Chandra Sekhar Seelamantula

Siddarth Asokan, Chandra Sekhar Seelamantula

We consider the problem of optimizing the discriminator in generative adversarial networks (GANs) subject to higher-order gradient regularization. We show analytically, via the least-squares (LSGAN) and Wasserstein (WGAN) GAN variants, that the discriminator optimization problem is one of interpolation in $n$-dimensions. The optimal discriminator, derived using variational Calculus, turns out to be the solution to a partial differential equation involving the iterated Laplacian or the polyharmonic operator. The solution is implementable in closed-form via polyharmonic radial basis function (RBF) interpolation. In view of the polyharmonic connection, we refer to the corresponding GANs as Poly-LSGAN and Poly-WGAN. Through experimental validation on multivariate Gaussians, we show that implementing the optimal RBF discriminator in closed-form, with penalty orders $m \approx\lceil \frac{n}{2} \rceil $, results in superior performance, compared to training GAN with arbitrarily chosen discriminator architectures. We employ the Poly-WGAN discriminator to model the latent space distribution of the data with encoder-decoder-based GAN flavors such as Wasserstein autoencoders.

Ashish Vashist, Qiranul Saadiyean, Suresh Sundaram et al.

Foreign Object Debris (FOD) within aircraft fuel tanks presents critical safety hazards including fuel contamination, system malfunctions, and increased maintenance costs. Despite the severity of these risks, there is a notable lack of dedicated datasets for the complex, enclosed environments found inside fuel tanks. To bridge this gap, we present a novel dataset, FOD-S2R, composed of real and synthetic images of the FOD within a simulated aircraft fuel tank. Unlike existing datasets that focus on external or open-air environments, our dataset is the first to systematically evaluate the effectiveness of synthetic data in enhancing the real-world FOD detection performance in confined, closed structures. The real-world subset consists of 3,114 high-resolution HD images captured in a controlled fuel tank replica, while the synthetic subset includes 3,137 images generated using Unreal Engine. The dataset is composed of various Field of views (FOV), object distances, lighting conditions, color, and object size. Prior research has demonstrated that synthetic data can reduce reliance on extensive real-world annotations and improve the generalizability of vision models. Thus, we benchmark several state-of-the-art object detection models and demonstrate that introducing synthetic data improves the detection accuracy and generalization to real-world conditions. These experiments demonstrate the effectiveness of synthetic data in enhancing the model performance and narrowing the Sim2Real gap, providing a valuable foundation for developing automated FOD detection systems for aviation maintenance.

Aadithya Srikanth, Siddarth Asokan, Nishanth Shetty et al.

Diffusion models are a state-of-the-art generative modeling framework that transform noise to images via Langevin sampling, guided by the score, which is the gradient of the logarithm of the data distribution. Recent works have shown empirically that the generation quality can be improved when guided by classifier network, which is typically the discriminator trained in a generative adversarial network (GAN) setting. In this paper, we propose a theoretical framework to analyze the effect of the GAN discriminator on Langevin-based sampling, and show that the IPM-GAN optimization can be seen as one of smoothed score-matching, wherein the scores of the data and the generator distributions are convolved with the kernel function associated with the IPM. The proposed approach serves to unify score-based training and optimization of IPM-GANs. Based on these insights, we demonstrate that closed-form kernel-based discriminator guidance, results in improvements (in terms of CLIP-FID and KID metrics) when applied atop baseline diffusion models. We demonstrate these results on the denoising diffusion implicit model (DDIM) and latent diffusion model (LDM) settings on various standard datasets. We also show that the proposed approach can be combined with existing accelerated-diffusion techniques to improve latent-space image generation.

