With the introduction of compressed sensing and sparse representation,many image processing and computer vision problems have been looked at in a new way. Recent trends indicate that many challenging computer vision and image processing problems are being solved using compressive sensing and sparse representation algorithms. This thesis assays some applications of compressive sensing and sparse representation with regards to image enhancement, restoration and classication. The first application deals with image Super-Resolution through compressive sensing based sparse representation. A novel framework is developed for understanding and analyzing some of the implications of compressive sensing in reconstruction and recovery of an image through raw-sampled and trained dictionaries. Properties of the projection operator and the dictionary are examined and the corresponding results presented. In the second application a novel technique for representing image classes uniquely in a high-dimensional space for image classification is presented. In this method, design and implementation strategy of the image classification system through unique affine sparse codes is presented, which leads to state of the art results. This further leads to analysis of some of the properties attributed to these unique sparse codes. In addition to obtaining these codes, a strong classier is designed and implemented to boost the results obtained. Evaluation with publicly available datasets shows that the proposed method outperforms other state of the art results in image classication. The final part of the thesis deals with image denoising with a novel approach towards obtaining high quality denoised image patches using only a single image. A new technique is proposed to obtain highly correlated image patches through sparse representation, which are then subjected to matrix completion to obtain high quality image patches. Experiments suggest that there may exist a structure within a noisy image which can be exploited for denoising through a low-rank constraint.