Optimal Restoration of Spatially Variant Degraded Images using Intelligent Methods

Abstract

Image restoration is fundamental to visual information processing systems. In many real world scenarios, noise and blur are the two main unavoidable sources of degra- dation in images. The problem is deemed as an ill-posed inverse by nature due to the simultaneous occurrences of noise and blur in the image. Blurring function categorizes the degradation as space variant (SVD) if di erent spatial locations of the recorded scene are convolved by varying point spread function. In contrast, the degradation is categorized as spatially invariant (SID) if a unique point spread function blurs the whole image. This dissertation focuses on spatial degradations, initiating from space invariant towards space variant. Existing methods for restoration of SVD images, for example, neural networks and numerical optimization bear the limitations of high cost, lower restoration, less gen- eralization, discontinuity and instability for di erent spatial locations. It is learnt that three factors are vital to develop an e ective framework for restoration, which are: 1. The optimization of the ill-posed inverse restoration problem by minimizing constrained error function 2. A smoothness constraint 3. A regularization scheme The main objective of this dissertation is to improve the restoration results, by possible applications of new intelligent methods. This dissertation provides com- prehensive solutions to both spatial degradation problems, by considering above three factors. Firstly, SID images are restored, by a steepest descent based restora- tion approach. In this approach, an e cient smoothness constraint is proposed, to model the error function. In the next step, the steepest descent based approach is improved and a novel fuzzy regularization scheme is also proposed to better model the error function. It performed better than the existing methods on a speci c blur function and low power additive noise. However, local search properties of gradient based approaches and eventually lower restoration for SVD images, due to their high sensitivity for varying textures, noise powers and blurs allowed for the possible application of computational intelligence models. Finally, in this dissertation, a new optimization framework is proposed for image restoration of SVD images. In the proposed framework, particle swarm optimiza- tion based evolution is retained to minimize the Modi ed Error Estimate (MEE), for better restoration. The framework added hyper-heuristic layer to combine local and global search properties. Therefore, randomness in the evolution, augmented with apriori knowledge from problem domain, assisted in achieving the objective of better restoration. It introduced new swarm initialization and mutation of global best particle of the swarm. In addition, an adaptive weighted regularization scheme is introduced in MEE to cater with the uncertainty due to ill-posed nature of the in- verse problem. Furthermore, a new fuzzy logic and mathematical morphology based regularization scheme is also proposed in the framework, to improve the restoration stability and generalization, for SVD images. Di erent experiments are performed to observe the performance of proposed solu- tions. Visual and quantitative results are obtained and provided for each experiment. Signal-to-noise ratio (SNR) and mean-squared-error (MSE) are computed for com- parative analysis, which endorsed better restoration quantitatively, over well-known restoration methods. However, the stability in restoration performance of proposed framework is observed in visual results, for SVD images. Detailed experimental and comparative analysis shown better restoration, stabilization and generalization of the proposed framework for varied textures in standard and simulated images, and noises over well-known restoration approaches.