A CT Image Reconstruction Method Based on Variational Inequality under Sparse Sampling Angles

Abstract

The invention discloses a CT (Computed Tomography) image reconstruction method based on a variational inequality at a sparse sampling angle. The CT image reconstruction method comprises the following steps: (1) carrying out equal-angle interval projection scanning within an angle range of 0-180 degrees by aiming at a fan-beam CT to obtain spare projection data y, wherein an angle interval in a projection direction is between 2 and 6 degrees; (2) calculating a projection matrix A through an X-ray source, a detector and the position information of an object to be reconstructed; (3) according to the projection data y obtained in the step (1) and the projection matrix A obtained in the step (2), simultaneously introducing the sparsity and the non-negativity of an image gradient to serve as priori knowledge to obtain a reconstruction model of an image reconstruction problem at the sparse sampling angle; (4) converting the reconstruction model in the step (3) into a variational inequality form; and (5) solving the variational inequality in the step (4) to obtain a reconstructed image. On the premise that image reconstruction quality is guaranteed, reconstruction convergence speed can be quickened, and single-iteration time is shortened.

Description

Technical field [0001] The invention relates to the field of internal image reconstruction of components and medical CT image reconstruction in the process of precision electronic packaging, in particular to a CT image reconstruction method based on variational inequality under sparse sampling angles. Background technique [0002] Computed Tomography (CT) is a product of the combination of X-ray photography technology and complex computer signal processing methods. X-ray projections are performed on objects in different directions, and the cross-sectional information of the objects is obtained through the measured projection data. The internal structure of the object can be reconstructed accurately and intuitively. At present, CT technology has been widely used in security inspection, industrial non-destructive inspection, and medical diagnosis. [0003] In the process of CT reconstruction, we often can only obtain incomplete, sparsely sampled projection data. For example, consid...

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Problems solved by technology

However, these iterative reconstruction methods that consider regularization, such as the Projection On Convex Sets-Total Variation (POCS-TV) algorithm, have a significant impact on the reconstruction speed due to the incompleteness of the projection data. It often takes many iterations to obtain a high-quality reconstructed image, the convergence speed is slow, and the single iteration time is long

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