Mrityunjoy Chakraborty

Anit Kumar Sahu, Mrityunjoy Chakraborty

Frequency Estimation of a complex exponential is a problem relevant to a large number of fields. In this paper a computationally efficient and accurate frequency estimator is presented using the guaranteed stable Sliding DFT which gives stability as well as computational efficiency. The estimator approaches Jacobsen's estimator and Candan's estimator for large N with an extra correction term multiplied to it for the stabilization of the sliding DFT. Simulation results show that the performance of the proposed estimator were found to be better than Jacobsen's estimator and Candan's estimator.

Aleksandar Armacki, Himkant Sharma, Dragana Bajović et al.

We study the effects of center initialization on the performance of a family of distributed gradient-based clustering algorithms introduced in [1], that work over connected networks of users. In the considered scenario, each user contains a local dataset and communicates only with its immediate neighbours, with the aim of finding a global clustering of the joint data. We perform extensive numerical experiments, evaluating the effects of center initialization on the performance of our family of methods, demonstrating that our methods are more resilient to the effects of initialization, compared to centralized gradient clustering [2]. Next, inspired by the $K$-means++ initialization [3], we propose a novel distributed center initialization scheme, which is shown to improve the performance of our methods, compared to the baseline random initialization.

Samrat Mukhopadhyay, Mrityunjoy Chakraborty

In this paper we propose a distributed iterated hard thresholding algorithm termed DiFIGHT over a network that is built on the diffusion mechanism and also propose a modification of the proposed algorithm, termed MoDiFIGHT, that has low complexity in terms of communication in the network. We additionally propose four different strategies termed RP, RNP, RGP$_r$, and RGNP$_r$ that are used to randomly select a subset of nodes that are subsequently activated to take part in the distributed algorithm, so as to reduce the mean number of communications during the run of the distributed algorithm. We present theoretical estimates of the long run communication per unit time for these different strategies, when used by the two proposed algorithms. Also, we present analysis of the two proposed algorithms and provide provable bounds on their recovery performance with or without using the random node selection strategies. Finally we use numerical studies to show that both when the random strategies are used as well as when they are not used, the proposed algorithms display performances far superior to distributed IHT algorithm using consensus mechanism .

Samrat Mukhopadhyay, Mrityunjoy Chakraborty

Recovery of an unknown sparse signal from a few of its projections is the key objective of compressed sensing. Often one comes across signals that are not ordinarily sparse but are sparse blockwise. Existing block sparse recovery algorithms like BOMP make the assumption of uniform block size and known block boundaries, which are, however, not very practical in many applications. This paper addresses this problem and proposes a two step procedure, where the first stage is a coarse block location identification stage while the second stage carries out finer localization of a non-zero cluster within the window selected in the first stage. A detailed convergence analysis of the proposed algorithm is carried out by first defining the so-called pseudoblock-interleaved block RIP of the given generalized block sparse signal and then imposing upper bounds on the corresponding RIC. We also extend the analysis for complex vector as well as matrix entries where it turns out that the extension is non-trivial and requires special care. Furthermore, assuming real Gaussian sensing matrix entries, we find a lower bound on the probability that the derived recovery bounds are satisfied. The lower bound suggests that there are sets of parameters such that the derived bound is satisfied with high probability. Simulation results confirm significantly improved performance of the proposed algorithm as compared to BOMP.

Samrat Mukhopadhyay, Mrityunjoy Chakraborty

Hard thresholding pursuit (HTP) is a recently proposed iterative sparse recovery algorithm which is a result of combination of a support selection step from iterated hard thresholding (IHT) and an estimation step from the orthogonal matching pursuit (OMP). HTP has been seen to enjoy improved recovery guarantee along with enhanced speed of convergence. Much of the success of HTP can be attributed to its improved support selection capability due to the support selection step from IHT. In this paper, we propose a generalized HTP algorithm, called regularized HTP (RHTP), where the support selection step of HTP is replaced by a IHT-type support selection where the cost function is replaced by a regularized cost function, while the estimation step continues to use the least squares function. With decomposable regularizer, satisfying certain regularity conditions, the RHTP algorithm is shown to produce a sequence dynamically equivalent to a sequence evolving according to a HTP-like evolution, where the identification stage has a gradient premultiplied with a time-varying diagonal matrix. RHTP is also proven, both theoretically, and numerically, to enjoy faster convergence vis-a-vis HTP with both noiseless and noisy measurement vectors.

Bijit Kumar Das, Mrityunjoy Chakraborty

Recently, the l0-least mean square (l0-LMS) algorithm has been proposed to identify sparse linear systems by employing a sparsity-promoting continuous function as an approximation of l0 pseudonorm penalty. However, the performance of this algorithm is sensitive to the appropriate choice of the some parameter responsible for the zero-attracting intensity. The optimum choice for this parameter depends on the signal-to-noise ratio (SNR) prevailing in the system. Thus, it becomes difficult to fix a suitable value for this parameter, particularly in a situation where SNR fluctuates over time. In this work, we propose several adaptive combinations of differently parameterized l0-LMS to get an overall satisfactory performance independent of the SNR, and discuss some issues relevant to these combination structures. We also demonstrate an efficient partial update scheme which not only reduces the number of computations per iteration, but also achieves some interesting performance gain compared with the full update case. Then, we propose a new recursive least squares (RLS)-type rule to update the combining parameter more efficiently. Finally, we extend the combination of two filters to a combination of M number adaptive filters, which manifests further improvement for M > 2.

