Multiplicative Noise Removal Based on the Smooth Diffusion Equation

Shan, Xiujie; Sun, Jinwei; Guo, Zhichang

doi:10.1007/s10851-018-00870-z

Cited by 24 publications

(12 citation statements)

References 43 publications

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“…The two-dimensional discretisation of the procedure is presented in Appendix B. This scheme has been adopted due to its simplicity, though it should be noted that alternative and more computationally efficient approaches have been developed, based on operator splitting or factored schemes [15,40,32] The behaviour of the anisotropic diffusion equation can be observed with simple tests. Here we take as examples two 1D functions: i) a smooth trigonometric function f (x) = sin(x) + cos(3x), and ii) a series of incremental step functions.…”

Section: An Overview Of the Perona-malik Methodsmentioning

confidence: 99%

Robust and effective automatic parameter choice for medical image filtering.

João

Gambaruto

Pereira

et al. 2019

Computer Methods in Biomechanics and Biomedical Engineering: Im

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The analysis of medical image data currently requires the interpretation of a trained and experienced user. The technological advances in imaging machinery and the understanding of disease onset, as well as medical planning, all favour the need for ever more automatic and robust methods for evaluating the health state of a subject. Here, we concentrate on methods for processing medical image data, as currently provided by existing imaging technologies, in particular the effectiveness of automatic image filtering in order to remove noise and improve the sharpness of distinct objects. The filtering approach is based on a partial differential equation, namely the Perona-Malik anisotropic diffusion equation. The approach adopted for terminating the iterative filtering procedure is based on image quality descriptors. In specific, we observe the rate of change of these to infer the transient effects of the filtering process. The entire pipeline is demonstrated to work effectively on different sets of medical image data, including MRI, CTA and CT, both in individual 2-D images in a stack, as well as treating the complete 3D volumetric dataset.

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Section: An Overview Of the Perona-malik Methodsmentioning

confidence: 99%

Robust and effective automatic parameter choice for medical image filtering.

João

Gambaruto

Pereira

et al. 2019

Computer Methods in Biomechanics and Biomedical Engineering: Im

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“…There are adaptive filters such as filters based on MAP estimator [2,3] and nonlocal means filter [6].Wavelet method or wavelet MAP combined method are reported in the despeckling problems [7]. Anisotropic diffusion methods [8,9] and nonlinear diffusion equation based method [4,5] are also proposed for speckle reduction. Unlike additive Gaussian noise, speckle noise is much more difficult to be removed from the corrupted images, mainly because of not only their multiplicative nature, but also their statistical characteristic [10].…”

Section: Introductionmentioning

confidence: 99%

“…In [13], a convex variational model based on generalized Kullback-Leibler distance was proposed to remove the speckles in ultrasound images. For the multiplicative Gamma noise removal, a nonlinear diffusion equation with smooth solution was proposed in [14]. Methods based on total variation (TV), which have outstanding performance in the removal of additive Gaussian noise and the preservation of edges, such as Rudin-Osher-Fatami (ROF) model [15], have been introduced in the literature of speckle reduction.…”

Section: Introductionmentioning

confidence: 99%

An Adaptive Data-Fitting Model for Speckle Reduction of Log-Compressed Ultrasound Images

Gao¹

2020

CSIAM-AM

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A good statistical model of speckle formation is useful to design a good speckle reduction model for clinical ultrasound images. We propose a new general distribution to describe the distribution of speckle in clinical ultrasound images according to a log-compression algorithm of clinical ultrasound imaging. A new variational model is designed to remove the speckle noise with the proposed general distribution. The efficiency of the proposed model is confirmed by experiments on synthetic images and real ultrasound images. Compared with previous variational methods which assign a designated distribution, the proposed method is adaptive to remove different kinds of speckle noise by estimating parameters to find suitable distribution. The experiments show that the proposed method can adaptively remove different types of speckle noise.

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“…In addition, the rapid development of sensors in the last few years has brought us new opportunities, resulting in the birth of optical-driven non-local SAR speckle removal technology. Secondly, the popularity of PDE-based methods [42,32,31] relies on nonlinear diffusion techniques. The second order equation usually has the extremum principle to ensure the stability and smoothness of the restoration results.…”

mentioning

confidence: 99%

“…The second order equation usually has the extremum principle to ensure the stability and smoothness of the restoration results. In particular, a nonlinear diffusion equation with smooth solution is proposed in [31]. The fourth order equation can improve the staircase effect, but the equation theory is difficult to carry out.…”

mentioning

confidence: 99%

An adaptive total variational despeckling model based on gray level indicator frame

Li¹,

Guo²,

Wu³

2021

IPI

Self Cite

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For the characteristics of the degraded images with multiplicative noise, the gray level indicators for constructing adaptive total variation are proposed. Based on the new regularization term, we propose the new convex adaptive variational model. Then, considering the existence, uniqueness and comparison principle of the minimizer of the functional. The finite difference method with rescaling technique and the primal-dual method with adaptive step size are used to solve the minimization problem. The paper ends with a report on numerical tests for the denoising of images subject to multiplicative noise, the comparison with other methods is provided as well.

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Multiplicative Noise Removal Based on the Smooth Diffusion Equation

Cited by 24 publications

References 43 publications

Robust and effective automatic parameter choice for medical image filtering.

Robust and effective automatic parameter choice for medical image filtering.

An Adaptive Data-Fitting Model for Speckle Reduction of Log-Compressed Ultrasound Images

An adaptive total variational despeckling model based on gray level indicator frame

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