Ultra-limited-angle CT image reconstruction algorithm based on reweighting and edge-preserving

BACKGROUND: Ultra-limited-angle image reconstruction problem with a limited-angle scanning range less than or equal to π 2 is severely ill-posed. Due to the considerably large condition number of a linear system for image reconstruction, it is extremely challenging to generate a valid reconstructed image by traditional iterative reconstruction algorithms. OBJECTIVE: To develop and test a valid ultra-limited-angle CT image reconstruction algorithm. METHODS: We propose a new optimized reconstruction model and Reweighted Alternating Edge-preserving Diffusion and Smoothing algorithm in which a reweighted method of improving the condition number is incorporated into the idea of AEDS image reconstruction algorithm. The AEDS algorithm utilizes the property of image sparsity to improve partially the results. In experiments, the different algorithms (the Pre-Landweber, AEDS algorithms and our algorithm) are used to reconstruct the Shepp-Logan phantom from the simulated projection data with noises and the flat object with a large ratio between length and width from the real projection data. PSNR and SSIM are used as the quantitative indices to evaluate quality of reconstructed images. RESULTS: Experiment results showed that for simulated projection data, our algorithm improves PSNR and SSIM from 22.46db to 39.38db and from 0.71 to 0.96, respectively. For real projection data, our algorithm yields the highest PSNR and SSIM of 30.89db and 0.88, which obtains a valid reconstructed result. CONCLUSIONS: Our algorithm successfully combines the merits of several image processing and reconstruction algorithms. Thus, our new algorithm outperforms significantly other two algorithms and is valid for ultra-limited-angle CT image reconstruction.

Γ -convergence of Onsager–Machlup functionals: I. With applications to maximum a posteriori estimation in Bayesian inverse problems

The Bayesian solution to a statistical inverse problem can be summarised by a mode of the posterior distribution, i.e. a maximum a posteriori (MAP) estimator. The MAP estimator essentially coincides with the (regularised) variational solution to the inverse problem, seen as minimisation of the Onsager–Machlup (OM) functional of the posterior measure. An open problem in the stability analysis of inverse problems is to establish a relationship between the convergence properties of solutions obtained by the variational approach and by the Bayesian approach. To address this problem, we propose a general convergence theory for modes that is based on the Γ-convergence of OM functionals, and apply this theory to Bayesian inverse problems with Gaussian and edge-preserving Besov priors. Part II of this paper considers more general prior distributions.

Particle Swarm Optimization and Fuzzy C-means for Domain-independent Noisy Image Segmentation

<p>Image segmentation is considered to be one of the foremost image analysis techniques for high-level real-world applications in computer vision. Its task is to change or simplify the representation of an image in order to make it easier to understand or analyze. Although image segmentation has been studied for many years, evolving technology and transformation of demands make image segmentation a continuing challenge. Noise as a side effect of imaging devices is an inevitable part of images in many computer vision applications. Therefore, an important topic in image segmentation is noisy image segmentation which requires extra effort to deal with image segmentation in the presence of noise. Generally, different strategies are needed for different noisy images with different levels/types of noise. Therefore, many approaches in the literature are domain-dependent and applicable only to specific images. A well-recognized approach in noisy image segmentation uses clustering algorithms, among which Fuzzy C-Means (FCM) is one of the most popular. FCM is unsupervised, efficient, and can deal with uncertainty and complexity of information in an image. Dealing with uncertainties is easier with the fuzzy characteristic of FCM, and complexity of information is being taken care of by utilizing different features in FCM, and also combining FCM with other techniques. Many modifications have been introduced to FCM to deal with noisy image segmentation more effectively. Common approaches include, adding spatial information into the FCM process, addressing the FCM initialization problem, and enhancing features used for segmentation. However, existing FCM-based noisy image segmentation approaches in the literature generally suffer from three drawbacks. First, they are applicable to specific domains and images, and impotent in others. Second, they don’t perform well on severely noisy image segmentation. Third, they are effective on specific type and level of noise, and they don’t explore the effect of noise level variation. Recently, evolutionary computation techniques due to their global search abilities have been used in hybridization with FCM, mostly to address FCM stagnation in local optima. Particle Swarm Optimization (PSO) is particularly of interest because of its lower computational costs, easy implementation, and fast convergence, but its potential in this area has not been fully investigated. This thesis develops new domain-independent PSO-based algorithms for an automatic non-supervised FCM-based segmentation of severely noisy images which are capable of extracting the main coherent/homogeneous regions while preserving details and being robust to noise variation. The key approach taken in the thesis is to explore the use of PSO to manipulate and enhance local spatial and spatial-frequency information. This thesis introduces a new PSO feature enhancement approach in wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using evaluation based on FCM clustering performance. The results show great accuracy in the case of severe noise because of the enhanced features. Also, due to adaptivity, no parameter-tuning is required according to the type or volume of noise, and the performance is consistent under noise level variation. This thesis presents a scheme under which a fusion of two different denoising algorithms for more effective segmentation is possible. This fusion retains the advantages of each algorithm while leaving out their drawbacks. The fusion scheme uses the noisy image segmentation system introduced above and anisotropic diffusion, the edge-preserving denoising algorithm. Results show greater accuracy and stability in comparison to the individual algorithms on a variety of noisy images. This thesis introduces another PSO-based edge-preserving adaptive wavelet shrinkage system using wavelet packets, bilateral filtering, and a detail-respecting shrinkage scheme. The analysis of the results provide a comparison between the two feature enhancement systems. The first system uses wavelets and the second uses wavelet packets as a domain to enhance features for an FCM-based noisy image segmentation. Also, the highest segmentation accuracy among all the algorithms introduced in this thesis on some benchmarks belong to this system.</p>

