Research On Video/Image Compressive Sensing Reconstruction Based On Fractional-Order Total Variation

As a novel signal representation and compression sampling theory, compressive sensing theory could reconstruct the original signal with low sampling rate. It has gained much attention of scholars in the past few years due to its advantage of sampling and compressing with low speed at the same time. Reconstruction algorithm is a crucial issue of compressive sensing, it plays a key role in the application of compressive sensing. It is a hot topic to design a reconstruction algorithm with low complexity and high reconstruction precision to reconstruct signals, especially the large scale image/video signals. Under this background, by taking the image/video signals as the research object, this dissertation has deeply studied the compressive sensing sparse representation and reconstruction algorithm. Aiming at the problem of losing the details and textures of images reconstructed by the total variation model, this dissertation introduces the fractional-order total variation model into compressive sensing reconstruction and designs reconstruction algorithms. The major contributions and innovative points of this dissertation are as follows:(1) Aiming at the problem of losing details and textures of images reconstructed by the total variation model, a fractional-order total variation two-dimensional compressive sening sparse image reconstruction algorithm based on majorization minimization algorithm is proposed. In this algorithm, the one-dimensional random measurement of compressive sensing theory is extended to two-directional two-dimensional random measurement and a two-dimensional compressive sensing framework is established. Besides, the fractional-order difference technology is introduced into the total variation model and a fractional-order total variation model for image sprase representation is designed. This model is changed into a sequence of quadratic surrogate penalties by using the majorization minimization. The experimental results show that:compared with sevearal compressive sensing sparse image reconstruction algorithms based on total variation model, the proposed algorithm has lower computational complexity, not only yielding higher peak-signal-to-noise ratio and structural similarity indexes but also reconstructing images of better subjective visual quality.(2) In order to have more flexibility to achieve sparser representation for images, a two-dimensional compressive sensing sparse image reconstruction algorithm based on multi fearture sparse representation is proposed. In this algorithm, a new model for natural images sparse representation is proposed, in which the multi direction dual-tree discrete wavelet transform and the fractional-order total variation are applied simultaneously. A gradient projection algorithm is proposed to solve this model. The experimental results on the standard test images show the effectiveness of the proposed algorithm and the higher reconstruction precision than several state-of-art algorithms.(3)Aiming at the problem of high computational complexity of video Kronecker compressive sensing, a video Kronecker compressive sensing reconstruction algorithm based on fractional-order total variation model is proposed. In this algorithm, the fractional-order total variation model is extended using Kronecker product and a video Kronecker compressive sensing sparse representation model based on fractional-order total variation model is proposed, an alternating direction method is proposed to solve this sparse model. In this sparse model, video signals could not be stacked into a large vector, so the computational complexity and memory requirements are lower. Besides, the reconstruction quality is improved by introducing the fractional-order total variation model. The experimental results on the standard test images show that:compared with Kronecker compressive sensing and sevearal state-of-art video compressive sensing algorithms, the proposed algorithm has lower computational complexity and has higher peak-signal-to-noise ratio and better visual detail preservation, yielding images of better subjective visual quality.(4) In order to improve the reconstruction quality and reduce the computational complexity of video tensor compressive sensing, a video compressive sensing reconstruction algorithm based on fractional-order total variation and tensor sparse representation is proposed. In the proposed algorithm, the fractional-order total variation model is generalized to high-order tensor and a sparse representation model based on joint fractional-order total variation and tensor sparse representation is established. By using the mathematical properties of tensor calculus, a tensor smoothed Lo alrorithm is proposed to solve this reconstruction model. The experimental results show that:compared with sevearal state-of-art video compressive sensing reconstruction algorithms, the proposed algorithm could signifcantly improves the reconstruction quality of the videos and reduces the computational complexity.