Nonlinear total variation based noise removal algorithms
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Convex analysis and variational problems
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The mathematics of computerized tomography
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Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
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A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
IEEE Transactions on Information Theory
IEEE Transactions on Image Processing
Iterative Regularization and Nonlinear Inverse Scale Space Applied to Wavelet-Based Denoising
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Mapping of visual receptive fields by tomographic reconstruction
Neural Computation
X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting
Journal of Scientific Computing
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We develop two new algorithms for tomographic reconstruction which incorporate the technique of equally-sloped tomography (EST) and allow for the optimized and flexible implementation of regularization schemes, such as total variation constraints, and the incorporation of arbitrary physical constraints. The founding structure of the developed algorithms is EST, a technique of tomographic acquisition and reconstruction first proposed by Miao et al. in 2005 for performing tomographic image reconstructions from a limited number of noisy projections in an accurate manner by avoiding direct interpolations. EST has recently been successfully applied to coherent diffraction microscopy, electron microscopy, and computed tomography for image enhancement and radiation dose reduction. However, the bottleneck of EST lies in its slow speed due to its higher computation requirements. In this paper, we formulate the EST approach as a constrained problem and subsequently transform it into a series of linear problems, which can be accurately solved by the operator splitting method. Based on these mathematical formulations, we develop two iterative algorithms for tomographic image reconstructions through EST, which incorporate Bregman and continuative regularization. Our numerical experiment results indicate that the new tomographic image reconstruction algorithms not only significantly reduce the computational time, but also improve the image quality. We anticipate that EST coupled with the novel iterative algorithms will find broad applications in X-ray tomography, electron microscopy, coherent diffraction microscopy, and other tomography fields.