Parallel-beam CT sparse angle reconstruction method based on non-standard fast fourier transform and alternating direction method

Abstract

The invention discloses a parallel-beam CT sparse angle reconstruction method based on non-standard fast Fourier transformation and alternating direction method, which overcomes the problem that the image reconstruction method still has defects in the prior art. The steps of the invention are as follows: perform one-dimensional FFT transformation on the projection data collected by parallel beam CT to obtain the corresponding projection frequency domain data in polar coordinates; based on the projection frequency domain based on polar coordinates, use NUFFT technology to realize image space Frequency domain transformation to avoid the loss of precision caused by frequency domain interpolation, and establish a TV minimization image reconstruction model; in the process of restoring the image to be reconstructed from the projected frequency domain, a frequency domain optimization model based on TV minimization is designed, using alternate The direction method is used to iteratively solve the TV minimization model through the augmented Lagrangian function method and the alternating direction multiplier method. The invention combines the NUFFT technology and the advanced alternating direction idea in the optimization strategy, can avoid interpolation in the frequency domain, requires less computing and storage resources, and has good convergence performance.

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 projection, the NUFFT method is used to calculate Projection and back-projection, thus speeding up the reconstruction speed. The disadvantage of this method is that the iterative framework adopts the traditional CG method. This method has a slow convergence speed and requires a high number of angles for the projection data. It is difficult to reconstruct sparse angles. Get 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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