Kunal Swami, Sudha Velusamy, Chandra Sekhar Seelamantula

Removing fence occlusions from single images is a challenging task that degrades visual quality and limits downstream computer vision applications. Existing methods often fail on static scenes or require motion cues from multiple frames. To overcome these limitations, we introduce the first framework to leverage dual-pixel (DP) sensors for this problem. We propose Freq-DP Net, a novel dual-branch network that fuses two complementary priors: a geometric prior from defocus disparity, modeled using an explicit cost volume, and a structural prior of the fence's global pattern, learned via Fast Fourier Convolution (FFC). An attention mechanism intelligently merges these cues for highly accurate fence segmentation. To validate our approach, we build and release a diverse benchmark with different fence varieties. Experiments demonstrate that our method significantly outperforms strong general-purpose baselines, establishing a new state-of-the-art for single-image, DP-based fence removal.

Nishanth Shetty, Madhava Prasath, Chandra Sekhar Seelamantula

Gradient descent has proven to be a powerful and effective technique for optimization in numerous machine learning applications. Recent advances in computational neuroscience have shown that learning in standard gradient descent optimization formulation is not consistent with learning in biological systems. This has opened up interesting avenues for building biologically inspired learning techniques. One such approach is inspired by Dale's law, which states that inhibitory and excitatory synapses do not swap roles during the course of learning. The resulting exponential gradient descent optimization scheme leads to log-normally distributed synaptic weights. Interestingly, the density that satisfies the Fokker-Planck equation corresponding to the stochastic differential equation (SDE) with geometric Brownian motion (GBM) is the log-normal density. Leveraging this connection, we start with the SDE governing geometric Brownian motion, and show that discretizing the corresponding reverse-time SDE yields a multiplicative update rule, which surprisingly, coincides with the sampling equivalent of the exponential gradient descent update founded on Dale's law. Furthermore, we propose a new formalism for multiplicative denoising score-matching, subsuming the loss function proposed by Hyvaerinen for non-negative data. Indeed, log-normally distributed data is positive and the proposed score-matching formalism turns out to be a natural fit. This allows for training of score-based models for image data and results in a novel multiplicative update scheme for sample generation starting from a log-normal density. Experimental results on MNIST, Fashion MNIST, and Kuzushiji datasets demonstrate generative capability of the new scheme. To the best of our knowledge, this is the first instance of a biologically inspired generative model employing multiplicative updates, founded on geometric Brownian motion.

Satyapreet Singh Yadav, Akash K S, Chandra Sekhar Seelamantula et al.

We present a neuromorphic radar framework for real-time, low-power hand gesture recognition (HGR) using an event-driven architecture inspired by biological sensing. Our system comprises a 24 GHz Doppler radar front-end and a custom neuromorphic sampler that converts intermediate-frequency (IF) signals into sparse spike-based representations via asynchronous sigma-delta encoding. These events are directly processed by a lightweight neural network deployed on a Cortex-M0 microcontroller, enabling low-latency inference without requiring spectrogram reconstruction. Unlike conventional radar HGR pipelines that continuously sample and process data, our architecture activates only when meaningful motion is detected, significantly reducing memory, power, and computation overhead. Evaluated on a dataset of five gestures collected from seven users, our system achieves > 85% real-time accuracy. To the best of our knowledge, this is the first work that employs bio-inspired asynchronous sigma-delta encoding and an event-driven processing framework for radar-based HGR.

Siddarth Asokan, Chandra Sekhar Seelamantula

Training Generative adversarial networks (GANs) stably is a challenging task. The generator in GANs transform noise vectors, typically Gaussian distributed, into realistic data such as images. In this paper, we propose a novel approach for training GANs with images as inputs, but without enforcing any pairwise constraints. The intuition is that images are more structured than noise, which the generator can leverage to learn a more robust transformation. The process can be made efficient by identifying closely related datasets, or a ``friendly neighborhood'' of the target distribution, inspiring the moniker, Spider GAN. To define friendly neighborhoods leveraging proximity between datasets, we propose a new measure called the signed inception distance (SID), inspired by the polyharmonic kernel. We show that the Spider GAN formulation results in faster convergence, as the generator can discover correspondence even between seemingly unrelated datasets, for instance, between Tiny-ImageNet and CelebA faces. Further, we demonstrate cascading Spider GAN, where the output distribution from a pre-trained GAN generator is used as the input to the subsequent network. Effectively, transporting one distribution to another in a cascaded fashion until the target is learnt -- a new flavor of transfer learning. We demonstrate the efficacy of the Spider approach on DCGAN, conditional GAN, PGGAN, StyleGAN2 and StyleGAN3. The proposed approach achieves state-of-the-art Frechet inception distance (FID) values, with one-fifth of the training iterations, in comparison to their baseline counterparts on high-resolution small datasets such as MetFaces, Ukiyo-E Faces and AFHQ-Cats.

