Extension of Sparse Randomized Kaczmarz Algorithm for Multiple Measurement Vectors

The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the Kaczmarz algorithm was shown to converge exponentially and independent of number of equations. Recently an algorithm for finding sparse solution to a linear system of equations has been proposed based on weighted randomized Kaczmarz algorithm. These algorithms solves single measurement vector problem; however there are applications were multiple-measurements are available. In this work, the objective is to solve a multiple measurement vector problem with common sparse support by modifying the randomized Kaczmarz algorithm. We have also modeled the problem of face recognition from video as the multiple measurement vector problem and solved using our proposed technique. We have compared the proposed algorithm with state-of-art spectral projected gradient algorithm for multiple measurement vectors on both real and synthetic datasets. The Monte Carlo simulations confirms that our proposed algorithm have better recovery and convergence rate than the MMV version of spectral projected gradient algorithm under fairness constraints

Vitamin D and COVID-19

The ongoing COVID -19 pandemic is caused by severe acute respiratory syndrome corona virus -2 (SARS-CoV-2). Since its emergence in Wuhan in Hubei province of China in December 2019, the virus has spread to every continent except Antartica. Currently, there is no registered treatment or vaccine for the disease. In the current scenario of the deadly virus spreading across continents and the absence of a specific treatment of novel corona virus, there is an urgent need to search for alternative strategies to prevent and control the rapid replication of virus. Vitamin D supplementation may reduce the incidence, severity and risk of death from pneumonia (consequent to the cytokine storm) in the current COVID pandemic. Through its effect on innate and adaptive immunity, vitamin D can reduce the risk of viral respiratory tract infections. 1, 25(OH) vitamin D directly stimulates the production of anti-microbial peptides like defensin and Cathelicidin that can reduce the rate of viral replication. In addition, it can also reduce the concentration of pro-inflammatory cytokines that are responsible for causing cytokine storm and resultant fatal pneumonia. In order to reduce the risk of infection especially in developing country like India, it is recommended that people at risk of COVDI19 may be considered for vitamin D supplementation

ENSURE: A General Approach for Unsupervised Training of Deep Image Reconstruction Algorithms

Image reconstruction using deep learning algorithms offers improved reconstruction quality and lower reconstruction time than classical compressed sensing and model-based algorithms. Unfortunately, clean and fully sampled ground-truth data to train the deep networks is often not available in several applications, restricting the applicability of the above methods. This work introduces the ENsemble Stein's Unbiased Risk Estimate (ENSURE) framework as a general approach to train deep image reconstruction algorithms without fully sampled and noise-free images. The proposed framework is the generalization of the classical SURE and GSURE formulation to the setting where the images are sampled by different measurement operators, chosen randomly from a set. We show that the ENSURE loss function, which only uses the measurement data, is an unbiased estimate for the true mean-square error. Our experiments show that the networks trained with this loss function can offer reconstructions comparable to the supervised setting. While we demonstrate this framework in the context of MR image recovery, the ENSURE framework is generally applicable to arbitrary inverse problems