Sparse Optimization Learning Based Image Modeling Methods

Sparse-land image modeling aims at exploring a compact and concise representation of images,and then digging the meaningful information for further processing.Lots of recent works have been devoted to the sparse model,which greatly promotes the development of computer vision.However,there still exist several bottlenecks in the sparse model,such as the limitation of restricted isometry property,the uncertainty towards sparsity,the lack of global structure,the non-compactness and high complexity,the strong coupling.This thesis makes a thorough study on the above issues,and purposefully puts forward some solutions based on evolutionary computation,low-rank representation and deep learning.The major contributions include:1.Matching pursuit provides an efficient way to select the atoms for sparse representation.Its main idea is selecting the atom which has the largest correlation with the residual in each iteration.But this correlation-driven greedy search can be easily restricted by the restricted isometry property,and thus gets stuck in the local optimum.To address this problem,this thesis proposes an evolutionary computation-based matching pursuit algorithm which treats the correlation as a heuristic information,and search the optimum solution in the framework of evolutionary computation.In this way,it achieves higher recovery probability and accuracy on one-dimension signals of different distributions than conventional matching pursuit algorithms,and also shows better reconstruction results on two-dimension images.2.The non-convexity of sparse model makes it hard to obtain an analytic solution.Facing the uncertainty of the solution,many approaches relax the constraint condition of the model or use the convex relaxation to get a solvable formulation.Even though they are efficient,they ignore the essence of the ?0norm,i.e.,combinatorial optimization,which restricts their search capability.Hence,inspired by the heuristic search of the evolutionary computation,a novel image representation framework based on Gaussian model and evolutionary optimization is proposed.The proposed framework uses different models to formulate the smooth and non-smooth patches respectively.It describes the smooth patches with a Gaussian model and obtains their analytic solutions by Bayesian inference.For non-smooth patches,a series of evolutionary operators are purposefully designed according to the properties of PCA dictionary to conduct anaccurate reconstruction from the perspective of combinatorial optimization.The proposed framework shows effectiveness on image compressed sensing,super-resolution and inpainting.3.Block processing is a widely used technique in sparse model.It greatly reduces the computational complexity,but at the same time brings the loss of the global structure which can not be repaired by the patch gathering and averaging.To tackle this problem,this thesis proposes a low-rank image restoration algorithm based on Gaussian mixture model which introduces the local statistical properties into the rank minimization.The proposed model can effectively recover the fine details via Gaussian mixture model,as well as the latent global low-rank structure via nuclear norm.Furthermore,the proposed model is proven to be structural sparse when it is analyzed in PCA domain.In contrast with the existing algorithms,the proposed algorithm obtains more robust and accurate results on image completion and text removal problems.4.When solving the cross-modality synthesis problems,such as image super-resolution and face sketch synthesis,sparse model often learns two coupled dictionaries alternately and independently.The parameters are not jointly optimized in a compact framework.In the testing phase,sparse model needs to solve complex optimization problems.To overcome these drawbacks,a modified convolutional neural network is proposed for face sketch synthesis,it learns an end-to-end mapping between face photos and sketches,and in the testing phase it only calculates some convolutions and primary operations.Besides,this thesis demonstrates the internal connections between sparse model and convolutional neural network.The experiments on face sketch synthesis show that the proposed method achieves a dramatic improvement in efficiency compared with the conventional methods.5.In the sparse model-based image super-resolution problems,the coefficients of the low-and high-resolution images in the same position are assumed to be equivalent,which enforces an identical structure between low-and high-resolution images.However,in fact the structure of high-resolution images is much more complicated than that of low-resolution images.In order to reduce the coupling between low-and high-resolution representations,a semi-coupled convolutional sparse coding method is proposed for image super-resolution.The proposed method uses the nonlinear convolution operations as the mapping function between the low/high-resolution features,and the conventional linear mapping can be seen as a special case of the proposedmethod.Hence,this work provides a more flexible and efficient approach for image super-resolution problem.