Magnetic resonance image reconstruction via L0-norm minimization

Chen, Hanjie; Tao, Jinxu; Sun, Yusheng; Ye, Z.; Qiu, Bensheng

doi:10.1049/cp.2015.0780

Cited by 4 publications

(3 citation statements)

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“…The optimization metric (i.e., the objective function) can be set up as the sum of the l 0 -norm of all pixels in the image as (5) One difficulty of minimizing (5) is that the l 0 -norm is not differentiable and is not easy to optimize. One common method to mitigate the difficulty is to use the l 1 -norm approximation [9][10][11][12][13].…”

Section: Methodsmentioning

confidence: 99%

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Morphing from the TV-Norm to the l0-Norm

L Zeng

2024

BJSTR

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For piecewise constant objects, the images can be reconstructed with under-sampled measurements. The gradient image of a piecewise image is sparse. If a sparse solution is a desired solution, an l 0 -norm minimization method is effective to solve an under-determined system. However, the l 0 -norm is not differentiable, and it is not straightforward to minimize an l 0 -norm. This paper suggests a function that is like the l 0 -norm function, and we refer to this function as meta l 0 -norm. The subdifferential of the meta l 0 -norm has a simple explicit expression. Thus, it is straightforward to derive a gradient descent algorithm to enforce the sparseness in the solution. In fact, the proposed meta norm is a transition that varies between the TV-norm and the l 0 -norm. As an application, this paper uses the proposed meta l 0 -norm for few-view tomography. Computer simulation results indicate that the proposed meta l 0 -norm effectively guides the image reconstruction algorithm to a piecewise constant solution. It is not clear whether the TV-norm or the l 0 -norm is more effective in producing a sparse solution.

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Section: Methodsmentioning

confidence: 99%

“…Many researchers have attempted to tackle the l 0 -norm minimization problem. The work in [5] converted the l 0 -norm minimization problem into an unconstrained augment Lagrange problem. The work in [6] solved the l 0 -norm minimization problem by introducing auxiliary variables.…”

Section: Introductionmentioning

confidence: 99%

Morphing from the TV-Norm to the l0-Norm

L Zeng

2024

BJSTR

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“…Quality evaluation methods at the acquisition stage involves modifying the design of system hardware, optimizing acquisition parameters and the implementation of undersampling and constrained reconstruction schemes to reduce acquisition time and generate high quality images. Proposed methods in this category include [20], [6], [37], [32], [53], [18]. There are very few contributions on post-acquisition quality evaluation for brain MRI images.…”

Section: Introductionmentioning

confidence: 99%

No‐reference quality measure in brain MRI images using binary operations, texture and set analysis

Osadebey

Pedersen

Arnold

et al. 2017

IET Image Processing

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We propose a new application-specific post-acquisition quality evaluation method for brain MRI images. The domain of a MRI slice is regarded as the universal set. Four feature images; grayscale, local entropy, local contrast and local standard deviation are extracted from the slice and transformed into the binary domain. Each feature image is regarded as a set enclosed by the universal set. Four qualities attribute; lightness, contrast, sharpness and texture details are described by four different combinations of the feature sets. In an ideal MRI slice the four feature sets are identically equal. The degree of distortion in real MRI slice is quantified by the fidelity between the sets that describe a quality attribute. Noise is the fifth quality attribute and it is described by the slice Euler number region property. The total quality score is the weighted sum of the five quality scores. Our proposed method addresses the current challenges in image quality evaluation. It is simple, easy-to-use and easy-to-understand. Incorporation of binary transformation in the proposed method reduces computational as well as operational complexity of the algorithm. We provide experimental results that demonstrate the efficacy of our proposed method on good quality images and on common distortions in MRI images of the brain.

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Structural smoothness low-rank matrix recovery via outlier estimation for image denoising

Wang

et al. 2021

Multimedia Systems

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Magnetic resonance image reconstruction via L0-norm minimization

Cited by 4 publications

References 0 publications

Morphing from the TV-Norm to the l0-Norm

Morphing from the TV-Norm to the l0-Norm

No‐reference quality measure in brain MRI images using binary operations, texture and set analysis

Structural smoothness low-rank matrix recovery via outlier estimation for image denoising

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