MNDL Sparsity Order Selection for Compressed Sensing with Application in ECG Compression.

Abstract

One of the main challenges in sparse signal recovery in compressed sensing framework is determining the sparsity order. Most model order selection methods introduce a penalty term for the number of parameters, however do not consider the variance of the observation and measurement noise. Minimum Noiseless Description Length (MNDL), on the other hand, considers these factors and provides a more robust results in order selection. Nevertheless, it requires noise variance (equivalently SNR) estimate for the order selection procedure. In this paper, a new method is introduced to estimate the variance of the observation noise within the MNDL order selection method. The fully automated method simultaneously provides the SNR estimate and sparsity order and does not require any prior partial knowledge or assumption on the noise variance. Simulation results for ECG compression show advantages of the proposed automated MNDL over the existing approaches in the sense of parameter estimation error and SNR improvement.