Increasing the quality of reconstructed signal in compressive sensing utilizing Kronecker technique

Zanddizari, H; Rajan, S; Zarrabi, Houman

Abstract

Quality of reconstruction of signals sampled using compressive sensing (CS) algorithm depends on the compression factor and the length of the measurement. A simple method to pre-process data before reconstruction of compressively sampled signals using Kronecker technique that improves the quality of recovery is proposed. This technique reduces the mutual coherence between the projection matrix and the sparsifying basis, leading to improved reconstruction of the compressed signal. This pre-processing method changes the dimension of the sensing matrix via the Kronecker product and sparsity basis accordingly. A theoretical proof for decrease in mutual coherence using the proposed technique is also presented. The decrease of mutual coherence has been tested with different projection matrices and the proposed recovery technique has been tested on an ECG signal from MIT Arrhythmia database. Traditional CS recovery algorithms has been applied with and without the proposed technique on the ECG signal to demonstrate increase in quality of reconstruction technique using the new recovery technique. In order to reduce the computational burden for devices with limited capabilities, sensing is carried out with limited samples to obtain a measurement vector. As recovery is generally outsourced, limitations due to computations do not exist and recovery can be done using multiple measurement vectors, thereby increasing the dimension of the projection matrix via the Kronecker product. The proposed technique can be used with any CS recovery algorithm and be regarded as simple pre-processing technique during reconstruction process.