arXiv subjects

Chandra Sekhar Seelamantula

Publications and source records attributed to Chandra Sekhar Seelamantula.

At least 37 records · Page 2Linked to original sources

arXiv2021

Time Encoding of Finite-Rate-of-Innovation Signals

Time-encoding of continuous-time signals is an alternative sampling paradigm to conventional methods such as Shannon's sampling. In time-encoding, the signal is encoded using a sequence of time instants where an event occurs, and hence fall under event-driven sampling methods. Time-encoding can be designed agnostic to the global clock of the sampling hardware, which makes sampling asynchronous. Moreover, the encoding is sparse. This makes time-encoding energy efficient. However, the signal representation is nonstandard and in general, nonuniform. In this paper, we consider time-encoding of finite-rate-of-innovation signals, and in particular, periodic signals composed of weighted and time-shifted versions of a known pulse. We consider encoding using both crossing-time-encoding machine (C-TEM) and integrate-and-fire time-encoding machine (IF-TEM). We analyze how time-encoding manifests in the Fourier domain and arrive at the familiar sum-of-sinusoids structure of the Fourier coefficients that can be obtained starting from the time-encoded measurements via a suitable linear transformation. Thereafter, standard FRI techniques become applicable. Further, we extend the theory to multichannel time-encoding such that each channel operates with a lower sampling requirement. We also study the effect of measurement noise, where the temporal measurements are perturbed by additive noise. To combat the effect of noise, we propose a robust optimization framework to simultaneously denoise the Fourier coefficients and estimate the annihilating filter accurately. We provide sufficient conditions for time-encoding and perfect reconstruction using C-TEM and IF-TEM, and furnish extensive simulations to substantiate our findings.

eess.SP↗

arXiv2021

Wavelet Design in a Learning Framework

Wavelets have proven to be highly successful in several signal and image processing applications. Wavelet design has been an active field of research for over two decades, with the problem often being approached from an analytical perspective. In this paper, we introduce a learning based approach to wavelet design. We draw a parallel between convolutional autoencoders and wavelet multiresolution approximation, and show how the learning angle provides a coherent computational framework for addressing the design problem. We aim at designing data-independent wavelets by training filterbank autoencoders, which precludes the need for customized datasets. In fact, we use high-dimensional Gaussian vectors for training filterbank autoencoders, and show that a near-zero training loss implies that the learnt filters satisfy the perfect reconstruction property with very high probability. Properties of a wavelet such as orthogonality, compact support, smoothness, symmetry, and vanishing moments can be incorporated by designing the autoencoder architecture appropriately and with a suitable regularization term added to the mean-squared error cost used in the learning process. Our approach not only recovers the well known Daubechies family of orthogonal wavelets and the Cohen-Daubechies-Feauveau family of symmetric biorthogonal wavelets, but also learns wavelets outside these families.

cs.LG↗

arXiv2021

Learning Generative Prior with Latent Space Sparsity Constraints

We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural network. Recently, it has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. SDLSS allows the range-space of the generator to be considered as a union-of-submanifolds. We also derive the sample complexity bounds within the SDLSS framework for the linear measurement model. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method. We first consider a comparison between linear and nonlinear sensing mechanisms on Fashion-MNIST dataset and show that the learned nonlinear version is superior to the linear one. Subsequent comparisons with the deep compressive sensing (DCS) framework proposed in the literature are reported. We also consider the effect of the dimension of the latent space and the sparsity factor in validating the SDLSS framework. Performance quantification is carried out by employing three objective metrics: peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and reconstruction error (RE).

cs.LG↗

arXiv2021

Quantized Proximal Averaging Network for Analysis Sparse Coding

We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the iterative algorithm into a trainable network that facilitates learning the sparsity prior. We also consider quantization of the network weights. Quantization makes neural networks efficient both in terms of memory and computation during inference, and also renders them compatible for low-precision hardware deployment. Our learning algorithm is based on a variant of the ADAM optimizer in which the quantizer is part of the forward pass and the gradients of the loss function are evaluated corresponding to the quantized weights while doing a book-keeping of the high-precision weights. We demonstrate applications to compressed image recovery and magnetic resonance image reconstruction. The proposed approach offers superior reconstruction accuracy and quality than state-of-the-art unfolding techniques and the performance degradation is minimal even when the weights are subjected to extreme quantization.

cs.LG↗

arXiv2020

Robust Segmentation of Optic Disc and Cup from Fundus Images Using Deep Neural Networks

