Sparse MRI and CT Reconstruction

Sparse signal reconstruction is of the utmost importance for efficient medical imaging, conducting accurate screening for security and inspection, and for non-destructive testing. The sparsity of the signal is dictated by either feasibility, or the cost and the screening time constraints of the system. In this work, two major sparse signal reconstruction systems such as compressed sensing magnetic resonance imaging (MRI) and sparse-view computed tomography (CT) are investigated. For medical CT, a limited number of views (sparse-view) is an option for whether reducing the amount of ionizing radiation or the screening time and the cost of the procedure. In applications such as non-destructive testing or inspection of large objects, like a cargo container, one angular view can take up to a few minutes for only one slice. On the other hand, some views can be unavailable due to the configuration of the system. A problem of data sufficiency and on how to estimate a tomographic image when the projection data are not ideally sufficient for precise reconstruction is one of two major objectives of this work. Three CT reconstruction methods are proposed: algebraic iterative reconstruction-reprojection (AIRR), sparse-view CT reconstruction based on curvelet and total variation regularization (CTV), and sparse-view CT reconstruction based on nonconvex L1-L2 regularization. The experimental results confirm a high performance based on subjective and objective quality metrics. Additionally, sparse-view neutron-photon tomography is studied based on Monte-Carlo modelling to demonstrate shape reconstruction, material discrimination and visualization based on the proposed 3D object reconstruction method and material discrimination signatures. One of the methods for efficient acquisition of multidimensional signals is the compressed sensing (CS). A significantly low number of measurements can be obtained in different ways, and one is undersampling, that is sampling below the Shannon-Nyquist limit. Magnetic resonance imaging (MRI) suffers inherently from its slow data acquisition. The compressed sensing MRI (CSMRI) offers significant scan time reduction with advantages for patients and health care economics. In this work, three frameworks are proposed and evaluated, i.e., CSMRI based on curvelet transform and total generalized variation (CT-TGV), CSMRI using curvelet sparsity and nonlocal total variation: CS-NLTV, CSMRI that explores shearlet sparsity and nonlocal total variation: SS-NLTV. The proposed methods are evaluated experimentally and compared to the previously reported state-of-the-art methods. Results demonstrate a significant improvement of image reconstruction quality on different medical MRI datasets

Sparse and low-rank techniques for the efficient restoration of images

Image reconstruction is a key problem in numerous applications of computer vision and medical imaging. By removing noise and artifacts from corrupted images, or by enhancing the quality of low-resolution images, reconstruction methods are essential to provide high-quality images for these applications. Over the years, extensive research efforts have been invested toward the development of accurate and efficient approaches for this problem. Recently, considerable improvements have been achieved by exploiting the principles of sparse representation and nonlocal self-similarity. However, techniques based on these principles often suffer from important limitations that impede their use in high-quality and large-scale applications. Thus, sparse representation approaches consider local patches during reconstruction, but ignore the global structure of the image. Likewise, because they average over groups of similar patches, nonlocal self-similarity methods tend to over-smooth images. Such methods can also be computationally expensive, requiring a hour or more to reconstruct a single image. Furthermore, existing reconstruction approaches consider either local patch-based regularization or global structure regularization, due to the complexity of combining both regularization strategies in a single model. Yet, such combined model could improve upon existing techniques by removing noise or reconstruction artifacts, while preserving both local details and global structure in the image. Similarly, current approaches rarely consider external information during the reconstruction process. When the structure to reconstruct is known, external information like statistical atlases or geometrical priors could also improve performance by guiding the reconstruction. This thesis addresses limitations of the prior art through three distinct contributions. The first contribution investigates the histogram of image gradients as a powerful prior for image reconstruction. Due to the trade-off between noise removal and smoothing, image reconstruction techniques based on global or local regularization often over-smooth the image, leading to the loss of edges and textures. To alleviate this problem, we propose a novel prior for preserving the distribution of image gradients modeled as a histogram. This prior is combined with low-rank patch regularization in a single efficient model, which is then shown to improve reconstruction accuracy for the problems of denoising and deblurring. The second contribution explores the joint modeling of local and global structure regularization for image restoration. Toward this goal, groups of similar patches are reconstructed simultaneously using an adaptive regularization technique based on the weighted nuclear norm. An innovative strategy, which decomposes the image into a smooth component and a sparse residual, is proposed to preserve global image structure. This strategy is shown to better exploit the property of structure sparsity than standard techniques like total variation. The proposed model is evaluated on the problems of completion and super-resolution, outperforming state-of-the-art approaches for these tasks. Lastly, the third contribution of this thesis proposes an atlas-based prior for the efficient reconstruction of MR data. Although popular, image priors based on total variation and nonlocal patch similarity often over-smooth edges and textures in the image due to the uniform regularization of gradients. Unlike natural images, the spatial characteristics of medical images are often restricted by the target anatomical structure and imaging modality. Based on this principle, we propose a novel MRI reconstruction method that leverages external information in the form of an probabilistic atlas. This atlas controls the level of gradient regularization at each image location, via a weighted total-variation prior. The proposed method also exploits the redundancy of nonlocal similar patches through a sparse representation model. Experiments on a large scale dataset of T1-weighted images show this method to be highly competitive with the state-of-the-art