Separable compressed coded aperture imaging via singular value decomposition

Abstract

Compressed Sensing (CS) encodes a signal or image into a relatively small number of incoherent linear measurements. Compressed Imaging (CI), as the application and promotion of CS theory in imaging, which exploits the sparsity of most images in nature and is expected to overcome some shortcomings of existing imaging theories. However, one of the main difficulties in implementing CI is that it involves a large amount of data, which has a profound impact on the complexity of optical design, calibration, data storage requirements, and computational burden. Compressed Coded Aperture Imaging (CCAI) is a practical CI method, which can reconstruct the true image from a single, low-resolution, noisy measurements, obtained under the convolution with a coded aperture and sampling operation. However, the key problem that existed in CCAI is the huge requirements for the storage of the measurement matrix and the computation burden for algorithm to recover the original image. As a result, CCAI is only limited to relatively small-size images. In this paper, separable compressed sensing (SCS) is introduced into CCAI, and the only separable compressed coded aperture imaging (SCCAI) method is proposed. The singular value decomposition (SVD) of the two separated measurement matrices are performed, and the measurement matrices and measurements are both optimized, which is the SCCAI-SVD method proposed in this paper. Our method has the advantages of optical implementation and computational feasibility. Numerical results demonstrate the superiority of our proposed method.