Comparison of different sparse dictionaries for compressive sampling

Compressive sampling/compressed sensing (CS) is building on the observation that most of the signals in nature are sparse or compressible concerning some transform domain. And by converse, the same can be reconstructed with high accuracy by making use of far fewer samples than what is required by violating Shannon-Nyquist theorem. Some of the transform techniques are discrete cosine transform, fast fourier transforms discrete wavelet transform, discrete fourier transforms. In this paper, novel CS techniques are FFTCoSAMP, DCTCoSaMP, and DWTCoSaMP are introduced and compared on different sparse transforms for CS in magnetic resonance (MR) images based on sparse signal sequences/dictionaries by means of transform techniques with respect to objective quality assessment algorithms like PSNR, SSIM and RMSE, where CoSaMP stands for compressive sampling matching pursuit. DWTCoSaMP is giving the PSNR values of 37.16 (DB4), 38.12 (Coif3), 38.5 (Sym8), for DCTCoSaMP and FFTCoSaMP, it’s 36.33 and 36.01 respectively. For DWTCoSaMP, SSIM value is 0.81, and for DCTCoSaMP and FFTCoSaMP, it’s 0.73 and 0.7 respectively. And finally, for DWTCoSaMP, RMSE value is 0.66, and for DCTCoSaMP and FFTCoSaMP, it’s 0.53 and 0.41 respectively. DWTCoSaMP reveals the best than rest of the methods and traditional CS techniques by the detailed comparison and analysis.