A Conjugate Gradient Reconstruction Method for Magnetic Resonance Image Based on Nonlinear Action Function

Abstract

The present invention relates to a conjugate gradient method based on a nonlinear action function, in particular to a magnetic resonance image reconstruction method based on a conjugate gradient method based on a nonlinear action function, comprising the following steps: Step 1: obtaining under-sampled k Spatial magnetic resonance image data; Step 2: Transform the L0 norm optimization into solving the L1 norm optimization problem; Step 3: Consider the noise in the imaging process; Step 4: Utilize the k-space data consistency; Step 5: Introduce a The non-linear action function Sigmoid function dynamically adjusts the step size of the conjugate gradient method; step six: use the modified conjugate gradient method in step five. This method can dynamically adjust the step size of the conjugate gradient method without line search, and greatly improves the convergence speed while ensuring the accuracy of the reconstructed image. The method can greatly improve the convergence speed of the conjugate gradient method while ensuring the accuracy of image reconstruction, and is suitable for undersampling magnetic resonance image reconstruction of different human body parts.

Description

technical field [0001] The invention relates to a conjugate gradient method for dynamically adjusting the step size based on a nonlinear action function, which belongs to the field of image processing. Background technique [0002] The sampling mode of k-space in traditional MRI satisfies the Nyquist criterion, and violation of the Nyquist criterion will lead to artifacts in the linear reconstruction of images. The redundancy of MRI data makes domestic and foreign scholars devote themselves to finding ways to reduce the amount of data without reducing the quality of imaging. The theory of compressed sensing breaks through the Nyquist criterion, and the compressibility of MR images in a specific transform domain makes it naturally suitable for the theory of compressed sensing. [0003] Accurately reconstructing images is an important step in the application of compressive sensing theory to MRI. MRI image reconstruction based on compressed sensing essentially solves a constr...

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Problems solved by technology

The conjugate gradient method is a classic and simpler algorithm for solving this problem, but its disadvantage is that it is too slow, so it lacks practicability in real applications

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