A Noise Reduced Hard Thresholding method for Noisy Sparse Reconstruction

Abstract

The problem of noisy sparse signal recovery has been studied in this paper. The generalized expectation maximization (GEM) algorithm provides solutions over state of the art convex relaxation methods for sparse signal recovery by considering the noisy measurements as missing data. However, in the case of images, artifacts in the reconstructed signal renders it to have low quality, especially based on qualitative performance metrics and so are unsuitable for further application specific processing. The problem may be reduced significantly by minimizing the total variation in the signal considering the constraints created by the statistics of noise in the reconstructed image. A modified iterative GEM for low noise reconstruction is presented and analyzed. Even though time consuming, simulations and numerical analysis show significantly higher performance metrics, especially PSNR and Structural Similarity, which imply reconstructed images may be suitable for further processing.