Multiscale entropy based compressive sensing for electrocardiogram signal compression

Classically, signal information is believed to be retrieved, if it is sampled at Nyquist rate. Since last decade compressive sensing is evolving which shows the signal reconstruction ability from insufficient data points. It reconstructs the signal from a set of reduced number of sparse samples that is lesser than Nyquist rate. It is required that the signal should be sparse in some basis. In wavelet domain, electrocardiogram signal shows sparseness. This paper suggests applying compressive sensing at wavelet scales. Also, the number of measurements taken at wavelet scales plays important role for successful reconstruction and to capture the maximum diagnostic information of electrocardiogram signal. At wavelet scales, the numbers of measurements are taken based on multiscale entropy. At scales, it uses random sensing matrix with independent identically distributed (i.i.d.) entries formed by sampling a Gaussian distribution. The compressed measurements are encoded using Huffman coding scheme. The reconstruction of signal is achieved by convex optimization problem by L1-norm minimization. Reconstruction error introduced due to L1-norm minimization and coding is evaluated using percentage root mean square difference (PRD), wavelet energy based diagnostic distortion (WEDD), root mean square error (RMSE), normalized maximum amplitude error (NMAX) and maximum absolute error (MAE). The highest compression ratio value is found 6.92:1 with PRD and WEDD values 8.18% and 2.33% respectively.