37 citations · 48 across the 15 of their papers we have counts for
9 papers · 1 filter
Convergence of Stochastic Approximation via Martingale and Converse Lyapunov Methods
M. Vidyasagar
In this paper, we study the almost sure boundedness and the convergence of the stochastic approximation (SA) algorithm. At present, most available convergence proofs are based on t…
New and Explicit Constructions of Unbalanced Ramanujan Bipartite Graphs
Shantanu Prasad Burnwal, Kaneenika Sinha, Mathukumalli Vidyasagar
The objectives of this article are three-fold. Firstly, we present for the first time explicit constructions of an infinite family of \textit{unbalanced} Ramanujan bigraphs. Second…
Deterministic Completion of Rectangular Matrices Using Asymmetric Ramanujan Graphs: Exact and Stable Recovery
Shantanu Prasad Burnwal, Mathukumalli Vidyasagar
In this paper we study the matrix completion problem: Suppose is unknown except for a known upper bound on its rank. By measuring a small n…
Compressed Sensing Using Binary Matrices of Nearly Optimal Dimensions
Mahsa Lotfi, Mathukumalli Vidyasagar
In this paper, we study the problem of compressed sensing using binary measurement matrices and -norm minimization (basis pursuit) as the recovery algorithm. We derive new…
An Approach to One-Bit Compressed Sensing Based on Probably Approximately Correct Learning Theory
Mehmet Eren Ahsen, Mathukumalli Vidyasagar
In this paper, the problem of one-bit compressed sensing (OBCS) is formulated as a problem in probably approximately correct (PAC) learning. It is shown that the Vapnik-Chervonenki…
Tight Performance Bounds for Compressed Sensing With Conventional and Group Sparsity
Shashank Ranjan, Mathukumalli Vidyasagar
In this paper, we study the problem of recovering a group sparse vector from a small number of linear measurements. In the past the common approach has been to use various "group s…
Error Bounds for Compressed Sensing Algorithms With Group Sparsity: A Unified Approach
M. Eren Ahsen, M. Vidyasagar
In compressed sensing, in order to recover a sparse or nearly sparse vector from possibly noisy measurements, the most popular approach is -norm minimization. Upper bounds…
Two New Approaches to Compressed Sensing Exhibiting Both Robust Sparse Recovery and the Grouping Effect
Mehmet Eren Ahsen, Niharika Challapalli, Mathukumalli Vidyasagar
In this paper we introduce a new optimization formulation for sparse regression and compressed sensing, called CLOT (Combined L-One and Two), wherein the regularizer is a convex co…
Near-Ideal Behavior of Compressed Sensing Algorithms
Mehmet Eren Ahsen, Mathukumalli Vidyasagar
In a recent paper, it is shown that the LASSO algorithm exhibits "near-ideal behavior," in the following sense: Suppose where satisfies the restricted isometry pro…