Particle Swarm Optimization and Fuzzy C-means for Domain-independent Noisy Image Segmentation

<p>Image segmentation is considered to be one of the foremost image analysis techniques for high-level real-world applications in computer vision. Its task is to change or simplify the representation of an image in order to make it easier to understand or analyze. Although image segmentation has been studied for many years, evolving technology and transformation of demands make image segmentation a continuing challenge. Noise as a side effect of imaging devices is an inevitable part of images in many computer vision applications. Therefore, an important topic in image segmentation is noisy image segmentation which requires extra effort to deal with image segmentation in the presence of noise. Generally, different strategies are needed for different noisy images with different levels/types of noise. Therefore, many approaches in the literature are domain-dependent and applicable only to specific images. A well-recognized approach in noisy image segmentation uses clustering algorithms, among which Fuzzy C-Means (FCM) is one of the most popular. FCM is unsupervised, efficient, and can deal with uncertainty and complexity of information in an image. Dealing with uncertainties is easier with the fuzzy characteristic of FCM, and complexity of information is being taken care of by utilizing different features in FCM, and also combining FCM with other techniques. Many modifications have been introduced to FCM to deal with noisy image segmentation more effectively. Common approaches include, adding spatial information into the FCM process, addressing the FCM initialization problem, and enhancing features used for segmentation. However, existing FCM-based noisy image segmentation approaches in the literature generally suffer from three drawbacks. First, they are applicable to specific domains and images, and impotent in others. Second, they don’t perform well on severely noisy image segmentation. Third, they are effective on specific type and level of noise, and they don’t explore the effect of noise level variation. Recently, evolutionary computation techniques due to their global search abilities have been used in hybridization with FCM, mostly to address FCM stagnation in local optima. Particle Swarm Optimization (PSO) is particularly of interest because of its lower computational costs, easy implementation, and fast convergence, but its potential in this area has not been fully investigated. This thesis develops new domain-independent PSO-based algorithms for an automatic non-supervised FCM-based segmentation of severely noisy images which are capable of extracting the main coherent/homogeneous regions while preserving details and being robust to noise variation. The key approach taken in the thesis is to explore the use of PSO to manipulate and enhance local spatial and spatial-frequency information. This thesis introduces a new PSO feature enhancement approach in wavelet domain for noisy image segmentation. This approach applies adaptive wavelet shrinkage using evaluation based on FCM clustering performance. The results show great accuracy in the case of severe noise because of the enhanced features. Also, due to adaptivity, no parameter-tuning is required according to the type or volume of noise, and the performance is consistent under noise level variation. This thesis presents a scheme under which a fusion of two different denoising algorithms for more effective segmentation is possible. This fusion retains the advantages of each algorithm while leaving out their drawbacks. The fusion scheme uses the noisy image segmentation system introduced above and anisotropic diffusion, the edge-preserving denoising algorithm. Results show greater accuracy and stability in comparison to the individual algorithms on a variety of noisy images. This thesis introduces another PSO-based edge-preserving adaptive wavelet shrinkage system using wavelet packets, bilateral filtering, and a detail-respecting shrinkage scheme. The analysis of the results provide a comparison between the two feature enhancement systems. The first system uses wavelets and the second uses wavelet packets as a domain to enhance features for an FCM-based noisy image segmentation. Also, the highest segmentation accuracy among all the algorithms introduced in this thesis on some benchmarks belong to this system.</p>