Compressive Sensing or Compressed sensing (CS) is a latest technique used for compression of medical signals and medical images which benefits both the speed and accuracy. The performance of CS based compression is mostly dependent on decoding methods rather than the CS encoding methods used in practice. It has been found in literature that CS encoding algorithms have got least importance than decoding algorithms. In this paper an efficient CS encoding scheme based on modified parallel block processing has been suggested for biomedical signal and image compression. The input signals and images are acquired and preprocessed with suitable filtering techniques and then the same have been divided into number of cells and blocks. Each block is then processed in parallel to enable faster computation. Three performance indices, i.e., the peak signal to noise ratio (PSNR), reconstruction time (RT) and structural similarity index (SSIM) have been analyzed with respect to the compression ratio. A comparative study has been carried out between the standard CS based compression and the suggested technique. The results showed that proposed algorithm provides better performance than standard CS based compression. More specifically, the parallel block CS reported the best results than standard CS with respect to less reconstruction time and satisfactory PSNR and SSIM. The suggested technique offers SSIM improvement approximately by 8% and reduction in RT by 99% than the standard CS based compression for CT scan image compression. In case of brain signal compression, the suggested technique offers SSIM improvement approximately by 25%, PSNR improvement by around 2% and reduction in RT by 75% than the standard CS.