Dhruv Jawali, Abhishek Kumar, Chandra Sekhar Seelamantula

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.

Vinayak Killedar, Praveen Kumar Pokala, Chandra Sekhar Seelamantula

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).

Kartheek Kumar Reddy Nareddy, Mani Madhoolika Bulusu, Praveen Kumar Pokala et al.

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.

Swapnil Mache, Praveen Kumar Pokala, Kusala Rajendran et al.

We solve the problem of sparse signal deconvolution in the context of seismic reflectivity inversion, which pertains to high-resolution recovery of the subsurface reflection coefficients. Our formulation employs a nonuniform, non-convex synthesis sparse model comprising a combination of convex and non-convex regularizers, which results in accurate approximations of the l0 pseudo-norm. The resulting iterative algorithm requires the proximal average strategy. When unfolded, the iterations give rise to a learnable proximal average network architecture that can be optimized in a data-driven fashion. We demonstrate the efficacy of the proposed approach through numerical experiments on synthetic 1-D seismic traces and 2-D wedge models in comparison with the benchmark techniques. We also present validations considering the simulated Marmousi2 model as well as real 3-D seismic volume data acquired from the Penobscot 3D survey off the coast of Nova Scotia, Canada.

Swapnil Mache, Praveen Kumar Pokala, Kusala Rajendran et al.

We consider the reflection seismology problem of recovering the locations of interfaces and the amplitudes of reflection coefficients from seismic data, which are vital for estimating the subsurface structure. The reflectivity inversion problem is typically solved using greedy algorithms and iterative techniques. Sparse Bayesian learning framework, and more recently, deep learning techniques have shown the potential of data-driven approaches to solve the problem. In this paper, we propose a weighted minimax-concave penalty-regularized reflectivity inversion formulation and solve it through a model-based neural network. The network is referred to as deep-unfolded reflectivity inversion network (DuRIN). We demonstrate the efficacy of the proposed approach over the benchmark techniques by testing on synthetic 1-D seismic traces and 2-D wedge models and validation with the simulated 2-D Marmousi2 model and real data from the Penobscot 3D survey off the coast of Nova Scotia, Canada.

Aniketh Manjunath, Subramanya Jois, Chandra Sekhar Seelamantula

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.

Siddarth Asokan, Chandra Sekhar Seelamantula

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.

Subhadip Mukherjee, Chandra Sekhar Seelamantula

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.

Sunil Rudresh, Aditya Vasisht, Karthika Vijayan et al.

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.

Jishnu Sadasivan, Chandra Sekhar Seelamantula, Nagarjuna Reddy Muraka

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.

Subhadip Mukherjee, Deepak R., Huaijin Chen et al.

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.

Debabrata Mahapatra, Subhadip Mukherjee, Chandra Sekhar Seelamantula

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.