Optic disc (OD) and optic cup (OC) are regions of prominent clinical interest in a retinal fundus image. They are the primary indicators of a glaucomatous condition. With the advent and success of deep learning for healthcare research, several approaches have been proposed for the segmentation of important features in retinal fundus images. We propose a novel approach for the simultaneous segmentation of the OD and OC using a residual encoder-decoder network (REDNet) based regional convolutional neural network (RCNN). The RED-RCNN is motivated by the Mask RCNN (MRCNN). Performance comparisons with the state-of-the-art techniques and extensive validations on standard publicly available fundus image datasets show that RED-RCNN has superior performance compared with MRCNN. RED-RCNN results in Sensitivity, Specificity, Accuracy, Precision, Dice and Jaccard indices of 95.64%, 99.9%, 99.82%, 95.68%, 95.64%, 91.65%, respectively, for OD segmentation, and 91.44%, 99.87%, 99.83%, 85.67%, 87.48%, 78.09%, respectively, for OC segmentation. Further, we perform two-stage glaucoma severity grading using the cup-to-disc ratio (CDR) computed based on the obtained OD/OC segmentation. The superior segmentation performance of RED-RCNN over MRCNN translates to higher accuracy in glaucoma severity grading.

eess.IV↗

arXiv2020

Teaching a GAN What Not to Learn

Generative adversarial networks (GANs) were originally envisioned as unsupervised generative models that learn to follow a target distribution. Variants such as conditional GANs, auxiliary-classifier GANs (ACGANs) project GANs on to supervised and semi-supervised learning frameworks by providing labelled data and using multi-class discriminators. In this paper, we approach the supervised GAN problem from a different perspective, one that is motivated by the philosophy of the famous Persian poet Rumi who said, "The art of knowing is knowing what to ignore." In the GAN framework, we not only provide the GAN positive data that it must learn to model, but also present it with so-called negative samples that it must learn to avoid - we call this "The Rumi Framework." This formulation allows the discriminator to represent the underlying target distribution better by learning to penalize generated samples that are undesirable - we show that this capability accelerates the learning process of the generator. We present a reformulation of the standard GAN (SGAN) and least-squares GAN (LSGAN) within the Rumi setting. The advantage of the reformulation is demonstrated by means of experiments conducted on MNIST, Fashion MNIST, CelebA, and CIFAR-10 datasets. Finally, we consider an application of the proposed formulation to address the important problem of learning an under-represented class in an unbalanced dataset. The Rumi approach results in substantially lower FID scores than the standard GAN frameworks while possessing better generalization capability.

stat.ML↗

arXiv2019

Unlimited Dynamic Range Analog-to-Digital Conversion

Analog-to-digital converters (ADCs) provide the link between continuous-time signals and their discrete-time counterparts, and the Shannon-Nyquist sampling theorem provides the mathematical foundation. Real-world signals have a variable amplitude range, whereas ADCs, by design, have a limited input dynamic range, which results in out-of-range signals getting clipped. In this paper, we propose an unlimited dynamic range ADC (UDR-ADC) that is based on the modulo operation (self-reset feature) to alleviate the problem of clipping. The self-reset feature allows for wrapping of the input amplitudes, which preserves the input dynamic range. We present the signal model and a reconstruction technique to recover the original signal samples from the modulo measurements. We validate the operation of the proposed ADC using circuit simulations in 65 nm complementary metal-oxide-semiconductor (CMOS) process technology. The validation is supplemented by a hardware prototype designed using discrete components. A performance assessment in terms of area, power requirement, and the signal-to-quantization-noise ratio (SQNR) shows that the UDR-ADC outperforms the standard ones.

eess.SP↗

arXiv2019

Generalized Design of Sampling Kernels for 2-D FRI Signals

One of the interesting problems in the finite-rate-of-innovation signal sampling framework is the design of compactly supported sampling kernels. In this paper, we present a generic framework for designing sampling kernels in 2-D. We consider both separable and nonseparable kernels. The design is carried out in the frequency domain, where a set of alias cancellation conditions are imposed on the kernel's frequency response. The Paley-Wiener theorem for 2-D signals is invoked to arrive at admissible kernels with a compact support. As a specific case, we show that a certain separable extension of the 1-D design framework results in 2-D sum-of-modulated-spline (SMS) kernels. Similar to their 1-D counterparts, the 2-D SMS kernels have the attractive feature of reproducing a class of 2-D polynomial-modulated exponentials of a desired order. Also, the support of the kernels is independent of the order. The design framework is generic and also allows one to design nonseparable sampling kernels. To this end, we demonstrate the design of a nonseparable kernel and present simulation results.