Bijit Kumar Das, Mrityunjoy Chakraborty

The sparsity-aware zero attractor least mean square (ZA-LMS) algorithm manifests much lower misadjustment in strongly sparse environment than its sparsity-agnostic counterpart, the least mean square (LMS), but is shown to perform worse than the LMS when sparsity of the impulse response decreases. The reweighted variant of the ZA-LMS, namely RZA-LMS shows robustness against this variation in sparsity, but at the price of increased computational complexity. The other variants such as the l 0 -LMS and the improved proportionate normalized LMS (IPNLMS), though perform satisfactorily, are also computationally intensive. The gradient comparator LMS (GC-LMS) is a practical solution of this trade-off when hardware constraint is to be considered. In this paper, we analyse the mean and the mean square convergence performance of the GC-LMS algorithm in detail. The analyses satisfactorily match with the simulation results.

Samrat Mukhopadhyay, Prateek Vashishtha and, Mrityunjoy Chakraborty

Though the method of least squares has been used for a long time in solving signal processing problems, in the recent field of sparse recovery from compressed measurements, this method has not been given much attention. In this paper we show that a method in the least squares family, known in the literature as Orthogonal Least Squares (OLS), adapted for compressed recovery problems, has competitive recovery performance and computation complexity, that makes it a suitable alternative to popular greedy methods like Orthogonal Matching Pursuit (OMP). We show that with a slight modification, OLS can exactly recover a $K$-sparse signal, embedded in an $N$ dimensional space ($K<<N$) in $M=\mathcal{O}(K\log (N/K))$ no of measurements with Gaussian dictionaries. We also show that OLS can be easily implemented in such a way that it requires $\mathcal{O}(KMN)$ no of floating point operations similar to that of OMP. In this paper performance of OLS is also studied with sensing matrices with correlated dictionary, in which algorithms like OMP does not exhibit good recovery performance. We study the recovery performance of OLS in a specific dictionary called \emph{generalized hybrid dictionary}, which is shown to be a correlated dictionary, and show numerically that OLS has is far superior to OMP in these kind of dictionaries in terms of recovery performance. Finally we provide analytical justifications that corroborate the findings in the numerical illustrations.

Vinay Chakravarthi Gogineni, Mrityunjoy Chakraborty

Distributed adaptive networks achieve better estimation performance by exploiting temporal and as well spatial diversity while consuming few resources. Recent works have studied the single task distributed estimation problem, in which the nodes estimate a single optimum parameter vector collaboratively. However, there are many important applications where the multiple vectors have to estimated simultaneously, in a collaborative manner. This paper presents multi-task diffusion strategies based on the Affine Projection Algorithm (APA), usage of APA makes the algorithm robust against the correlated input. The performance analysis of the proposed multi-task diffusion APA algorithm is studied in mean and mean square sense. And also a modified multi-task diffusion strategy is proposed that improves the performance in terms of convergence rate and steady state EMSE as well. Simulations are conducted to verify the analytical results.

Vinay Chakravarthi Gogineni, Mrityunjoy Chakraborty

Distributed multi-task adaptive strategies are useful to estimate multiple parameter vectors simultaneously in a collaborative manner. The existed distributed multi-task strategies use diffusion mode of cooperation in which during adaptation step each node gets the cooperation from it neighborhood nodes but not in the same cluster and during combining step each node combines the intermediate estimates of it neighboring nodes that belong to the same cluster. For this the nodes need to transmit the intermediate estimates to its neighborhood. In this paper we propose an extension to the multi-task diffusion affine projection algorithm by allowing partial sharing of the entries of the intermediate estimates among the neighbors. The proposed algorithm is termed as multi-task Partial diffusion Affine projection Algorithm (multi-task Pd-APA) which can provide the trade-off between the communication performance and the estimation performance. The performance analysis of the proposed multi-task partial diffusion APA algorithm is studied in mean and mean square sense. Simulations were conducted to verify the analytical results.

Bijit Kumar Das, Mrityunjoy Chakraborty, Jerónimo Arenas-García

In-network distributed estimation of sparse parameter vectors via diffusion LMS strategies has been studied and investigated in recent years. In all the existing works, some convex regularization approach has been used at each node of the network in order to achieve an overall network performance superior to that of the simple diffusion LMS, albeit at the cost of increased computational overhead. In this paper, we provide analytical as well as experimental results which show that the convex regularization can be selectively applied only to some chosen nodes keeping rest of the nodes sparsity agnostic, while still enjoying the same optimum behavior as can be realized by deploying the convex regularization at all the nodes. Due to the incorporation of unregularized learning at a subset of nodes, less computational cost is needed in the proposed approach. We also provide a guideline for selection of the sparsity aware nodes and a closed form expression for the optimum regularization parameter.