Abstract
X-ray based Phase-Contrast Imaging (PCI) techniques have been demonstrated to enhance the visualization of soft tissues in comparison to conventional imaging methods. Nevertheless the delivered dose as reported in the literature of biomedical PCI applications often equals or exceeds the limits prescribed in clinical diagnostics. The optimization of new computed tomography strategies which include the development and implementation of advanced image reconstruction procedures is thus a key aspect. In this scenario, we implemented a dictionary learning method with a new form of convex functional. This functional contains in addition to the usual sparsity inducing and fidelity terms, a new term which forces similarity between overlapping patches in the superimposed regions. The functional depends on two free regularization parameters: a coefficient multiplying the sparsity-inducing norm of the patch basis functions coefficients, and a coefficient multiplying the norm of the differences between patches in the overlapping regions. The solution is found by applying the iterative proximal gradient descent method with FISTA acceleration. The gradient is computed by calculating projection of the solution and its error backprojection at each iterative step. We study the quality of the solution, as a function of the regularization parameters and noise, on synthetic data for which the solution is a-priori known. We apply the method on experimental data in the case of Differential Phase Tomography. For this case we use an original approach which consists in using vectorial patches, each patch having two components: one per each gradient component. The resulting algorithm, implemented in the European Synchrotron Radiation Facility tomography reconstruction code PyHST, has proven to be efficient and well-adapted to strongly reduce the required dose and the number of projections in medical tomography.
Highlights
During the past two decades X-ray Phase Contrast Imaging (PCI) has shown a remarkable enhancement of image contrast and sensitivity for soft tissue
There are mainly two ways: either the sparsity structure is a-priori known and an appropriate basis of functions can be built from the beginning, or it must be automatically learned from a set with the dictionary learning technique [1]
This method consists in building an over-complete basis of functions, over an m|m domain, such that, taken an m|m patch from the studied image, the patch can be approximated with good precision as a linear combination of a small number Nvvm2 of basis functions
Summary
During the past two decades X-ray Phase Contrast Imaging (PCI) has shown a remarkable enhancement of image contrast and sensitivity for soft tissue. There are mainly two ways: either the sparsity structure is a-priori known and an appropriate basis of functions can be built from the beginning, or it must be automatically learned from a set with the dictionary learning technique [1]. This method consists in building an over-complete basis of functions, over an m|m domain, such that, taken an m|m patch from the studied image, the patch can be approximated with good precision as a linear combination of a small number Nvvm of basis functions. The noise will be reproduced only if we allow a large number of components (the patch basis is over-complete so it can represent the noise) while it will be effectively filtered out if we approximate the noisy image with a small number of components
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