Application of Compressive Sensing for Sampling and Reconstruction of MRI Images

Abstract

In recent years, a new theory of compressive sensing has evolved which asserts that super resolved signals and images can be recovered with far fewer samples than that demanded by the Nyquist sampling theorem. It is required that the signal being sensed has a low information-rate meaning that it is sparse in original or some transform domain. Former approaches capture the complete signal and process it to extract the information. The new paradigm captures lesser number of non-adaptive linear measurements of the signal and exploits sophisticated algorithms to determine its information content. In this work, we apply the compressive sensing theory as a general purpose signal compression scheme. Transform coding is applied along with compressive sensing on MRI images. The final transform coefficients provide alternative representation of the original signal, which is less redundant and appropriate for compression. Reconstruction of the signal is a linear optimization process which studies the sparsity in the transform domain, governed by the fact that higher the sparsity, better the recovery. Performances are analyzed using performance parameters viz. peak signal to noise ratio (PSNR), root mean square error (RMSE) and CoC (Correlation Coefficient). These values are extensively computed by varying the compression ratio (CR). Comparison is made between wavelet transform and discrete cosine transform implementation