Reweighted compressive sensing for image signals

Compressive Sampling (CS) is an emerging theory which points us to a promising direction of designing novel efficient data compression techniques. However, due to the complex nature of the natural images signals, the indiscriminate sampling scheme of conventional Compressive Sensing cannot sufficiently capture the important information of image signals, and as a result, the performance of Compressive Sensing drops greatly. The conventional Compressive Sensing is based on the assumption that we do not have any prior knowledge about the target signal. Therefore, an incoherent sampling scheme is a reasonable choice. However, for image signals, the knowledge about its spectrum characteristics is accessible, which enables us to adjust the conventional Compressive Sensing framework to achieve better performance by taking advantage of the prior knowledge. Based on this observation, we propose two reweighted Compressive Sensing frameworks which introduce weighting schemes into the measurement process. We developed two approaches of designing the weighting matrix from the perspectives of the human eye perception and the image spectrum statistics respectively. By utilizing the proposed weighting scheme, we can adjust the behavior of the measurement process to capture more information from the important frequency components; furthermore, our proposed weighting scheme can also improve performance of the optimization process in the reconstruction stage. Experiment results indicate that both of the proposed weighting schemes considerably enhance the performance of Compressive Sensing on image signals without increasing the size of measurements or computation complexity, while they can still keep the advantages of random sampling in the conventional Compressive Sensing framework