed signal is free from artifacts such as the autocorrelation noise that is normally encoun- tered in the conventional inverse Fourier transform techniques. We present results on synthesized data where we have a benchmark for comparing the performance of the technique. We also report results on experimental FDOCT measurements of the retina of the human eye.
Proceedings of the 2007 IEEE International Symposium on Biomedical Imaging: From Nano to Macro, Washington, DC, USA, April 12-16, 2007; 01/2007
[Show abstract][Hide abstract] ABSTRACT: We consider the problem of estimation of the signal-to-noise ratio (SNR) of an unknown deterministic complex phase signal in additive complex white Gaussian noise. The phase of the signal is arbitrary and is not assumed to be known a priori unlike many SNR estimation methods that assume phase synchronization. We show that the moments of the complex sequences exhibit useful mean-ergodicity properties enabling a “method-of-moments” (MoM)-SNR estimator. The Cramer–Rao bounds (CRBs) on the signal power, noise variance and logarithmic-SNR are derived. We conduct experiments to study the efficiency of the SNR estimator. We show that the estimator exhibits finite sample super-efficiency/inefficiency and asymptotic efficiency, depending on the choice of the parameters. At SNR, the mean square error in log-SNR estimation is approximately . The main feature of the MoM estimator is that it does not require the instantaneous phase/frequency of the signal, a priori. Infact, the SNR estimator can be used to track the instantaneous frequency (IF) of the phase signal. Using the adaptive pseudo-Wigner–Ville distribution technique, the IF estimation accuracy is the same as that obtained with perfect SNR knowledge and 8–10 dB better compared to the median-based SNR estimator.
[Show abstract][Hide abstract] ABSTRACT: We address the problem of estimating the instantaneous frequency (IF) of a phase signal using its level-crossing (LC) information based on front-end auditory processing motivation. We show that the problem of IF estimation using LC information can be cast in the framework of estimation from irregularly sampled data. The formulation has the generality of estimating different types of IF without the need for a quasistationary assumption. We consider two types of IF-polynomial and bandlimited; we use polynomial interpolating functions for the former, and for the latter, we propose a novel "line plus sum of sines" model. The model parameters are estimated by linear regression. Considering the noisy case, LC data for different levels is analyzed, and methods for combining different estimators from LCs are discussed. Theoretical and extensive simulation results show that the performance of the zero-crossing (ZC) based IF estimator and the level-crossing based IF estimator with smaller level values is better than those obtained with higher level values or their combinations. The new technique reaches the Crame´r-Rao bound (CRB) roughly above 4 dB signal-to-noise ratio (SNR), and its performance does not deteriorate rapidly with mismatch in the IF order compared with the other techniques in the literature.
IEEE Transactions on Signal Processing 05/2005; · 2.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present a new zero-crossing based algorithm for decomposing a bandpass signal into the amplitude modulation (AM) and frequency modulation (FM) components. In this sequential algorithm, the FM component is first estimated using zero-crossing instant information in a k-nearest neighbour (k-NN) framework. The AM component is estimated by coherent demodulation using a time-varying lowpass filter that uses the estimated instantaneous frequency. Simulation results show that the proposed algorithm gives more accurate envelope and frequency estimates compared to the discrete-energy separation algorithm (DESA) which uses the Teager energy operator. Using the proposed approach on bandpass filtered speech and music, we can extract the fine-structured modulations that occur on a micro-time scale, within an analysis frame.
Acoustics, Speech, and Signal Processing, 2004. Proceedings. (ICASSP '04). IEEE International Conference on; 06/2004 · 4.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).
EURASIP Journal on Advances in Signal Processing. 01/2004;
[Show abstract][Hide abstract] ABSTRACT: The peak of the polynomial Wigner–Ville distribution (PWVD) can be used for estimating the instantaneous frequency (IF) of monocomponent polynomial phase signals. However, the PWVD kernel, optimized to yield a time–frequency distribution (TFD) localized along the IF, comprises of fractional-time-sampled signals. When implemented in a discrete-time scenario, this calls for signal interpolation. We study three interpolation schemes—linear, cubic polynomial and sinc and derive expressions for the variance of the interpolated samples in the presence of noise. In representing nonstationary signals using the PWVD, the instantaneous energy content of noise auto-terms and signal-noise cross-terms is found to be the least for linear interpolation scheme. For polynomial IF estimation using the peak of the PWVD, it was found that linear interpolation is a computationally efficient way of obtaining reasonably good estimates at low signal-to-noise ratios (SNRs). For high SNRs, sinc interpolation outperforms the other two schemes. Similar results were found when the experiment was extended to sinusoidal IF signals also.
[Show abstract][Hide abstract] ABSTRACT: To estimate the instantaneous frequency (IF) using the peak of the spectrogram, we use an approach that automatically adapts the window length to the changes in IF and tracks it better than a fixed window approach. An adaptive window-based time–frequency representation is more useful for tracking events in time and frequency. The peak of the spectrogram obtained using the adaptive window length algorithm is used as an IF estimator and its performance in the presence of multiplicative and additive noise is studied. The performance is compared with that of pseudo-Wigner–Ville distribution (Ps.WVD). Both analytically and experimentally, adaptive spectrogram was found to be more robust than adaptive Ps.WVD.
[Show abstract][Hide abstract] ABSTRACT: We address the problem of estimating the fundamental frequency of voiced speech. We present a novel solution motivated by the importance of amplitude modulation in sound processing and speech perception. The new algo-rithm is based on a cumulative spectrum computed from the temporal envelope of various subbands. We provide theoretical analysis to derive the new pitch estimator based on the temporal envelope of the bandpass speech signal. We report extensive experimental performance for synthetic as well as natural vowels for both real-world noisy and noise-free data. Experimental results show that the new technique performs accurate pitch es-timation and is robust to noise. We also show that the technique is superior to the autocorrelation technique for pitch estimation.