Image Reconstruction Method Based Compressive Sensing

Compressed sensing (CS) theory has brought a revolutionary breakthrough for signal processing which takes both sampling and compression into consideration. Image reconstruction under CS is cast as the inverse problem of recovering the original high-resolution image from the observed images and recently the image reconstruction problem has been used widely in many practical field including medical imaging, satellite imaging and video applications and so on. Although the technique of compressed sensing is able to lower the dimension of the original signal through the way of observation, and, to some extent, decrease the measurement times and the quantity of computation. Especially, due to none of the elements in the measurement matrix being zero, some large images contain many data and the directly observation will cause the great consumption of memory and computation complexity and the storage of measurement matrix will bring pressure to the hardware. As a result some ideas of block CS have been introduced. Compared with treating the image as a whole to obtain the observed value, the block-operated is easier to implement. However, in the process of reconstruction, no matter what algorithm is used as the reconstruction methods, the image patch is reconstructed patch by patch independently which ignores the correlation among the patches. In practical application, while dealing with the images with great structural information, the artifact and the discontinuous of the structure will appear which will influence the reconstruction results. Under the framework of block CS, this paper introduces the idea of local and nonlocal structure feature and takes the pixel similarity into consideration. This paper is mainly about the image reconstruction under the framework of CS. The main works are as follows:(1) A non-local feature and POCS (projection on to convex set) based CS image reconstruction method is proposed. The local projected pixels estimation is added in the traditional reconstruction model and the similarity of each reconstructed patch in the local area of the image is considered. This process is mainly operated by the method of POCS. Besides, the non-local constraint is introduced into the model and is implemented by the idea of non-local mean filtering. The result is able to maintain the feature well and achieves better visual effect.(2) An adaptive kernel regression based CS image reconstruction method is proposed. The method approaches the reconstruction through the kernel regression framework which can effectively seize the local structure in the image. Besides, a non-local structured idea is added to consider the similarity of the image patches and the relativity among the different patches during the reconstruction work. The newly proposed method can be seen as a local smoothing part combined with the non-local weighted information part which will better express the reconstructed image. The results demonstrate that the proposed method outperforms some state of art reconstruction algorithms both in visual effect and numerical measures.(3) An iterative filtering and TV (total variation) model based CS image reconstruction method is proposed. Based on the TV model the similarity constraint which implies the structural self-similarity of patches is added into the cost function. And the function is solved by BM3D and the global update is used by the projection method iteratively. And the global optimization will contribute to the better integration and consistence. Due to the introduction of the block-operated and the global-operated method, the reconstruction will show higher efficiency. Therefore, some experiments on the images results show that it can improve the quality and visual effects of the image.The research is supported by NSFC(61072108,60601029,60971112,61173090), new century excellent talents item, Higher school subject innovation engineering plan (111plan), No. B0704and central university basic scientific research business expenses.