MagneticResonanceImaging(MRI)iswidelyusedinmedicaldiagnosticswithamajor limitation of long scan time. Long scan time makes MRI examinations vulnerable to patientmotion. Researchershaveproposeddifferentalgorithmstoreducethescantime. ParallelMagneticResonanceImaging(pMRI)andCompressedSensing(CS)havebeen recently used to accelerate data acquisition process in MRI. The advancements in MRI acquisition techniques come with a limitation of thousands of more computations than conventional reconstruction algorithms. The aim of this thesis is to investigate and propose reconstruction techniques which would be useful for fast reconstruction of undersampled data. Sensitivity Encoding (SENSE) is a reconstruction algorithm in pMRI to remove aliasing artefacts from the undersampled multi coil data and recovers fully sampled images. ThemainlimitationofSENSEiscomputinginverseoftheencodingmatrix. Thisthesis proposed to use Jacobi SVD algorithm for the inversion of encoding matrix. Further it is proposed to use Jacobi SVD algorithm on Graphics Processing Units (GPUs) to accelerate the reconstruction process. The performance of Jacobi SVD is compared with Gauss-Jordanalgorithm. TheresultsshowthatJacobiSVDalgorithmperformsbetterin terms of acceleration on GPUs as compared to Gauss-Jordan method. The proposed algorithm is suitable for any number of receiver coils and acceleration factors for SENSE reconstruction. The use of Jacobi SVD algorithm is also proposed in advance MRI reconstruction algorithms including GeneRalized Autocalibrating Partially Parallel Acquisitions (GRAPPA) and L+S reconstruction. The results show that the Jacobi SVD algorithm successfully reconstructs the images in GRAPPA and L+S algorithms. The benefitofusingJacobiSVDalgorithmforMRimagereconstructionisitssuitabilityfor parallel computation on GPUs, which will be a great help in reducing the image reconstruction time. x OptimizedImplementationof MR ImageReconstruction Algorithms Dynamic Contrast Enhanced (DCE) MRI plays an important role to diagnose cardiac diseases as it can be used to monitor the structure of heart and blood flowing through thevalves. L+SreconstructionusingIterativeSoftThresholding(IST)providesamechanism for the separation of heart structure (low-rank component, L) and blood flow in the heart (sparse component, S). This work proposes the use of Separable Surrogate Functional(SSF)methodaspartofL+Sreconstructionfortheseparationofheartstructure and blood flowing through the valves. The results show that the SSF algorithm provides better reconstruction results as compared to conventionally used Iterative Soft Thresholding (IST) and Projection onto Convex Sets (POCS). The results show that the proposed method also provides true separation of the heart structure in the form of low-rank component and the blood flow information in the sparse component. It is also shown that GPUs can be used to accelerate the reconstruction process of L+S decomposition model. The level of improvement in the reconstruction time gained by GPUs allows cardiovascular dataset to be reconstructed within clinically viable time. ImagingprocessinMRIisacceleratedbyacquiringlessdataandthenofflinereconstruction algorithms are applied to reconstruct fully sampled data for analysis. The offline reconstruction requires the acquired data to be transmitted to a processor which may introduce noise in the acquired signals. This thesis presents an Application Specific Integrated Circuit (ASIC) layout of SENSE algorithm which can reconstruct MR images from the acquired undersampled MRI data within the signal processing chain of MRI scanner. The proposed ASIC can be used for image reconstruction right on the scanner which can be very useful for MR image reconstruction especially in portable MRI scanners.