Abstract
State-of-the-art techniques for phase retrieval in propagation based X-ray phase-contrast imaging are aiming to solve an underdetermined linear system of equations. They commonly employ Tikhonov regularization - an L2-norm regularized deconvolution scheme - despite some of its limitations. We present a novel approach to phase retrieval based on Total Variation (TV) minimization. We incorporated TV minimization for deconvolution in phase retrieval using a variety of the most common linear phase-contrast models. The results of our TV minimization was compared with Tikhonov regularized deconvolution on simulated as well as experimental data. The presented method was shown to deliver improved accuracy in reconstructions based on a single distance as well as multiple distance phase-contrast images corrupted by noise and hampered by errors due to nonlinear imaging effects.
Highlights
The field of X-ray phase-contrast imaging (PCI) has been growing rapidly
In this paper we introduce a Total Variation (TV) minimization approach for solving the inverse problem of phase retrieval in propagation-based X-ray PCI based on various linear models
Reconstructions based on simulated and experimental data show that phase retrieval based on TV minimization can significantly outperform the current practice, a deconvolution approach with L2 regularization
Summary
The field of X-ray phase-contrast imaging (PCI) has been growing rapidly. X-ray PCI found applications in materials science, ranging from investigating the microstructure of carbon-based materials [1, 2] to in-situ measurements of dynamic processes taking place in metal alloys and semiconductors [3,4,5]. A major effort was aimed at the development of linear approximations to the image formation of PCI that would permit a stable solution of the resulting inverse problem [12,13,14,15,16] Using these approximations, the phase and attenuation images of the specimen can be calculated from a series of phase-contrast images acquired at different propagation distances. Such a solution may not be optimal, especially when it results in a strong suppression of a large band of low frequencies in multi-distance retrieval methods Another regularization approach that is currently used in an increasing number of image reconstruction applications is called Total Variation (TV) minimization. Frequency weighting permits to account for the frequency-dependent nature of the signal-to-noise ratio and is shown to have a significant influence on the accuracy of the phase retrieval
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