Signal Recovery From Missing Data

For any signal recovery algorithm, the access to error-free data is always desirable. However, owing to several limitations in either the channel for communicating the data , or due to insufficient storage facility, or maybe due to insufficient speed in data processing , signal processing algorithms are often presented with the challenge to recover a vector with measurement data whose entries are randomly missed, i.e., assigned to 0. Typically this is a signal recovery problem with multiplicative noise, and is inherently non-convex and therefore, challenging. Explorations in this field have led me to investigate the following questions:

• How to design an efficient adaptive filtering algorithm when input data is missed at random instances?

• How to accelerate the naive Stochastic Gradient Descent (SGD) for signal recovery from linear measurements when the matrix entries are randomly missed? Is there a way to achieve as good performance as SGD without any missing data phenomenon?

• What is the best we one can do when we try to estimate the l_2 norm of a random Gaussian vector from its measurements obtained after a random data missing of some of the entries of the vector, followed by addition of a additive white gaussian noise (AWGN)?

Related Publications

Adaptive Filtering With Randomly Missing Input Data

1. S. Mukhopadhyay and A. Mukherjee, "ImdLMS: An Imputation Based LMS Algorithm for Linear System Identification With Missing Input Data", IEEE Transactions on Signal Processing, vol 68, issue 1, December 2020, pp 2370-2385.

Stochastic Gradient Descent With Sequential Matrix Entry Accumulation for Missing Matrix Entries

1. S. Mukhopadhyay, "Stochastic gradient descent for linear systems with sequential matrix entry accumulation", Signal Processing, Elsevier, vol 171, No. 107494, June 2020.

Norm Estimation of A Random Gaussian Vector With Missing Entries and AWGN Measurement Noise

• S. Mukhopadhyay, "On the MMSE Estimation of Norm of a Gaussian Vector under Additive White Gaussian Noise with Randomly Missing Input Entries", Signal Processing, Elsevier, vol 179, No. 107848, February, 2021.