EFFICIENT NOVEL ALGORITHM FOR ILL-POSED INVERSE PROBLEMS

Abstract

Inverse problems are considered very important and well-research problems for the nature of the benefits their solution can provide us, as they help us infer something about a physical parameter that otherwise might not be directly observed. Unlike the forward problem, which predicts measured observation for a system, the inverse problem generally characterizes a system or physical model from observations measured in a specific case. They have applications in many areas such as signal processing, nondestructive testing (NDT), medical imaging (such as computed axial tomography or CT and EEG/ERP), geophysical prospecting, computer vision, ocean acoustic tomography, astronomy, physics and many other fields. This Ph.D. dissertation is directed towards one of the above mentioned areas; to develop novel algorithms for the solution of inverse problems specially in the domain of Computed Tomography (CT). The inverse problems here are ill-posed due to the non-uniqueness of the solution, particularly in the presence of measurement noise. Although CT is a very informative medical diagnosis tool, the radiation dose is a concern. However, the image quality of most CT reconstruction algorithms suffers if the radiation dose is reduced. As the extensive use of CT examinations increases the risk of cancer and other hazards; reduction in the radiation dose without degrading the reconstructed image quality is an active research area. This is also the motivation and targeted research problem of the presented work. Abstract vi This PhD dissertation presents efficient novel schemes for under-sampled (Sparse- View) CT. These offer an alternative method to reduce the radiation dose with good quality image reconstruction. The degraded features in the Sparse-View CT reconstructed images can be enhanced through post-processing. In which data enhancement and image processing techniques are widely used. The reported schemes use sophisticated post-processing technique to mitigate the drawbacks associated with Sparse-View CT. The reported schemes enhance the Sparse-View CT through combinations of various techniques, including sinogram interpolation, scaled reprojection and shape adaptive spatial filtering. The sinogram interpolation refers to directional view interpolation in the sparse projection data. This is carried out using existing state-of-the-art interpolation techniques, as well as the developed scheme using scale adjusted re-projections of enhanced CT image. The image enhancement is undertaken using various efficient image filtering techniques. These techniques include spatially non-variant morphological image filtering, introduction of spatially variant filtering kernels, Amoeba, customized for CT images. The developed amoeba filter kernel adapts its shape based on image contour/ boundaries, which ensures image smoothing without compromising on the edge details. The region-based segmentation (RBS) using multilevel thresholding is used for the amoeba kernel shaping, which is more effective Abstract vii in medical imaging applications as it is similar to the symmetric and region-based nature of human body anatomy. The schemes are implemented using simulated and clinically reconstructed phantoms. The proposed schemes are applied to noisy sparse projection data and the reconstructed image quality is investigated using multiple image quality metrics. The results of the proposed schemes are compared with various classical techniques. The robustness of the schemes is also investigated at various projection noise levels. Moreover, the performance at various Sparse-View angular sampling is also investigated. The reported schemes offer promising reconstruction results while subjecting patients with lesser radiation dose. The presented schemes demonstrate good quality Sparse-View CT images with up to 75% dose reduction. The sinogram interpolation (using scale-adjusted reprojections) contributes in mitigating data sparseness; while shape adaptive filtering provides efficient image enhancement. The reported schemes are also very robust in the presence of noise in projection data. The schemes demonstrate good quality reconstruction as comparable to various advance reconstruction techniques, while achieving very less reconstruction time. The use of self-shaping spatial filter kernel in the area of under-sampled CT reconstruction is a novel contribution. The research has the potential to serve and contribute in the medical industry, in commercial use and more importantly in the national benefit too.