Convex optimization based undersampled MRI recovery using method of multipliers

This paper analyses recovery of damaged or under sampled MRI (Magnetic Resonance Imaging) through alternating direction method of multipliers (ADMM) using different sparsity basis. The Discrete Cosine Transform (DCT) and Discrete Wavelet Transform (DWT) are tested. MRI is of great importance for medical diagnostics and must have a proper quality. It is a time consuming process to gain a good quality image. In order to reduce time needed for MRI acquisition, compressive sensing (CS) allows time reduction with little visible impact on image quality. This is done using mathematical algorithms and theoretical background which states that an image can be reconstructed using just a small set of randomly acquired samples. Image can be damaged in various procedures and CS can be used for repairing and reconstructing damaged parts. Reconstruction quality is measured with PSNR (Peak Signal-To-Noise Ratio).