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arXiv2018

Quantization-Aware Phase Retrieval

We address the problem of phase retrieval (PR) from quantized measurements. The goal is to reconstruct a signal from quadratic measurements encoded with a finite precision, which is indeed the case in many practical applications. We develop a rank-1 projection algorithm that recovers the signal subject to ensuring consistency with the measurement, that is, the recovered signal when encoded must yield the same set of measurements that one started with. The rank-1 projection stems from the idea of lifting, originally proposed in the context of PhaseLift. The consistency criterion is enforced using a one-sided quadratic cost. We also determine the probability with which different vectors lead to the same set of quantized measurements, which makes it impossible to resolve them. Naturally, this probability depends on how correlated such vectors are, and how coarsely/finely the measurements get quantized. The proposed algorithm is also capable of incorporating a sparsity constraint on the signal. An analysis of the cost function reveals that it is bounded, both above and below, by functions that are dependent on how well correlated the estimate is with the ground truth. We also derive the Cramér-Rao lower bound (CRB) on the achievable reconstruction accuracy. A comparison with the state-of-the- art algorithms shows that the proposed algorithm has a higher reconstruction accuracy and is about 2 to 3 dB away from the CRB. The edge, in terms of the reconstruction signal-to-noise ratio, over the competing algorithms is higher (about 5 to 6 dB) when the quantization is coarse.

cs.LG↗

arXiv2018

Epoch-Synchronous Overlap-Add (ESOLA) for Time- and Pitch-Scale Modification of Speech Signals

Time- and pitch-scale modifications of speech signals find important applications in speech synthesis, playback systems, voice conversion, learning/hearing aids, etc.. There is a requirement for computationally efficient and real-time implementable algorithms. In this paper, we propose a high quality and computationally efficient time- and pitch-scaling methodology based on the glottal closure instants (GCIs) or epochs in speech signals. The proposed algorithm, termed as epoch-synchronous overlap-add time/pitch-scaling (ESOLA-TS/PS), segments speech signals into overlapping short-time frames and then the adjacent frames are aligned with respect to the epochs and the frames are overlap-added to synthesize time-scale modified speech. Pitch scaling is achieved by resampling the time-scaled speech by a desired sampling factor. We also propose a concept of epoch embedding into speech signals, which facilitates the identification and time-stamping of samples corresponding to epochs and using them for time/pitch-scaling to multiple scaling factors whenever desired, thereby contributing to faster and efficient implementation. The results of perceptual evaluation tests reported in this paper indicate the superiority of ESOLA over state-of-the-art techniques. ESOLA significantly outperforms the conventional pitch synchronous overlap-add (PSOLA) techniques in terms of perceptual quality and intelligibility of the modified speech. Unlike the waveform similarity overlap-add (WSOLA) or synchronous overlap-add (SOLA) techniques, the ESOLA technique has the capability to do exact time-scaling of speech with high quality to any desired modification factor within a range of 0.5 to 2. Compared to synchronous overlap-add with fixed synthesis (SOLAFS), the ESOLA is computationally advantageous and at least three times faster.

eess.AS↗

arXiv2017

Phase Retrieval From Binary Measurements

We consider the problem of signal reconstruction from quadratic measurements that are encoded as +1 or -1 depending on whether they exceed a predetermined positive threshold or not. Binary measurements are fast to acquire and inexpensive in terms of hardware. We formulate the problem of signal reconstruction using a consistency criterion, wherein one seeks to find a signal that is in agreement with the measurements. To enforce consistency, we construct a convex cost using a one-sided quadratic penalty and minimize it using an iterative accelerated projected gradient-descent (APGD) technique. The PGD scheme reduces the cost function in each iteration, whereas incorporating momentum into PGD, notwithstanding the lack of such a descent property, exhibits faster convergence than PGD empirically. We refer to the resulting algorithm as binary phase retrieval (BPR). Considering additive white noise contamination prior to quantization, we also derive the Cramer-Rao Bound (CRB) for the binary encoding model. Experimental results demonstrate that the BPR algorithm yields a signal-to- reconstruction error ratio (SRER) of approximately 25 dB in the absence of noise. In the presence of noise prior to quantization, the SRER is within 2 to 3 dB of the CRB.

cs.IT↗

arXiv2017

A Non-Convex Optimization Technique for Sparse Blind Deconvolution -- Initialization Aspects and Error Reduction Properties

