Sujit Kumar Sahoo

Dictionary Training for Sparse Representation as Generalization of K-Means Clustering

Recent dictionary training algorithms for sparse representation like K-SVD, MOD, and their variation are reminiscent of K-means clustering, and this letter investigates such algorithms from that viewpoint. It shows: though K-SVD is sequential like K-means, it fails to simplify to K-means by destroying the structure in the sparse coefficients. In contrast, MOD can be viewed as a parallel generalization of K-means, which simplifies to K-means without perturbing the sparse coefficients. Keeping memory usage in mind, we propose an alternative to MOD; a sequential generalization of K-means (SGK). While experiments suggest a comparable training performances across the algorithms, complexity analysis shows MOD and SGK to be faster under a dimensionality condition.

Signal Recovery from Random Measurements via Extended Orthogonal Matching Pursuit

Orthogonal Matching Pursuit (OMP) and Basis Pursuit (BP) are two well-known recovery algorithms in compressed sensing. To recover a d-dimensional m-sparse signal with high probability, OMP needs O(m ln d) number of measurements, whereas BP needs only O(m ln d/m) number of measurements. In contrary, OMP is a practically more appealing algorithm due to its superior execution speed. In this piece of work, we have proposed a scheme that brings the required number of measurements for OMP closer to BP. We have termed this scheme as OMP_α, which runs OMP for (m+⌊αm⌋)-iterations instead of m-iterations, by choosing a value of α ∈ [0,1]. It is shown that OMP_α guarantees a high probability signal recovery with O(m ln d/⌊αm⌋+1) number of measurements. Another limitation of OMP unlike BP is that it requires the knowledge of m. In order to overcome this limitation, we have extended the idea of OMP_α to illustrate another recovery scheme called OMP∞, which runs OMP until the signal residue vanishes. It is shown that OMP∞ can achieve a close to ℓ₀-norm recovery without any knowledge of m like BP.

Detection of Atrial fibrillation from non-episodic ECG data: A review of methods

Atrial fibrillation (A-fib) is the most common cardiac arrhythmia. To effectively treat or prevent A-fib, automatic A-fib detection based on Electrocardiograph (ECG) monitoring is highly desirable. This paper reviews recently developed techniques for A-fib detection based on non-episodic surface ECG monitoring data. A-fib detection methods in the literature can be mainly classified into three categories: (1) time domain methods; (2) frequency domain methods; and (3) non-linear methods. In general the performances of these methods were evaluated in terms of sensitivity, specificity and overall detection accuracy on the datasets from the Physionet repository. Based on our survey, we conclude that no promising A-fib detection method that performs consistently well across various scenarios has been proposed yet.

Greedy pursuits assisted basis pursuit for compressive sensing

Fusion based Compressive Sensing (CS) reconstruction algorithms combine multiple CS reconstruction algorithms, which worked with different principles, to obtain a better signal estimate. Examples include Fusion of Algorithms for Compressed Sensing (FACS) and Committee Machine Approach for Compressed Sensing (CoMACS). However, these algorithms involve solving a least squares problem which may be ill-conditioned. Modified CS algorithms such as Modified Basis Pursuit (Mod-BP) ensured a sparse signal can efficiently be reconstructed when a part of its support is known. Since Mod-BP makes use of available signal knowledge to improve upon BP, we propose to employ multiple Greedy Pursuits (GPs) to derive a partial support for Mod-BP. As Mod-BP makes use of signal knowledge derived using GPs, we term our proposed algorithm as Greedy Pursuits Assisted Basis Pursuit (GPABP). Experimental results show that our proposed algorithm performs better than the state-of-the-art algorithms - FACS and its variants.

Enhancing Image Denoising by Controlling Noise Incursion in Learned Dictionaries

Existing image denoising frameworks via sparse representation using learned dictionaries have an weakness that the dictionary, trained from noisy image, suffers from noise incursion. This paper analyzes this noise incursion, explicitly derives the noise component in the dictionary update step, and provides a simple remedy for a desired signal to noise ratio. The remedy is shown to perform better both in objective and subjective measures for lesser computation, and complements the framework of image denoising.