Sagar Venkatesh Gubbi, Chandra Sekhar Seelamantula

We address the problem of image denoising in additive white noise without placing restrictive assumptions on its statistical distribution. In the recent literature, specific noise distributions have been considered and correspondingly, optimal denoising techniques have been developed. One of the successful approaches for denoising relies on the notion of unbiased risk estimation, which enables one to obtain a useful substitute for the mean-square error. For the case of additive white Gaussian noise contamination, the risk estimation procedure relies on Stein's lemma. Sophisticated wavelet-based denoising techniques, which are essentially nonlinear, have been developed with the help of the lemma. We show that, for linear, shift-invariant denoisers, it is possible to obtain unbiased risk estimates of the mean-square error without using Stein's lemma. An interesting consequence of this development is that the unbiased risk estimator becomes agnostic to the statistical distribution of the noise. As a proof of principle, we show how the new methodology can be used to optimize the parameters of a simple Gaussian smoother. By locally adapting the parameters of the Gaussian smoother, we obtain a shift-variant smoother, which has a denoising performance (quantified by the improvement in peak signal-to-noise ratio (PSNR)) that is competitive to far more sophisticated methods reported in the literature. The proposed solution exhibits considerable parallelism, which we exploit in a Graphics Processing Unit (GPU) implementation.

Manasij Venkatesh, Chandra Sekhar Seelamantula

We propose a bilateral filter with a locally controlled domain kernel for directional edge-preserving smoothing. Traditional bilateral filters use a range kernel, which is responsible for edge preservation, and a fixed domain kernel that performs smoothing. Our intuition is that orientation and anisotropy of image structures should be incorporated into the domain kernel while smoothing. For this purpose, we employ an oriented Gaussian domain kernel locally controlled by a structure tensor. The oriented domain kernel combined with a range kernel forms the directional bilateral filter. The two kernels assist each other in effectively suppressing the influence of the outliers while smoothing. To find the optimal parameters of the directional bilateral filter, we propose the use of Stein's unbiased risk estimate (SURE). We test the capabilities of the kernels separately as well as together, first on synthetic images, and then on real endoscopic images. The directional bilateral filter has better denoising performance than the Gaussian bilateral filter at various noise levels in terms of peak signal-to-noise ratio (PSNR).

Subhadip Mukherjee, Rupam Basu, Chandra Sekhar Seelamantula

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.

Subhadip Mukherjee, Chandra Sekhar Seelamantula

In big data image/video analytics, we encounter the problem of learning an overcomplete dictionary for sparse representation from a large training dataset, which can not be processed at once because of storage and computational constraints. To tackle the problem of dictionary learning in such scenarios, we propose an algorithm for parallel dictionary learning. The fundamental idea behind the algorithm is to learn a sparse representation in two phases. In the first phase, the whole training dataset is partitioned into small non-overlapping subsets, and a dictionary is trained independently on each small database. In the second phase, the dictionaries are merged to form a global dictionary. We show that the proposed algorithm is efficient in its usage of memory and computational complexity, and performs on par with the standard learning strategy operating on the entire data at a time. As an application, we consider the problem of image denoising. We present a comparative analysis of our algorithm with the standard learning techniques, that use the entire database at a time, in terms of training and denoising performance. We observe that the split-and-merge algorithm results in a remarkable reduction of training time, without significantly affecting the denoising performance.

Jayanth Krishna Mogali, Adithya Kumar Pediredla, Chandra Sekhar Seelamantula

We develop a generalized active contour formalism for image segmentation based on shape templates. The shape template is subjected to a restricted affine transformation (RAT) in order to segment the object of interest. RAT allows for translation, rotation, and scaling, which give a total of five degrees of freedom. The proposed active contour comprises an inner and outer contour pair, which are closed and concentric. The active contour energy is a contrast function defined based on the intensities of pixels that lie inside the inner contour and those that lie in the annulus between the inner and outer contours. We show that the contrast energy functional is optimal under certain conditions. The optimal RAT parameters are computed by maximizing the contrast function using a gradient descent optimizer. We show that the calculations are made efficient through use of Green's theorem. The proposed formalism is capable of handling a variety of shapes because for a chosen template, optimization is carried with respect to the RAT parameters only. The proposed formalism is validated on multiple images to show robustness to Gaussian and Poisson noise, to initialization, and to partial loss of structure in the object to be segmented.