Incoherence

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.