Image enhancement and denoising by complex diffusion processes

Gilboa, Guy; Sochen, Nir; Zeevi, Yehoshua Y.

doi:10.1109/tpami.2004.47

Cited by 424 publications

(349 citation statements)

References 21 publications

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“…[11][12][13]. First, the image is processed with a DWT [15] for decomposition purpose. As a result, the image is decomposed into low-low, low-high, high-low, and high-high sub-band.…”

Section: Methodsmentioning

confidence: 99%

“…The complex fundamental solution h(x;t) should satisfy the following relationship [15] I x; t ( ) = I 0 * h x; t ( )…”

Section: Complex Diffusion Processesmentioning

confidence: 99%

“…Finally, the denoised image is reconstructed based on the denoised BIMFs. Similarly, we apply the DWT [11][12][13], fourth-order PDE (FOPDE) [14], and linear and non-linear complex diffusion processes (NLCDP) [15] to each extracted tBIMF (BIMFs where Student's PDF is incorporated in mean envelope computation) for denoising purpose. The denoised image is recovered by summing up all the denoised tBIMFs.…”

Section: Introductionmentioning

confidence: 99%

“…The FOPDE is employed as it avoids blocky effects while achieving good tradeoff between noise removal and edge preservation [14]. The LCDP and NLCDP combine the diffusion equation with the free Schrödinger equation [15]. The main advantages of complex diffusion processes follow [15].…”

Section: Introductionmentioning

confidence: 99%

“…The LCDP and NLCDP combine the diffusion equation with the free Schrödinger equation [15]. The main advantages of complex diffusion processes follow [15]. First, there exists a stable diffusion process over the wide range of the angular orientation.…”

Section: Introductionmentioning

confidence: 99%

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Image denoising in bidimensional empirical mode decomposition domain: the role of Student's probability distribution function

Lahmiri

2015

Healthcare Technology Letters

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Hybridisation of the bi-dimensional empirical mode decomposition (BEMD) with denoising techniques has been proposed in the literature as an effective approach for image denoising. In this Letter, the Student's probability density function is introduced in the computation of the mean envelope of the data during the BEMD sifting process to make it robust to values that are far from the mean. The resulting BEMD is denoted tBEMD. In order to show the effectiveness of the tBEMD, several image denoising techniques in tBEMD domain are employed; namely, fourth order partial differential equation (PDE), linear complex diffusion process (LCDP), non-linear complex diffusion process (NLCDP), and the discrete wavelet transform (DWT). Two biomedical images and a standard digital image were considered for experiments. The original images were corrupted with additive Gaussian noise with three different levels. Based on peaksignal-to-noise ratio, the experimental results show that PDE, LCDP, NLCDP, and DWT all perform better in the tBEMD than in the classical BEMD domain. It is also found that tBEMD is faster than classical BEMD when the noise level is low. When it is high, the computational cost in terms of processing time is similar. The effectiveness of the presented approach makes it promising for clinical applications. Introduction:The bi-dimensional empirical mode decomposition (BEMD) is the two-dimensional (2D) version of the original empirical mode decomposition of Huang et al. [1] which is an adaptive multi-resolution analysis technique that decomposes a given signal into a finite sum of components called intrinsic mode functions (IMFs), plus a residue. The empirical mode decomposition algorithm is based on a sifting process that successively estimates the mean envelope of an unknown signal as the average of the upper and lower envelopes, minus a residual component. In particular, low order IMFs represent fast oscillations (high frequency modes), and high order IMFs represent slow oscillations (low frequency modes). The IMFs are local and auto-adaptive to the input data. Hence, the merit of using the EMD is that it is driven by the input data. Unlike the wavelet transform, the EMD does not require a-priori basis function selection, since the IMFs are automatically derived from the input signal. In addition, the EMD is effective for the analysis of both stationary and non-stationary signals, and it is a non-linear decomposition technique.To address the problem of mean sensibility to outliers during the sifting process, an adjusted empirical mode decomposition method built on Student's probability density function (PDF) denoted by tEMD [2] where the data was transformed with the Student PDF prior to computation. Because Student's PDF has longer tails than the normal distribution, it is more robust to values that are far from the mean. In particular, it is less susceptible to signal variance fluctuations, which may lead to more representative mean envelope curves when applying the EMD algorithm. The tEMD was found to be mo...

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“…[11][12][13]. First, the image is processed with a DWT [15] for decomposition purpose. As a result, the image is decomposed into low-low, low-high, high-low, and high-high sub-band.…”

Section: Methodsmentioning

confidence: 99%

“…The complex fundamental solution h(x;t) should satisfy the following relationship [15] I x; t ( ) = I 0 * h x; t ( )…”

Section: Complex Diffusion Processesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Image denoising in bidimensional empirical mode decomposition domain: the role of Student's probability distribution function

Lahmiri

2015

Healthcare Technology Letters

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A Modified Guided Filter to Denoise Seismic Attributes

Chaki¹,

Happy²,

Routray³

et al. 2022

Handbook of Petroleum Geoscience

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Processing the image gradient field using a topographic primal sketch approach

Gambaruto

2015

Numer Methods Biomed Eng

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Processing the image gradient field using a topographic primal sketch approachComputer Applications in Science & Engineering (CASE) Nexus I -Campus Nord UPC, C/ Jordi Girona 2, 08034 Barcelona, Spain AbstractThe spatial derivatives of the image intensity provide topographic information that may be used to identify and segment objects. The accurate computation of the derivatives is often hampered in medical images by the presence of noise and a limited resolution. This paper focuses on accurate computation of spatial derivatives and their subsequent use to process an image gradient field directly, from which an image with improved characteristics can be reconstructed. The improvements include noise reduction, contrast enhancement, thinning object contours and the preservation of edges.Processing the gradient field directly instead of the image is shown to have numerous benefits. The approach is developed such that the steps are modular, allowing the overall method to be improved and possibly tailored to different applications. As presented, the approach relies on a topographic representation and primal sketch of an image.Comparisons with existing image processing methods on a synthetic image and different medical images show improved results and accuracy in segmentation. Here the focus is on objects with low spatial resolution, which is often the case in medical images. The methods developed show the importance of improved accuracy in derivative calculation, and the potential in processing the image gradient field directly.

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Image enhancement and denoising by complex diffusion processes

Cited by 424 publications

References 21 publications

Image denoising in bidimensional empirical mode decomposition domain: the role of Student's probability distribution function

Image denoising in bidimensional empirical mode decomposition domain: the role of Student's probability distribution function

A Modified Guided Filter to Denoise Seismic Attributes

Processing the image gradient field using a topographic primal sketch approach

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