Block Compressive sensing technique has been proposed to exploit the sparse nature of medical images in a transform domain to reduce the storage space. Block based compressive sensing is applied to dicom image, where original dicom image is divided in terms of blocks and each block is processed separately. The main advantage of block compressive sensing is that each block is processed independently and combined with parallel processing to reduce the amount of time required for processing. Compressed sensing exploits the sparse nature of images to reduce the volume of the data required for storage purpose. Inspired by this, we propose a new algorithm for image compression that combines compressed sensing with different transforms. Different sparse basis like discrete cosine transform, discrete wavelet transform and contourlet are used to compress the original input image. Among these transforms, Dct transform has block artifacts problem [14]. Wavelet transform can overcome the block artifacts introduced in the reconstructed image. Contourlet transform effectively captures smooth contours[4] and hence Contourlet transform provides better reconstruction quality image. In order to reconstruct original image, different techniques such as basis pursuit, orthogonal matching pursuit etc. are used at the decoder.