Sparse Optimization Algorithms Based On L₀ Norm Constraint With Application To Image Reconstruction

The visual signal,such as image and video,plays an important role in the digitized media epoch.Also,its quality directly influences people's visual perception and communication.The explosion of people's demands for information leads to the high cost of sampling system and the difficulty of data transferring and storage for the signal processing technology based on Nyquist sampling theory.Compressive sensing?CS?theory is a novel sampling theory,synchronously conducts the sampling and compressing based on the sparsity and compressibility of the original signal,and can accurately reconstruct the original signal based on a smaller sampling rate,which is far smaller than the Nyquist sampling rate.While effective sparse reconstruction algorithm is an important guarantee for successfully extending and applying the CS theory for actual data acquisition systems and data models.The sparse optimization based on the l₀ minimization is the essential problem of reconstruction,which is also an NP-hard problem with huge computational complexity and can not be solved using traditional optimization algorithms.This thesis studies the sparse reconstruction algorithms based on l₀ minimization with its application to image reconstruction.The main contributions of this thesis can be summarized as follows:We propose a novel sparse optimization algorithm based on intelligent greedy pursuit model,which can solve the sparse reconstruction problem based on l₀ norm constraint.There are three drawbacks in greedy algorithm: 1)the accurate sparsity level must be set as the prior,which limits the application of CS theory;2)the use of the fast searching strategies makes it easy to fall into a sub-optimal solution;3)it needs more measurements to achieve the accurate reconstruction.To solve the above shortcomings,we firstly model the CS reconstruction as a novel optimization objective function based on l₀ minimization when the accurate sparsity level is unknown,which can break through the application limit of CS theory.Then,the advantages of intelligent optimization algorithm for global searching and the superiorities of greedy algorithm for fast reconstruction are combined to design a two-cycle optimization algorithm,to efficiently solve the new optimization objective function based on l₀ minimization and obtain the global optimization solution.The experimental results of sparse signal reconstruction demonstrate that the proposed IGP model achieves the better reconstruction performance.Also,IGP can achieve an accurate reconstruction using less measurements.We propose a novel image reconstruction algorithm based on edge prior.As image is a signal containing mass of data,image reconstruction belongs to large-scale optimization problem with huge computational complexity.However,if we just utilize the sparsity as prior,image reconstruction can not achieve a satisfying performance.To solve the problems mentioned above,IGP model is applied to image reconstruction with high sparsity in orthogonal dictionary domain,we first model the image reconstruction problem based on multi-variable sampling scheme as sparse optimization objective function based on l₀ norm constraint.Also,the edge prior is obtained to restrain the reconstruction,which can reduce the computational complexity significantly.Then,under the constraint of edge prior,the IGP model is utilized to solve the image reconstruction based on l₀ norm constraint to efficiently improve the reconstruction performance.In the application of image reconstruction with obvious edge and high sparsity in wavelet domain,the proposed algorithm achieves the better reconstruction performance than the state-of-the-art image reconstruction algorithms.We propose a novel image sequences reconstruction algorithm based on multi-variable prior.The traditional image sequences reconstruction based on space-time signal is such a large-scale optimization problem with huge computational complexity,while image sequences reconstruction based on each frame reconstruction needs more measurements to achieve the better reconstruction performance.To solve the above problem,IGP model is applied to image sequences reconstruction with high sparsity in orthogonal dictionary domain.Based on the property that the sparse pattern of each two adjacent images are much similar,we obtain the multi-variable prior to restrain the reconstruction of the current image,which can not only reduce the computational complexity but also improve the reconstruction performance.Under the constraint of multi-variable prior,IGP model is utilized to solve the image sequence reconstruction based on l₀ norm constraint.In the application of image sequences reconstruction,the proposed algorithm obtains the better reconstruction performance when the measurements is relatively small.We propose a novel natural image reconstruction algorithm based on nonlocal prior.For natural images that can not achieve the desired sparsity level in orthogonal dictionary domain,the over-completed dictionary is usually utilized for sparse representation.However,the over-completed dictionary for sparse representation has strong redundancy,which increases the size of optimization space to further increase the computation complexity of reconstruction algorithms.To solve this problem,IGP model is applied to natural image reconstruction with high sparsity in over-completed dictionary domain.Based on the nonlocal self-similarity property to obtain the nonlocal prior,which can reduce the computational complexity of image reconstruction based on over-completed dictionary sparse representation.Under the constraint of nonlocal self-similarity prior,the IGP model is utilized to solve the image reconstruction based on l₀ minimization.In the application of natural image reconstruction,the proposed algorithm can efficiently improve the reconstruction performance.We propose a novel natural image reconstruction algorithm based on geometric prior.The traditional image reconstruction algorithms could not take the reconstruction of image structures into full consideration,which leads to the low reconstruction accuracy of image structures.To solve this problem,we first establish the collaborative sparsity reconstruction model based on geometric structure to improve the reconstruction accuracy of image structures.Then,the geometric prior is obtained based on the nonlocal self-similarity property of geometric structures.Under the constraint of geometric prior,the IGP model is utilized to solve the image reconstruction based on l₀ minimization.In the application of natural image reconstruction,the proposed algorithm can efficiently improve the reconstruction performance,especially the reconstruction accuracy of image structures.