Increasing the Quality of Reconstructed Signal in Compressive Sensing Utilizing Kronecker Technique

Quality of reconstruction of signals sampled using compressive sensing (CS) algorithmdepends on the compression factor and the length of the measurement.A simple method to pre-process data before reconstruction of compressively sampled signals using Kroneckertechnique that  improves  thequality  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.Thispre-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  burdenfor  devices  with  limited  capabilities,sensing  is carried  out withlimited  samples  to obtain a measurement vector. As recovery is generally outsourced,limitations due to computations do not exist and recovery can bedone using multiple measurement vectors, thereby increasing the dimension of the projection matrix via the Kronecker product.The proposedtechnique can be used with any CS recovery algorithmand be regarded as simple pre-processing technique during reconstruction process