Image Structural Information-Driven Compressive Sensing Reconstruction Algorithms And Quality Assessment

Compressive sensing (CS) theory which relies on the sparsity or compressibility of the natural signals breaks the limitation of the traditional Nyquist-Shannon sampling theorem, and demonstrates that CS sampling signal could be accurately reconstructed by acquiring far fewer samples or measurements than that from Nyquist sampling rate, so the signal sampling and compression processes are completed simultaneously. As a novel efficient signal acquisition mode, CS provides a theoretical foundation for studying the low-power bandwidth-limited imaging system. CS theory contains three important components:sparse representation, linear compressive measurement and nonlinear reconstruction. Among the three components, the nonlinear reconstruction process determines the reconstruction accuracy and quality of the acquired signal which could influence the signal postprocessing and application. Hence the nonlinear reconstruction is the key step for the whole CS theory research. Specially, this CS reconstruction process is an ill-posed inverse problem with respect to the fixed linear measurement matrix. In order to improve the reconstruction performance and strengthen the recoverability of sampling signal, the signal sparsity or other prior information could be introuduced into the CS reconstruction model. In addition, the proper evaluation criterion is needed to quantify and analyse the quality of the reconstruction results, while it could be utilized to direct the CS reconstruction algorithm design and development. Based on image structural information and sparity prior, this paper focuses on the image CS reconstruction and evaluation. The main achievements and innovations are listed as follows:(1) Based on the sparsity of the image gradient, the classical total variation (TV) regularization reconstruction model always results in a piecewise constant solutions. In order to improve the reconstruction performance, we propose a novel re weighted TV image CS reconstruction model via nonlocal structural similarity. To overcome the weakness of TV regularization which makes the reconstructed image too smooth and lose some details such as edges and textures, robust function of image gradient value is utilized to estimate the weights of reweighted TV, and ROF (Rudin-Osher-Fatemi) model is used to optimize these weights further in order to decrease the effects of noise. Next, the structure tensor is utilized to represent the nonlocal similarity prior and edge adptive steering kernel regression model is used to describe the local regression prior of the natural image. By integrating these prior models and the reweighted TV model, a new compound regularized optimization model is achieved. At last, the optimization model could be efficiently solved with a combination of the projection method and operator splitting method. Extended experiment results indicate that the proposed CS reconstruction method has a better improvement in terms of objective criterion and visual fidelity over other related TV-based reconstruction methods, wihle more edges and textures are kept in the reconstructed image.(2) The TV regularization prior could not efficiently describe the structural orientation information of the natural image, and usually make the results too smooth in edge or texture areas. In order to reduce these influences and utilize the image orientation information, directional TV is introduced to describe the sparsity of the image gradient. However, it is difficult to estimate orientation field robustly and accurately from CS measurements. Hence, a directivity structure-driven adaptive directional TV model for CS reconstruction is proposed and contains two stages:first, the initial orientation field is estimated and refined; second, the CS reconstruction model is presented by utilizing directional TV regularizer. Some experimental results demonstrate that the refined estimation of natural image structural orientation is helpful to improve the reconstruction quality in edge and texture areas. Comparing with other related reconstruction methods, this proposed algorithm improves the Peak Signal-to-Noise Rate (PSNR) and image recovery quality.(3) As a hotspot issue in distributed compressive sensing networks, compressive sensing multi-camera network reconstruction usually recovers every image separately, but views dependency and geometrical structure are rarely considered among these multi-view images, so joint reconstruction results are not ideal. In this paper, multiple view geometry of multi-view images is utilized to construct views dependency observation model. Based on the proposed parametric transformation observation model, a novel spatial correlation and low rank background guided compressive sensing for multi-view image joint reconstruction is proposed. At last, the optimization model could be reduced to a series of convex minimization problems that can be efficiently solved with a combination of the variable splitting and alternate iteration technique. Simulation results demonstrate the rationality and effectiveness of the proposed model, and the robustness to noise.(4) The conventional image quality evaluation criterion based on pixel errors fails to judge the geometry structure information in which our human visual system (HVS) is interested. Recently, most of structural similarity (SSIM)-based methods and its variants have sprung up which take advantage of the similarity of the image structure information, and lead to the development of the image quality evaluation. However, an important HVS phenomenon, perceptural error visual masking, is not considered in these mothods. Hence, a perceptural image quality assessment (PIQA) algorithm based on visual masking and structural similarity is proposed in this paper. Inspired by the structure tensor which is more efficient for describing the structure information, we define the geometry structure orientation and introduce it into the structure comparison measure. Meanwhile, based on the coutourlet transform and the perceptual characters of HVS perceptual process, the contrast masking and neighborhood masking are integrated to the contrast comparison measure. Simulation results show that our approach is highly consistent with HVS perceptual process, and also delivers better performance. At last, we compare all proposed reconstruction methods and other related algorithms under the proposed evaluation criterion, and analyse their advantages and disadvantages.