Abstract
This paper introduces new gridding projectors designed to efficiently perform analytical and iterative tomographic reconstruction, when the forward model is represented by the derivative of the Radon transform. This inverse problem is tightly connected with an emerging X-ray tube- and synchrotron-based imaging technique: differential phase contrast based on a grating interferometer. This study shows, that the proposed projectors, compared to space-based implementations of the same operators, yield high quality analytical and iterative reconstructions, while improving the computational efficiency by few orders of magnitude.
Highlights
The gridding method is a technique designed to retrieve a 2D or 3D signal from samples of its Fourier transform located on a non-Cartesian lattice [1]
The gridding method (GM) retrieves a signal from samples of its Fourier transform located on a non Cartesian lattice: the samples are, first, convolved with a smooth and rapidly decaying window function, the inverse fast Fourier transform (IFFT) is computed and, the contribution of the window function is removed from the signal in real space [1]
An approach disregarding the specific choice of iterative algorithm is followed: the forward projection computed with differentiated forward gridding projector (DFRP) is compared to the analytical sinogram and is, reconstructed with the Hilbert-filtered DBRP
Summary
The gridding method is a technique designed to retrieve a 2D or 3D signal from samples of its Fourier transform located on a non-Cartesian lattice [1]. This work introduces a gridding forward and backprojector designed to perform analytical and iterative reconstruction of tomographic datasets, where the forward model is represented by the derivative of the Radon transform These operators are, in particular, applied to the reconstruction of differential phase contrast (DPC) tomographic data acquired with a grating interferometer. Recent interest in the biomedical field for grating interferometry, when investigating dose sensitive specimens, has lead to several studies aimed at extending established CT iterative algorithms to the DPC case In this regard, ad-hoc forward projectors working with a blob [22] and a cubic B-spline [23] basis and iterative schemes relying on different algorithms (the regularized maximum likelihood [22], the separable paraboloidal surrogate [24], the alternate direction method of multipliers [25] and a combination of statistical model and thresholding [26]) have been proposed. The projectors proposed here greatly reduce the computational times required for analytical and, in particular, iterative reconstruction, while preserving the accuracy of the results
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