Optimal selection of regularization parameter in total variation method for reducing noise in magnetic resonance images of the brain

Osadebey, Michael; Bouguila, Nizar; Arnold, Douglas L.

doi:10.1007/s13534-014-0126-2

Cited by 6 publications

(3 citation statements)

References 51 publications

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“…There are some proposals available in the literature; see Solo (1999), Osadebey et al (2014), Langer (2017. Soon after we uploaded our paper, a different tuning parameter free method appeared in Ortelli and van de Geer (2019b) which also achieves the optimal worst case ‹ O(V/ √ N ) rate of convergence.…”

Section: Tuning Free Tvdmentioning

confidence: 99%

“…The usual way out is to to do some form of cross validation. There are some proposals available in the literature; see Solo (1999), Osadebey et al (2014), Langer (2017. However, to the best of our knowledge, we do not know of a tuning parameter free method which provably achieves the optimal worst case ‹ O(V/ √ N ) rate of convergence.…”

Section: No Tuning Tvdmentioning

confidence: 99%

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New Risk Bounds for 2D Total Variation Denoising

Chatterjee

Goswami

2021

IEEE Trans. Inform. Theory

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2D Total Variation Denoising (TVD) is a widely used technique for image denoising. It is also an important nonparametric regression method for estimating functions with heterogenous smoothness. Recent results have shown the TVD estimator to be nearly minimax rate optimal for the class of functions with bounded variation. In this paper, we complement these worst case guarantees by investigating the adaptivity of the TVD estimator to functions which are piecewise constant on axis aligned rectangles. We rigorously show that, when the truth is piecewise constant with few pieces, the ideally tuned TVD estimator performs better than in the worst case. We also study the issue of choosing the tuning parameter.In particular, we propose a fully data driven version of the TVD estimator which enjoys similar worst case risk guarantees as the ideally tuned TVD estimator.

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Section: Tuning Free Tvdmentioning

confidence: 99%

Section: No Tuning Tvdmentioning

confidence: 99%

New Risk Bounds for 2D Total Variation Denoising

Chatterjee

Goswami

2021

IEEE Trans. Inform. Theory

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“…Biomedical signal denoising is one of the topics that are receiving an increasing interest in biomedical engineering applications; including images [1][2][3][4][5][6][7] and electroencephalogram (EEG) and electrocardiogram (ECG) [8][9][10]. For instance, biomedical signals such as ECG signal used to assess the cardiovascular condition of humans can be contaminated by noise due to physical parameters of recording instrument or background activity [11].…”

Section: Introductionmentioning

confidence: 99%

A weighted bio-signal denoising approach using empirical mode decomposition

Lahmiri

Boukadoum

2015

Biomed. Eng. Lett.

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Purpose The purpose of this study is to show the effectiveness of a physiological signal denoising approach called EMD-DWT-CLS. Methods This paper presents a new approach for signal denoising based on empirical mode decomposition (EMD), discrete wavelet transform (DWT) thresholding, and constrained least squares (CLS). In particular, the noisy signal is decomposed by empirical mode decomposition (EMD) to obtain intrinsic mode functions (IMFs) plus a residue. Then, each IMF is denoised by using the discrete wavelet transform (DWT) thresholding technique. Finally, the denoised signal is recovered by performing a weighted summation of the denoised IMFs except the residue. The weights are determined by estimating a constrained least squares coefficients; where, the sum of the coefficients is constrained to unity. We used human ECG and EEG signals, and also two EEG signals from left and right cortex of two healthy adult rats. Results The 36 experimental results show that the proposed EMD-DWT-CLS provides higher signal-to-noise ratio (SNR) and lower mean of squared errors (MSE) than the classical EMD-DWT model. Conclusions Based on comparison with classical EMD-DWT model used in the literature, the proposed approach was found to be effective in human and animal physiological signals denoising.

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Intelligent Wavelet Coefficients Thresholding: Speckle Reduction Approach in SAR Imagery

Jannati,

Valadan Zoej

2024

J Indian Soc Remote Sens

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Optimal selection of regularization parameter in total variation method for reducing noise in magnetic resonance images of the brain

Cited by 6 publications

References 51 publications

New Risk Bounds for 2D Total Variation Denoising

New Risk Bounds for 2D Total Variation Denoising

A weighted bio-signal denoising approach using empirical mode decomposition

Intelligent Wavelet Coefficients Thresholding: Speckle Reduction Approach in SAR Imagery

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