Research On Image Restoration And Its Related Technology Within The Bayesian Framework

As the foundation of image processing and computer vision, image restoration can solve the problem of image degradation. In many applications, such as remote sensing, medical imaging, and military reconnaissance, image degradation remainds a common and urgent problem to be solved. Thus, image restoration has always been followed with interest and studied earnestly.This thesis focuses on the image restoration in Bayesian framework, which mainly contains research on model parameter estimation, image denoising, and image deblurring. By studying classical algorithm in Bayesian framework, several problems are found, such as the lack of a close-formed solution for posterior probability, the Maximum a Posteriori (MAP) method falling into the point estimation, and the lack of good principles for parameter estimation. This thesis proposes a hierarchical maximum likelihood method and introduces the variational Bayesian method in response to these problems. Both methods are experimentally analyzed and verified.These are the major achievements and innovations:1. Due to the difficulty of using the evidence analysis method in achieving close-formed solutions, we propose a novel hierarchical maximum likelihood method. The experiments demonstrate that the proposed method can obtain better results with satisfactory speeds when used in image restoration.2. A novel Bayesian parameter estimation algorithm is proposed to overcome the drawbacks in Morozov discrepancy principle, L-curve method, generalized cross validation, and expectation maximum method. The proposed algorithm uses the hierarchical maximum likelihood method to estimate multiple model parameters together with image restoration.3. We propose a diffusion-based image denoising algorithm that introduces the gradient operator as the prior model of the original image and utilizes the variational Bayesian method to estimate the original image. Results show that the proposed algorithm overcomes the shortcomings of the classical empirical Bayesian method.4. We propose a novel color image denoising algorithm based on space projection and hybrid model. In the YCbCr space, the proposed algorithm uses the hybrid model to characterize the original image, and the hierarchical maximum likelihood framework is used to estimate the original image. Experiments indicate that the SNR values of denoised images are improved by 1dB to 2dB on average.5. By studying the distribution properties of the noise, we introduce the Laplace distribution model to characterize the noises. We also propose the total variation to model the original image. To solve the problem of L1-optimization difficulty caused by the Laplace model and the total variation, we incorporate the iteratively reweighted norm method into our algorithm. Experiments clearly show that the Laplace model gives a true reflection of the noise natures, and the iteratively reweighted norm truly speeds up the proposed algorithm.6. By combining the sparse representation with the hierarchical maximum likelihood method, a sparse representation-based image deblurring method is proposed. This algorithm introduces Donoho's sparse model to characterize the sparse coefficient vector, and the total variation model is used to characterize the original image, which is estimated using the hierarchical maximum likelihood method. We theoretically and experimentally prove that the proposed algorithm supplies a unified framework for sparse image restoration.7. We propose a novel harmonic image deblurring algorithm that uses the harmonic model to characterize the original image, and the hierarchical maximum likelihood method to estimate it. Experiments demonstrate that the proposed algorithm achieves better results with faster speed compared to the MAP-based algorithms.8. We propose a novel Bayesian multichannel image deblurring algorithm that utilizes a hybrid model composed of the cross relation model and the smoothing model to characterize point spread function. The proposed algorithm also utilizes total variation to model the original image. Point spread function, together with original image, is estimated alternatively using the hierarchical maximum likelihood method. Results show the competitive performance of the proposed algorithm in vision effects and speed compared to other algorithms.