Magnetic Resonance Imaging (MRI) is a non-invasive and non-ionizing medical imaging technique that provides essential clinical information about both the anatomy and physiology of the human body. One of the major limitations of MRI is long scan time. The reduction in scan time is vital for many MRI applications. There are two different stages in MRI scanning process and multiple strategies can be applied to reduce the overall scan time: (i) MRI data acquisition time and (ii) processing the acquired data to reconstruct artifact free high-resolution image (reconstruction time). This thesis mainly focusesonthesecondparti.e. toreducethescantimeofMRI.ThefirstphaseofthisthesispresentsanovelimplementationofGPUbasedSENSEalgorithm(apMRImethod), that employs QR decomposition for the inversion of the rectangular encoding matrix. For a fair comparison, the performance of the proposed GPU based SENSE reconstructionisevaluatedagainstsingleandmulti-coreCPUusingOpenMP.Severalexperiments against various Acceleration Factors (AFs) are performed using multichannel phantom, in-vivo human head and cardiac datasets. Experimental results show that the proposed GPU implementation significantly reduces the computation time of SENSE reconstructionascomparedtomulti-coreCPUwithoutanydegradationinthequalityofthereconstructed images. In the second phase, an iterative sequential combination of Linear Conjugate Gradient (LCG) based pMRI algorithm with p-thresholding based CS algorithm for MR image reconstruction is proposed to reconstruct images from a highly under-sampled data. Theproposedmethod(CGSENSE-CS)exploitsthecomplementarycharacteristics of CGSENSE (making reconstruction algorithm faster and accurate) and CS (efficient method in removing noise) to improve the reconstruction results. The proposed method is compared with contemporary methods CG-SENSE and `1-SPIR-iT, using Phantom and in-vivo human head datasets. Experimental results show that CGSENSE-CS (proposed method) achieves better Artifact Power (AP), Root Mean Square Error (RMSE) and high Peak Signal-to-Noise Ratio (PSNR). Second major limitation of the current MRI technology is that it detects and diagnoses abnormalities in the patient’s body based on the contrast between different tissues. Absolute measurements from a single tissue have proven extremely valuable for the diagnosis, prognosis, and therapeutic assessment. The lack of quantification in current MRI limits an objective evaluation, leads to a variability in interpretation, and potentially limits the utility of the technology in some clinical scenarios. However, Magnetic Resonance Fingerprinting (MRF), a latest innovation in MRI, can quantitatively examine many magnetic resonance tissue parameters, simultaneously. MRF algorithm in current form is highly computation and memory intensive because it inherently requires all the possible combinations of tissue parameters and inner product is computed between the observedsignalandeverysinglecombinationofthetissueparameters. Inthethirdphase ofthisPhDthesis,MRFalgorithmisacceleratedbyproposingaparallelframeworkand implementing it on a parallel architecture.