Node-Adaptive Regularization for Graph Signal Reconstruction

Background: Image reconstruction of magnetic induction tomography (MIT) is a typical ill-posed inverse problem, which means that the measurements are always far from enough. Thus, MIT image reconstruction results using conventional algorithms such as linear back projection and Landweber often suffer from limitations such as low resolution and blurred edges. Methods: In this paper, based on the recent finite rate of innovation (FRI) framework, a novel image reconstruction method with MIT system is presented. Results: This is achieved through modeling and sampling the MIT signals in FRI framework, resulting in a few new measurements, namely, fourier coefficients. Because each new measurement contains all the pixel position and conductivity information of the dense phase medium, the illposed inverse problem can be improved, by rebuilding the MIT measurement equation with the measurement voltage and the new measurements. Finally, a sparsity-based signal reconstruction algorithm is presented to reconstruct the original MIT image signal, by solving this new measurement equation. Conclusion: Experiments show that the proposed method has better indicators such as image error and correlation coefficient. Therefore, it is a kind of MIT image reconstruction method with high accuracy.

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An Algorithm Combining Analysis-based Blind Compressed Sensing and Nonlocal Low-rank Constraints for MRI Reconstruction

Current Medical Imaging Formerly Current Medical Imaging Reviews ◽

10.2174/1573405614666180130151333 ◽

2019 ◽

Vol 15 (3) ◽

pp. 281-291 ◽

Cited By ~ 1

Author(s):

Mei Sun ◽

Jinxu Tao ◽

Zhongfu Ye ◽

Bensheng Qiu ◽

Jinzhang Xu ◽

...

Keyword(s):

Compressed Sensing ◽

Signal Reconstruction ◽

Low Rank ◽

Mr Images ◽

Scanning Time ◽

Previous State ◽

Rank Approximation ◽

Mri Reconstruction ◽

Magnetic Resonance Imaging Mri ◽

Rank Constraints

Background: In order to overcome the limitation of long scanning time, compressive sensing (CS) technology exploits the sparsity of image in some transform domain to reduce the amount of acquired data. Therefore, CS has been widely used in magnetic resonance imaging (MRI) reconstruction. </P><P> Discussion: Blind compressed sensing enables to recover the image successfully from highly under- sampled measurements, because of the data-driven adaption of the unknown transform basis priori. Moreover, analysis-based blind compressed sensing often leads to more efficient signal reconstruction with less time than synthesis-based blind compressed sensing. Recently, some experiments have shown that nonlocal low-rank property has the ability to preserve the details of the image for MRI reconstruction. Methods: Here, we focus on analysis-based blind compressed sensing, and combine it with additional nonlocal low-rank constraint to achieve better MR images from fewer measurements. Instead of nuclear norm, we exploit non-convex Schatten p-functionals for the rank approximation. </P><P> Results & Conclusion: Simulation results indicate that the proposed approach performs better than the previous state-of-the-art algorithms.

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