Single-image super-resolution using sparsity constraints and non-local similarities at multiple resolution scales

Traditional super-resolution methods produce a clean high-resolution image from several observed degraded low-resolution images following an acquisition or degradation model. Such a model describes how each output pixel is related to one or more input pixels and it is called data fidelity term in the regularization framework. Additionally, prior knowledge such as piecewise smoothness can be incorporated to improve the image restoration result. The impact of an observed pixel on the restored pixels is thus local according to the degradation model and the prior knowledge. Therefore, the traditional methods only exploit the spatial redundancy in a local neighborhood and are therefore referred to as local methods. Recently, non-local methods, which make use of similarities between image patches across the whole image, have gained popularity in image restoration in general. In super-resolution literature they are often referred to as exemplar-based methods. In this paper, we exploit the similarity of patches within the same scale (which is related to the class of non-local methods) and across different resolution scales of the same image (which is also related to the fractal-based methods). For patch fusion, we employ a kernel regression algorithm, which yields a blurry and noisy version of the desired high-resolution image. For the final reconstruction step, we develop a novel restoration algorithm. The joint deconvolution/denoising algorithm is based on the split Bregman iterations and, as prior knowledge, the algorithm exploits the sparsity of the image in the shearlet-transformed domain. Initial results indicate an improvement over both classical local and state-of-the art non-local super-resolution methods