A Novel Differential Evolution and Its Effective Applications to Camera Raw Image Denoising and Constrained Min-Max Optimization Problems

Abstract

Recently with the rapid advance of imaging devices there are more and more pixels in a color image taken by a camera However the sensitivity of image sensor output signals to photon noise has become greater with the smaller size of each pixel Therefore denoising becomes one of the most important issue in image processing How to design an optimal denoising algorithm by differential evolution for camera raw images is the first application in this dissertation Uncertainties are often occurred and unable to avoid in real-world optimization scenarios The global optimum might be very sensitive to small variations in parameters Therefore a preferable solution is probably not the global optimum but one with high tolerance and robustness to uncertainties In this dissertation the most robust solution is defined under the best possible worst-case performance which can be described by a constrained min-max optimization problem How to use differential evolution to effectively find the most robust solution is the second application in this dissertation Four topics are studied in this dissertation First an eigenvector-based crossover operator is proposed to solve the problem of differential evolution of which the performance is sensitive to the rotation of coordinate systems Second a successful-parent-selecting framework is proposed to solve the stagnation problem of differential evolution in high-dimensional multimodal objective functions Third with the analysis of the noise model and denoising method for raw images acquired by a digital camera the differential evolution is used to design a fuzzy block-matching based denoising algorithm for camera raw image restoration Finally the definition and theorem of the constrained min-max optimization problem are specified and proposed and a constraint-activated differential evolution is proposed to solve the constrained min-max optimization problem In the first topic differential evolution is one of the most effective method to solve global optimization problems in continuous search domain However the performance of differential evolution is sensitive to the rotation of coordinate systems especially when the objective function is with high-conditioning The performance of differential evolution may decrease dramatically Therefore an eigenvector-based crossover operator is proposed to enhance the performance of differential evolution The eigenvector information of the covariance matrix of the solutions is utilized to make the crossover operator become rotationally invariant and solves the sensitivity problem on the rotation of coordinate systems The proposed operator can be applied to any crossover strategy with minimal changes The experimental results show that the proposed eigenvector-based crossover significantly enhances the performance of differential evolution on non-separable unimodal functions In standard test functions the proposed operator also significantly improves the overall performance of differential evolution The stagnation problem of differential evolution is discussed in the second topic When stagnation is happening differential evolution cannot converge solutions to a fixed point and the algorithm cannot find any better solutions To solve this problem a successful-parent-selecting framework is proposed to improve the performance of differential evolution During evolution recently updated solutions are stored into an alternative set of parents which provides a solution which is continuously not updated for more than unacceptable times an alternative selection of parents The proposed successful-parent-selecting framework can be applied to any differential evolution and effectively helps the algorithm escaping the situation of stagnation The simulation results show that the proposed framework accelerates the convergence speed of differential evolution and increases the update rate of solutions In addition the proposed framework significantly improves the performance of differential evolution in terms of Wilcoxon rank-sum test on almost all standard test functions The overall performance is also increased significantly Image denoising in practical cases is discussed in the third topic Recently many studies on image denoising assume image noise is a sequence of independent and identical distributed random variables which follow a Gaussian distribution However in fact the variance of photon noise depends on the magnitude of signal In addition the arrangement design of image sensors also affects the noise variance Therefore an image denoising algorithm should be designed for an RAW image In this dissertation a fuzzy block-matching based image denoising algorithm is proposed to remove noise from an RAW image The proposed block-matching finds similar blocks by the use of a fuzzy logic system Then these similar blocks are averaged with the weightings which are determined by the fuzzy logic system A variance stabilization transform is used to stabilize the noise variance and thus make the proposed method suitable to eliminate noise for both of bright and dark regions Finally the proposed differential evolution is used to further improve the performance of the proposed denoising algorithm The experimental results show that the proposed denoising algorithm effectively improves the performance of image denoising Furthermore the average performance of the proposed method is better than those of two state-of-the-art image denoising algorithms in subjective and objective measure Finally an optimal system which is designed from simulated environment might not be optimal in real world with uncertainties To deal with the uncertainties the most robust solution should be considered in design level and it can be described as a constrained min-max optimization problem To provide theoretical understanding of this problem the desired solution is specified in the proposed definition Based on the definition a theorem is proposed to prove that a min-max algorithm can be used to solve a max-min problem without any algorithmic changes Based on the theorem a constraint-activated differential evolution is proposed to solve the constrained min-max optimization problem The proposed constraint activation directly finds a solution which can best activate constraints to improve efficiency on finding a robust solution The simulation results show that the proposed method attains 100% success rate on all of the five numerical benchmarks in terms of 1E–6 solution error

Date of Award	2015 Feb 5
Original language	English
Supervisor	Shu-Mei Guo (Supervisor)