Publication

Iterative FBP For Improved Reconstruction Of X-Ray Differential Phase-Contrast Tomograms

Michaël Unser, Cédric René Jean Vonesch, Masih Nilchian, Peter Modregger, Marco Stampanoni
2013
Conference Papers

Abstract

X-ray differential phase-contrast tomography is a recently-developed modality for the imaging of low-contrast biological samples. Its mathematical model is based on the first derivative of the Radon transform and the images, in practice, are reconstructed using a variant of filtered back-projection (FBP). In this paper, we develop an alternative reconstruction algorithm with the aim of reducing the number of required views, while maintaining image quality. To that end, we discretize the forward model based on polynomial B-spline functions. Then, we formulate the reconstruction as a regularized weighted-norm optimization problem with a penalty on the total variation (TV) of the solution. This leads to the derivation of a novel iterative algorithm that involves an alternation of gradient updates (FBP step) and shrinkage-thresholding (within the framework of the fast iterative shrinkage-thresholding algorithm). Experiments with real data suggest that the proposed method significantly improves upon FBP; it can handle a drastic reduction in the number of projections without noticeable degradation of the quality with respect to the standard procedure.

Official source

https://infoscience.epfl.ch/entities/publication/ba1eeb71-508b-4208-95ba-7385205beb8b

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Michaël Unser, Cédric René Jean Vonesch, Masih Nilchian, Peter Modregger, Marco Stampanoni
2013
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ba1eeb71-508b-4208-95ba-7385205beb8b

About this result

Related concepts (30)

Iterative reconstruction

Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step.

Tomographic reconstruction

Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner.

Radon transform

In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the line integral of the function over that line. The transform was introduced in 1917 by Johann Radon, who also provided a formula for the inverse transform. Radon further included formulas for the transform in three dimensions, in which the integral is taken over planes (integrating over lines is known as the X-ray transform).

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