Single-shot multispectral imaging with a monochromatic camera

Multispectral imaging plays an important role in many applications, from astronomical imaging and earth observation to biomedical imaging. However, current technologies are complex with multiple alignment-sensitive components and spatial and spectral parameters predetermined by manufacturers. Here, we demonstrate a single-shot multispectral imaging technique that gives flexibility to end users with a very simple optical setup, thanks to spatial correlation and spectral decorrelation of speckle patterns. These seemingly random speckle patterns are point spread functions (PSFs) generated by light from point sources propagating through a strongly scattering medium. The spatial correlation of PSFs allows image recovery with deconvolution techniques, while the spectral decorrelation allows them to play the role of tunable spectral filters in the deconvolution process. Our demonstrations utilizing optical physics of strongly scattering media and computational imaging present a cost-effective approach for multispectral imaging with many advantages.

Modified adaptive basis pursuits for recovery of correlated sparse signals

In Distributed Compressive Sensing (DCS), correlated sparse signals stand for an ensemble of signals characterized by presenting a sparse correlation. If one signal is known apriori, the remaining signals in the ensemble can be reconstructed using l1-minimization with far fewer measurements compared to separate CS reconstruction. Reconstruction of such correlated signals is possible via Modified-CS and Regularized-Modified-BP. However, these methods are greatly influenced by the support set of the known signal that includes locations irrelevant to the target signal. While recovering each signal, prior to Modified-CS or Regularized-Modified-BP, we propose an adaptation step to retain only the sparse locations significant to that signal. We call our proposed methods as Modified-Adaptive-BP and Regularized-Modified-Adaptive-BP. Theoretical guarantees and experimental results show that our proposed methods provide efficient recovery compared to that of the Modified-CS and its regularized version.

Image denoising via sparse representations over Sequential Generalization of K-means (SGK)

We have recently proposed a Sequential Generalization of K-means (SGK) to train dictionary for sparse representation. SGKs training performance is as effective as the standard dictionary training algorithm K-SVD, alongside it has a simpler implementation to its advantage. In this piece of work, through the problem of image denoising, we are making a fair comparison between the usability of SGK and K-SVD. The obtained results suggest that we can successfully replace K-SVD with SGK, due to its quicker execution and comparable outcomes. Similarly, it is possible to extend the use of SGK to other applications of sparse representation.

Image inpainting using sparse approximation with adaptive window selection

In this paper the problem of image inpainting is addressed using sparse approximation of local image patches. The small patches are extracted by sliding square windows. An adaptive window selection procedure for local sparse approximation is proposed, which affects the global recovery of underlying image. Ideally the adaptive window selection yields the minimum mean square error (MMSE) in a recovered image. This framework gives us a clustered image based on the selected window size, each cluster is then inpainted separately using sparse approximation. The results obtained using the proposed framework are comparable with the recently proposed inpainting techniques based on sparse representation.

Recovery of correlated sparse signals using adaptive backtracking matching pursuit

In distributed compressive sensing, if one signal in a joint-sparse signal ensemble is known apriori, the remaining signals can be reconstructed using modified Compressive Sensing (CS) algorithms such as Modified Basis Pursuit (Mod-BP) which makes use of Partially Known Support (PKS). Though Mod-BP reconstructs the joint-sparse signals with high accuracy, it takes a huge amount of time to converge. This might not be desirable in some practical applications like CS reconstruction of video frames. Carrillo et al have illustrated the use of PKS in iterative greedy algorithms to improve the recovery performance at a much shorter time. However, PKS based iterative greedy algorithms are totally blind about the wrong atoms present in the PKS, which is likely for video frames. To overcome this, we propose Adaptive Backtracking Matching Pursuit (AdBMP) which makes effective use of the PKS to reconstruct the sparse signal. Experimental results show that AdBMP gives a better reconstruction accuracy compared to that of the existing PKS based iterative greedy algorithms.