Parallel beam CT sparse angle reconstruction method based on nonuniform fast Fourier transformation and alternating direction method

Abstract

The invention discloses a parallel beam CT sparse angle reconstruction method based on nonuniform fast Fourier transformation and an alternating direction method. The problem that defects still exist in an image reconstruction method in the prior art is solved. The method includes the following steps that one-dimensional FFT transformation is performed on projection data acquired through parallel beam CT, and projection frequency domain data under corresponding polar coordinates are obtained; on the basis of a projection frequency domain of the polar coordinates, image space frequency domain transformation is achieved through the NUFFT technology so that precision loss caused by frequency domain interpolation can be avoided, and a TV minimization image reconstruction model is established; when an image to be reconstructed is restored from the projection frequency domain, a frequency domain optimization model based on TV minimization is designed, and by means of the alternating direction method, iteration solving is performed on a TV minimization model through an augmented Lagrangian function method and an alternating direction multiplier method. According to the method, due to the combination of the NUFFT technology and an advanced alternating direction idea in an optimization strategy, frequency domain interpolation can be avoided, the demand for calculation and storage resources is small, and convergence performance is good.

Description

technical field [0001] The invention relates to a CT image reconstruction method, in particular to a parallel beam CT sparse angle reconstruction method based on non-standard fast Fourier transform and alternating direction method. Background technique [0002] Computed Tomography (CT) is an advanced perspective imaging technology. With its advantages of non-destructive, accurate and three-dimensional visualization, CT has been widely used in various fields such as industrial non-destructive testing and medical diagnosis. With the continuous improvement of the performance of CT equipment, the problem of X-ray radiation generated in its clinical application has also aroused widespread concern. Effectively reducing the radiation dose of CT scanning is a hot spot and difficulty that needs to be solved urgently in the field of CT. [0003] In recent years, CT reconstruction using sparse angle projection is an effective way to reduce radiation dose by sampling CT sparse angle ima...

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Problems solved by technology

[0006] Through the literature search of the existing technology, it is found that the implementation method adopted in the literature of parallel beam CT reconstruction using non-standard fast Fourier transform has the shortcomings of high requirements for the integrity of the projection data set and slow iterative convergence.

In 2004, Matej S, Fessler J and Kazantsev G published the paper "Iterative tomographic image reconstruction using Fourier-based forward and back-projectors" in the journal IEEE Transactions on Medical Imaging. In the iterative reconstruction of parallel beam projections, the NUFFT method was used to Calculate the projection and back-projection, thereby speeding up the reconstruction speed. The disadvantage of this method is that the iterative framework uses the traditional CG method, which has a slow convergence speed and requires a high number of angles for the projection data. For the reconstruction of sparse angles It is difficult to obtain high-quality reconstructed images

[0012] The above reconstruction methods based on TV minimization are all airspace iterative reconstruction algorithms. Although the iterative framework structure is better than the traditional iterative algorithm, there are still problems of large consumption of computing resources and storage resources.

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