Sparse blind deconvolution is the problem of estimating the blur kernel and sparse excitation, both of which are unknown. Considering a linear convolution model, as opposed to the standard circular convolution model, we derive a sufficient condition for stable deconvolution. The columns of the linear convolution matrix form a Riesz basis with the tightness of the Riesz bounds determined by the autocorrelation of the blur kernel. Employing a Bayesian framework results in a non-convex, non-smooth cost function consisting of an $\ell_2$ data-fidelity term and a sparsity promoting $\ell_p$-norm ($0 \le p \le 1$) regularizer. Since the $\ell_p$-norm is not differentiable at the origin, we employ an $ε$-regularized $\ell_p$-norm as a surrogate. The data term is also non-convex in both the blur kernel and excitation. An iterative scheme termed alternating minimization (Alt. Min.) $\ell_p-\ell_2$ projections algorithm (ALPA) is developed for optimization of the $ε$-regularized cost function. Further, we demonstrate that, in every iteration, the $ε$-regularized cost function is non-increasing and more importantly, bounds the original $\ell_p$-norm-based cost. Due to non-convexity of the cost, the accuracy of estimation is largely influenced by the initialization. Considering regularized least-squares estimate as the initialization, we analyze how the initialization errors are concentrated, first in Gaussian noise, and then in bounded noise, the latter case resulting in tighter bounds. Comparisons with state-of-the-art blind deconvolution algorithms show that the deconvolution accuracy is higher in case of ALPA. In the context of natural speech signals, ALPA results in accurate deconvolution of a voiced speech segment into a sparse excitation and smooth vocal tract response.

cs.IT↗

arXiv2017

PROSE: Perceptual Risk Optimization for Speech Enhancement

The goal in speech enhancement is to obtain an estimate of clean speech starting from the noisy signal by minimizing a chosen distortion measure, which results in an estimate that depends on the unknown clean signal or its statistics. Since access to such prior knowledge is limited or not possible in practice, one has to estimate the clean signal statistics. In this paper, we develop a new risk minimization framework for speech enhancement, in which, one optimizes an unbiased estimate of the distortion/risk instead of the actual risk. The estimated risk is expressed solely as a function of the noisy observations. We consider several perceptually relevant distortion measures and develop corresponding unbiased estimates under realistic assumptions on the noise distribution and a priori signal-to-noise ratio (SNR). Minimizing the risk estimates gives rise to the corresponding denoisers, which are nonlinear functions of the a posteriori SNR. Perceptual evaluation of speech quality (PESQ), average segmental SNR (SSNR) computations, and listening tests show that the proposed risk optimization approach employing Itakura-Saito and weighted hyperbolic cosine distortions gives better performance than the other distortion measures. For SNRs greater than 5 dB, the proposed approach gives superior denoising performance over the benchmark techniques based on the Wiener filter, log-MMSE minimization, and Bayesian nonnegative matrix factorization.

eess.AS↗

arXiv2017

Online Reweighted Least Squares Algorithm for Sparse Recovery and Application to Short-Wave Infrared Imaging

We address the problem of sparse recovery in an online setting, where random linear measurements of a sparse signal are revealed sequentially and the objective is to recover the underlying signal. We propose a reweighted least squares (RLS) algorithm to solve the problem of online sparse reconstruction, wherein a system of linear equations is solved using conjugate gradient with the arrival of every new measurement. The proposed online algorithm is useful in a setting where one seeks to design a progressive decoding strategy to reconstruct a sparse signal from linear measurements so that one does not have to wait until all measurements are acquired. Moreover, the proposed algorithm is also useful in applications where it is infeasible to process all the measurements using a batch algorithm, owing to computational and storage constraints. It is not needed a priori to collect a fixed number of measurements; rather one can keep collecting measurements until the quality of reconstruction is satisfactory and stop taking further measurements once the reconstruction is sufficiently accurate. We provide a proof-of-concept by comparing the performance of our algorithm with the RLS-based batch reconstruction strategy, known as iteratively reweighted least squares (IRLS), on natural images. Experiments on a recently proposed focal plane array-based imaging setup show up to 1 dB improvement in output peak signal-to-noise ratio as compared with the total variation-based reconstruction.

