Matrix estimation using shrinkage of singular values with applications to signal denoising

Abstract

This thesis documents investigations on developing the better spectral shrinkage functions for matrix estimation It proposes two effective spectral shrinkage estimators The first estimator exploits the correlation present in the data matrix by decoupling the shrinkage and the truncation of singular values It employs a logistic function based shrinkage of singular values and shows better rank estimation than the existing methods The parameters of this estimator are tuned by grid search soluti