De-Noising of Sparse Signals Using Mixture Model Shrinkage Function

Abstract

In this work a new thresholding function referred to as ’mixture model shrinkage’ (MMS) based on the minimization of a convex cost function is proposed. Normally, thresholding functions underestimate<br/>larger signal amplitudes during the de-noising process. The proposed model is a more flexible shrinkage function as it solves the underestimation problem to a greater extent and thus efficiently de-noises the signal<br/>without affecting signal amplitudes. The Expectation minimization (EM) algorithm is used to find the model parameters along with the majorization-minimization (MM) algorithm that minimize the monotonic cost<br/>function. The proposed model is then applied for de-noising group sparse signals and Shepp Logan phantom images. Our experimental study shows that MMS outclasses current thresholding functions and overlapping<br/>group shrinkage algorithm without results suffering from underestimation. Furthermore, the proposed model has the smallest Root Mean Square Error (RMSE) for de-noising group sparse signals.<br/>