Compressed Sensing and Adaptive Graph Total Variation for Tomographic Reconstructions

Compressed Sensing (CS) and Total Variation (TV)- based iterative image reconstruction algorithms have received increased attention recently. This is due to the ability of such methods to reconstruct from limited and noisy data. Local TV methods fail to preserve texture details and fine structures, which are tedious for the method to distinguish from noise. In many cases local methods also create additional artifacts due to over smoothing. Non-Local Total Variation (NLTV) has been increasingly used for medical imaging applications. However, it is not updated in every iteration of the algorithm, has a high computational complexity and depends on the scale of pairwise parameters. In this work we propose using Adaptive Graph- based TV in combination with CS (ACSGT). Similar to NLTV our proposed method goes beyond spatial similarity between different regions of an image being reconstructed by establishing a connection between similar regions in the image regardless of spatial distance. However, it is computationally much more efficient and scalable when compared to NLTV due to the use of approximate nearest neighbor search algorithm. Moreover, our method is adaptive, i.e, it involves updating the graph prior every iteration making the connection between similar regions stronger. Since TV is a special case of graph TV the proposed method can be seen as a generalization of CS and TV methods. We test our proposed algorithm by reconstructing a variety of different phantoms from limited and corrupted data and observe that we achieve a better result with ACSGT in every case

Enhanced imaging of microcalcifications in digital breast tomosynthesis through improved image-reconstruction algorithms

PURPOSE: We develop a practical, iterative algorithm for image-reconstruction in under-sampled tomographic systems, such as digital breast tomosynthesis (DBT). METHOD: The algorithm controls image regularity by minimizing the image total $p$-variation (TpV), a function that reduces to the total variation when $p=1.0$ or the image roughness when $p=2.0$. Constraints on the image, such as image positivity and estimated projection-data tolerance, are enforced by projection onto convex sets (POCS). The fact that the tomographic system is under-sampled translates to the mathematical property that many widely varied resultant volumes may correspond to a given data tolerance. Thus the application of image regularity serves two purposes: (1) reduction of the number of resultant volumes out of those allowed by fixing the data tolerance, finding the minimum image TpV for fixed data tolerance, and (2) traditional regularization, sacrificing data fidelity for higher image regularity. The present algorithm allows for this dual role of image regularity in under-sampled tomography. RESULTS: The proposed image-reconstruction algorithm is applied to three clinical DBT data sets. The DBT cases include one with microcalcifications and two with masses. CONCLUSION: Results indicate that there may be a substantial advantage in using the present image-reconstruction algorithm for microcalcification imaging.Comment: Submitted to Medical Physic

Iterative CT reconstruction from few projections for the nondestructive post irradiation examination of nuclear fuel assemblies

The core components (e.g. fuel assemblies, spacer grids, control rods) of the nuclear reactors encounter harsh environment due to high temperature, physical stress, and a tremendous level of radiation. The integrity of these elements is crucial for safe operation of the nuclear power plants. The Post Irradiation Examination (PIE) can reveal information about the integrity of the elements during normal operations and off‐normal events. Computed tomography (CT) is a tool for evaluating the structural integrity of elements non-destructively. CT requires many projections to be acquired from different view angles after which a mathematical algorithm is adopted for reconstruction. Obtaining many projections is laborious and expensive in nuclear industries. Reconstructions from a small number of projections are explored to achieve faster and cost-efficient PIE. Classical reconstruction algorithms (e.g. filtered back projection) cannot offer stable reconstructions from few projections and create severe streaking artifacts. In this thesis, conventional algorithms are reviewed, and new algorithms are developed for reconstructions of the nuclear fuel assemblies using few projections. CT reconstruction from few projections falls into two categories: the sparse-view CT and the limited-angle CT or tomosynthesis. Iterative reconstruction algorithms are developed for both cases in the field of compressed sensing (CS). The performance of the algorithms is assessed using simulated projections and validated through real projections. The thesis also describes the systematic strategy towards establishing the conditions of reconstructions and finds the optimal imaging parameters for reconstructions of the fuel assemblies from few projections. --Abstract, page iii

Adaptive image synthesis for compressive displays

Recent years have seen proposals for exciting new computational display technologies that are compressive in the sense that they generate high resolution images or light fields with relatively few display parameters. Image synthesis for these types of displays involves two major tasks: sampling and rendering high-dimensional target imagery, such as light fields or time-varying light fields, as well as optimizing the display parameters to provide a good approximation of the target content. In this paper, we introduce an adaptive optimization framework for compressive displays that generates high quality images and light fields using only a fraction of the total plenoptic samples. We demonstrate the framework for a large set of display technologies, including several types of auto-stereoscopic displays, high dynamic range displays, and high-resolution displays. We achieve significant performance gains, and in some cases are able to process data that would be infeasible with existing methods.University of British Columbia (UBC Four Year Doctoral Fellowship)Natural Sciences and Engineering Research Council of Canada (Postdoctoral Fellowship)United States. Defense Advanced Research Projects Agency (DARPA SCENICC program)Alfred P. Sloan Foundation (Sloan Research Fellowship)United States. Defense Advanced Research Projects Agency (DARPA Young Faculty Award)University of British Columbia (Dolby Research Chair at UBC

Mini-Workshop: Deep Learning and Inverse Problems

Machine learning and in particular deep learning offer several data-driven methods to amend the typical shortcomings of purely analytical approaches. The mathematical research on these combined models is presently exploding on the experimental side but still lacking on the theoretical point of view. This workshop addresses the challenge of developing a solid mathematical theory for analyzing deep neural networks for inverse problems