Magnetic Resonance Imaging is a painless procedure to produce high-resolution diagnostic images. Today, it is one of the essential clinical imaging modalities. One of the major challenges involved with this imaging modality is its long scanning time. Parallel imaging in combination with compressed sensing has overcome this challenge to a great extent. As a quid pro quo for this reduced scan time is the increase in image reconstruction time. An extensive research is focused to develop algorithms to make the image reconstruction faster. Fast Iterative Shrinkage Threshold algorithm is one of these algorithms (which is clinically viable) that speeds up the image reconstruction process. The present project focuses to speed up the particular algorithm, fast iterative shrinkage threshold algorithm, by preconditioning the convex optimization problem. This work proposes two new preconditioners, specifically in the context of the given algorithm, but otherwise can be used with different frameworks solving similar problems. The first preconditioner is a degree one polynomial of the system matrix and the second preconditioner is a block diagonal matrix where each block is a circulant matrix. The preconditioners are evaluated using two stopping criteria: residual error and relative error. The computation complexity of both the preconditioners are evaluated by measuring the floating point operations and total time consumption. Additionally, the simulations are performed by undersampling the data at two factors r=2 and r=4. The results indicate that the polynomial preconditioner reduces the overall time by a factor of 0.25 however is computationally expensive to construct. On the other side, block diagonal circulant preconditioner is extremely cheap to construct and evaluate on a vector but does not provide the desired results within the current framework. The study concludes that a suitable preconditioner for FISTA is the one that without affecting the largest eigenvalue of the system matrix improves the condition number and simultaneously is cheap to construct and evaluate.