cs.LG↗

arXiv2017

Deep Sparse Coding Using Optimized Linear Expansion of Thresholds

We address the problem of reconstructing sparse signals from noisy and compressive measurements using a feed-forward deep neural network (DNN) with an architecture motivated by the iterative shrinkage-thresholding algorithm (ISTA). We maintain the weights and biases of the network links as prescribed by ISTA and model the nonlinear activation function using a linear expansion of thresholds (LET), which has been very successful in image denoising and deconvolution. The optimal set of coefficients of the parametrized activation is learned over a training dataset containing measurement-sparse signal pairs, corresponding to a fixed sensing matrix. For training, we develop an efficient second-order algorithm, which requires only matrix-vector product computations in every training epoch (Hessian-free optimization) and offers superior convergence performance than gradient-descent optimization. Subsequently, we derive an improved network architecture inspired by FISTA, a faster version of ISTA, to achieve similar signal estimation performance with about 50% of the number of layers. The resulting architecture turns out to be a deep residual network, which has recently been shown to exhibit superior performance in several visual recognition tasks. Numerical experiments demonstrate that the proposed DNN architectures lead to 3 to 4 dB improvement in the reconstruction signal-to-noise ratio (SNR), compared with the state-of-the-art sparse coding algorithms.

cs.LG↗

arXiv2017

Signal Denoising Using the Minimum-Probability-of-Error Criterion

We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an $ε$-neighborhood of the actual value. However, the MPE, similar to the mean-squared error (MSE), depends on the ground-truth parameter, and has to be estimated from the noisy observations. We consider linear shrinkage-based denoising functions, wherein the optimum shrinkage parameter is obtained by minimizing an estimate of the MPE. When the probability of error is integrated over $ε$, it leads to the expected $\ell_1$ distortion. The proposed MPE and $\ell_1$ distortion formulations are applicable to various noise distributions by invoking a Gaussian mixture model approximation. Within the realm of MPE, we also develop an extension of the transform-domain shrinkage by grouping transform coefficients, resulting in $\textit{subband shrinkage}$. The denoising performance obtained within the proposed framework is shown to be better than that obtained using the minimum MSE-based approaches formulated within $\textbf{$\textit {Stein's unbiased risk estimation}$}$ (SURE) framework, especially in the low measurement signal-to-noise ratio (SNR) regime. Performance comparison with three state-of-the-art denoising algorithms, carried out on electrocardiogram signals and two test signals taken from the $\textit{Wavelab}$ toolbox, exhibits that the MPE framework results in consistent SNR gains for input SNRs below $5$ dB.

stat.AP↗

arXiv2016

Super-Resolution From Binary Measurements With Unknown Threshold

We address the problem of super-resolution of point sources from binary measurements, where random projections of the blurred measurement of the actual signal are encoded using only the sign information. The threshold used for binary quantization is not known to the decoder. We develop an algorithm that solves convex programs iteratively and achieves signal recovery. The proposed algorithm, which we refer to as the binary super-resolution (BSR) algorithm, recovers point sources with reasonable accuracy, albeit up to a scale factor. We show through simulations that the BSR algorithm is successful in recovering the locations and the amplitudes of the point sources, even in the presence of significant amount of blurring. We also propose a framework for handling noisy measurements and demonstrate that BSR gives a reliable reconstruction (correspondingly, reconstruction signal-to-noise ratio (SNR) of about 22 dB) for a measurement SNR of 15 dB.

cs.IT↗

arXiv2015

$\ell_1$-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update

We develop a dictionary learning algorithm by minimizing the $\ell_1$ distortion metric on the data term, which is known to be robust for non-Gaussian noise contamination. The proposed algorithm exploits the idea of iterative minimization of weighted $\ell_2$ error. We refer to this algorithm as $\ell_1$-K-SVD, where the dictionary atoms and the corresponding sparse coefficients are simultaneously updated to minimize the $\ell_1$ objective, resulting in noise-robustness. We demonstrate through experiments that the $\ell_1$-K-SVD algorithm results in higher atom recovery rate compared with the K-SVD and the robust dictionary learning (RDL) algorithm proposed by Lu et al., both in Gaussian and non-Gaussian noise conditions. We also show that, for fixed values of sparsity, number of dictionary atoms, and data-dimension, the $\ell_1$-K-SVD algorithm outperforms the K-SVD and RDL algorithms when the training set available is small. We apply the proposed algorithm for denoising natural images corrupted by additive Gaussian and Laplacian noise. The images denoised using $\ell_1$-K-SVD are observed to have slightly higher peak signal-to-noise ratio (PSNR) over K-SVD for Laplacian noise, but the improvement in structural similarity index (SSIM) is significant (approximately $0.1$) for lower values of input PSNR, indicating the efficacy of the $\ell_1$ metric.

cs.CV↗