Research On Compressed Sensing Reconstruction Technology And Its Application In Image Fusion

Compressed sensing (CS) is an emerging compressive sampling technology and has attractedconsiderable attention in many fields especially the image processing field by suggesting that itsamples a signal and compresses it meanwhile. Compressed sensing contains three ideas: sparserepresentation/approximation, measurement and reconstruction, and one of the key ideas of it is torecover a sparse signal from very few nonadaptive, linear measurements by nonlinear optimization.It is a goal of CS to tailor a stable, low computational complexity and fast convergencereconstruction algorithm. Besides，in actual applications, noises may inevitably exist, and thus tostudy the robustness of compressed sensing reconstruction technology is of great significance. It isimportant and necessary to tailor more robust reconstruction algorithms so as to improve thereconstruction performance, and apply the CS reconstruction technology to the multifocus imagefusion field. In this dissertation, the main contributions are as follows:(1) Alternating direction exterior point continuation method (ADEPCM) is proposed to solve the1-regularization problem, which is a nonsmooth problem of signal reconstruction for CS. Byintroducing the penalty function, the two variables are alternatively minimized, and the penaltyvariable is updated by a continuation scheme. Besides, ADEPCM is applied to reconstruct idealimages and noisy images. And the experimental simulations demonstrate that ADEPCM algorithmhas a faster convergence rate, a higher reconstructed peak signal to noise ratio (PSNR) and astronger robustness than other state-of-the-art CS reconstruction algorithms such as interior-pointmethod, gradient projection for sparse reconstruction algorithm, two-step iterativeshrinkage/thresholding algorithm, and split augmented Lagrangian shrinkage algorithm.(2) Fast Alternating Direction Method of Multipliers (FADMM) is proposed to solve the0-regularization problem, which is a nonconvex optimization problem of signal reconstruction forCS. The first step of FADMM is to express the0-regularization problem of the sparse coefficientas an equivalent constrained optimization problem by using variable splitting technology. Then, byintroducing the function of multipliers, the two variables are alternatively minimized byGauss-Seidel method. And the two variables are updated once again to speed up the convergencerate, and then, the variable of multipliers is updated. Finally, the original signal is reconstructed bythe orthogonal inverse transform. FADMM is also applied to reconstruct ideal images and noisy images. And the experimental simulations demonstrate that the FADMM algorithm has a higherreconstructed PSNR, a faster convergence rate and a stronger robustness than some existing CSreconstruction algorithms, for example, split augmented Lagrangian shrinkage algorithm,accelerated iterative hard thresholding algorithm, iterative hard thresholding algorithm, andtwo-step iterative shrinkage/thresholding algorithm..(3) The problem of reconstructing a sparse signal from an underdetermined linear systemcaptures many applications in the compressed sensing field. And it has been shown that thisNP-hard problem can be well approached via heuristically solving the1-regularized problem,which is a convex relaxation problem. However, this convex relaxation problem is nonsmooth andthus not tractable in general, besides, some existing CS reconstruction algorithms have a lowerconvergence rate for solving this problem. For these reasons, an implementable numerical algorithmwhich is called fast linearized alternating direction method of multipliers (FLADMM) is proposedto solve the Lagrangian dual problem of1-regularized problem. Besides, to capture moreapplications, the augmented1-regularized problem is proposed, which is a more general setting ofthe1-regularized problem. The FLADMM is also used to solve this novel CS reconstructionproblem. Finally, FLADMM is applied to reconstruct ideal images and noisy images. Ourexperimental results show that the FLADMM yields a higher reconstructed PSNR as well as a fasterconvergence rate at the same sampling rate as compared to some existing CS reconstructionmethods such as alternating direction method of multipliers, accelerated linearized Bregman method,basis pursuit algorithm, and orthogonal matching pursuit algorithm. Besides, this method is morerobust than these state-of-the-art CS reconstruction methods at the same noise level.(4) An efficient multifocus image fusion and reconstruction framework based on CS in thewavelet domain is proposed. The new framework is composed of three phases. Firstly, the sourceimages are represented with their sparse coefficients using the discrete wavelet transform (DWT).Secondly, the measurements are obtained by the random Gaussian matrix from their sparsecoefficients, and are then fused by the proposed adaptive local energy metrics (ALEM) fusionscheme. Finally, a fast continuous linearized augmented Lagrangian method (FCLALM) isproposed to reconstruct the sparse coefficients from the fused measurement, which will beconverted by the inverse discrete wavelet transform (IDWT) to the fused image. Our experimental results show that the proposed ALEM image fusion scheme can achieve a higher fusion quality thansome existing fusion schemes such as maximum selection and standard deviation weighted averagefusion schemes. In addition, the proposed FCLALM reconstruction algorithm has a higherreconstructed PSNR and a faster convergence rate as compared to some existing CS reconstructionmethods such as fixed-point continuation, fast iterative shrinkage/thresholding algorithm, andorthogonal matching pursuit algorithm.