Structured Signal Recovery

The problem of structured signal recovery is one of the cornerstones of signal processing in the twenty-first century, bringing forth the exciting field of Compressed Sensing (CS). The fundamental idea of CS is that unknown vector recovery from a set of linear measurements becomes fairly easy if some structure of the unknown vector is known. With this principle in mind, my quest has led me to design and analyze several novel algorithms which can efficiently recover a structured signal from a few of its linear measurements. Following are some of the questions I have addressed positively in my research:

• Can a low complexity greedy algorithm with efficient recovery be proposed and analyzed for sparse recovery with correlated measurement matrices?

• Why does the algorithm Orthogonal Least Squares (OLS) can recover well with correlated measurement matrices, while Orthogonal Matching Pursuit (OMP) fails miserably?

• How to recover the support of block structured vectors with variable block sizes and unknown block boundaries?

• Can an algorithm for CS be further accelerated with extra side information about the unknown vector?

• How to extend an algorithm for CS for distributed recovery in diffusion networks. Can such implementation be communication efficient?

• Is there a unified theory for performance analysis of a class of non-convex optimization problems called J-minimization, for sparse recovery in CS?

Related Publications

Compressed Sensing with Correlated Measurement Matrices

• S. Mukhopadhyay, S. Satpathi, and M. Chakraborty, "A Modified Multiple OLS (m2OLS) Algorithm for Signal Recovery in Compressive Sensing", Signal Processing, Elsevier, vol 168, no. 107337, March 2020.

• S. Mukhopadhyay, S. Satpathi, and M. Chakraborty, "A Low Complexity Orthogonal Least Squares Algorithm for Sparse Signal Recovery", 2018 International Conference on Signal Processing and Communications (SPCOM), July 2018, Bangalore, India, pp. 75-79.

• P. Vashishtha, S. Mukhopadhyay, and M. Chakraborty, "Signal Recovery in Uncorrelated and Correlated Dictionaries Using Orthogonal Least Squares", [arXiv preprint]

Compressed Sensing for Generalized Block Sparse Vector Recovery

• S. Mukhopadhyay, and M. Chakraborty, "A Two Stage Generalized Block Orthogonal Matching Pursuit (TSGBOMP) Algorithm", IEEE Transactions on Signal Processing, doi:10.1109/TSP.2021.3114977 .

Distributed and Communication-Efficient Compressed Sensing

• S. Mukhopadhyay, and M. Chakraborty, "Deterministic and Randomized Diffusion based Iterative Generalized Hard Thresholding (DiFIGHT) for Distributed Sparse Signal Recovery", IEEE Transactions on Information and Signal Processing over Networks, doi:10.1109/TSIPN.2021.3124362 .

Accelerated Greedy Algorithm for Compressed Sensing With Partial Signal Information

• S. Mukhopadhyay, and M. Chakraborty, "Regularized Hard Thresholding Pursuit (RHTP) for Sparse Signal Recovery", 2020 International Conference on Signal Processing and Communications (SPCOM), July 2020, Bangalore, India, pp. 1-5.

• S. Mukhopadhyay, and M. Chakraborty, "Modified Hard Thresholding Pursuit with Regularization Assisted Support Identification", [arXiv preprint]

A Theory of Sparse Recovery for Compressed Sensing by Solving the General Nonconvex J-minimization

• S. Mukhopadhyay, "Sparse Recovery Analysis of Generalized J-Minimization with Results for Sparsity Promoting Functions with Monotonic Elasticity", Signal Processing, Elsevier, vol 180, No. 107853, March, 2021.