Magnetic resonance imaging (MRI) is a widely employed imaging modality that allows observation of the interior of human body. Compared to other imaging modalities such as the computed tomography (CT), MRI features a relatively long scan time that gives rise to many potential issues. The advent of parallel MRI, which employs multiple receiver coils, has started a new era in speeding up the scan of MRI by reducing the number of data acquisitions. However, the finally recovered images from under-sampled data sets often suffer degraded image quality. This thesis explores methods that incorporate prior knowledge of the image to be reconstructed to achieve improved image recovery in parallel MRI, following the philosophy that ‘if some prior knowledge of the image to be recovered is known, the image could be recovered better than without’. Specifically, the prior knowledge of image sparsity is utilized. Image sparsity exists in different domains. Image sparsity in the image domain refers to the fact that the imaged object only occupies a portion of the imaging field of view; image sparsity may also exist in a transform domain for which there is a high level of energy concentration in the image transform. The use of both types of sparsity is considered in this thesis. There are three major contributions in this thesis. The first contribution is the development of ‘GUISE’. GUISE employs an adaptive sampling design method that achieves better exploitation of image domain sparsity in parallel MRI. Secondly, the development of ‘PBCS’ and ‘SENSECS’. PBCS achieves better exploitation of transform domain sparsity by incorporating a prior estimate of the image to be recovered. SENSECS is an application of PBCS that achieves better exploitation of transform domain sparsity in parallel MRI. The third contribution is the implementation of GUISE and PBCS in contrast enhanced MR angiography (CE MRA). In their applications in CE MRA, GUISE and PBCS share the common ground of exploiting the high sparsity of the contrast enhanced angiogram. The above developments are assessed in various ways using both simulated and experimental data. The potential extensions of these methods are also suggested.