Euler’s Approximations to Image Reconstruction

Borkowski, Dariusz

doi:10.1007/978-3-642-33564-8_4

Cited by 4 publications

(6 citation statements)

References 13 publications

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“…The two parameters, dt and p, can be viewed as a single dt with a small value for the classical Euler scheme. In Figure 5, from [7], we can observe that implementing the modified Euler scheme resulted in a remarkable 30fold acceleration in the reconstruction process! The introduction of this scheme played a pivotal role in the further development of denoising methods based on backward stochastic differential equations.…”

Section: Approximation Parametersmentioning

confidence: 98%

“…are the maximum and the minimum of F x while the orthogonal eigenvectors θ + (u, x) and θ − (u, x) are Algorithm 1: Pseudo-code for Example 2. input : u 0 -noisy image, σ -standard deviation of the noise N , j, m, dt, p -approximation parameters (a k ) k=0,1...,m−1 -coefficients defined by formulas ( 5), ( 6), (7) output: u -reconstructed image foreach pixel position x do…”

Section: Generalization To Color Spaces Rgb Spacementioning

confidence: 99%

“…However, in the field of stochastic methods, this parameter is pivotal, and setting it too low can disqualify the method due to excessively long running times. To achieve a favorable reconstruction result, a value of dt = 0.05 is recommended for the classical Euler scheme [7], albeit at the expense of running time. To address this issue, we introduced a modified Euler scheme (as detailed in Section 4), which introduced another parameter, denoted as p. This modification enabled us to use larger values of dt.…”

Section: Approximation Parametersmentioning

confidence: 99%

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Implementation of Image Denoising based on Backward Stochastic Differential Equations

Borkowski

2023

Image Processing on Line

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In this paper, we give the implementation of an image denoising algorithm based on backward stochastic differential equations. In our algorithm, we consider two stochastic processes. One of them has values in the image domain and determines pixels that will be involved in the reconstruction, the second one has values in the image codomain and gives weights to values of pixels. The reconstructed image is characterized by smoothing noisy pixels and at the same time enhancing edges. Our experiments show that the new approach gives very good results and can be successfully used to reconstruct images. Source CodeThe reviewed source code and documentation for this algorithm are available at the IPOL web page of this article 1 . Compilation and usage instructions are included in the README.txt file of the archive.

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Section: Approximation Parametersmentioning

confidence: 98%

Section: Generalization To Color Spaces Rgb Spacementioning

confidence: 99%

Section: Approximation Parametersmentioning

confidence: 99%

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Implementation of Image Denoising based on Backward Stochastic Differential Equations

Borkowski

2023

Image Processing on Line

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“…After these remarks the request is the following: to fast implementation we need fast counting of the value X x tj (ω). In order to get X x tj (ω) we use the following modification of Euler's approximation taken from [5]:…”

Section: 2mentioning

confidence: 99%

Forward and backward filtering based on backward stochastic differential equations

Borkowski¹

2016

IPI

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In this paper we explore the problem of reconstruction of blurred and noisy images. The idea presented here provides a new methodology based on advanced tools of stochastic analysis which can be successfully used to solve the inverse problem. In order to solve this problem we use backward stochastic differential equations. The reconstructed image is characterized by smoothing noisy pixels and at the same time enhancing and sharpening edges. Our experiments show that the new approach gives very good results and compares favourably with deterministic partial differential equation methods.

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“…At locations where gradient is large in all directions it is possible that condition Θ does not hold as many times as we would expect. To avoid this we propose the following modification [6]:…”

Section: Modified Diffusion With Random Terminal Timementioning

confidence: 99%

Image Restoration Using Anisotropic Stochastic Diffusion Collaborated with Non Local Means

Borkowski

Jańczak-Borkowska

2013

Computer Information Systems and Industrial Management

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Part 4: Pattern Recognition and Image ProcessingInternational audienceIn this paper we explore the problem of the reconstruction of images with additive Gaussian noise. In order to solve this inverse problem we use stochastic differential equations with reflecting boundary and famous non local means algorithm. Expressing anisotropic diffusion in terms of stochastic equations allows us to adapt the concept of similarity patches used in non local means. This novel look on the reconstruction problem is fruitful, gives encouraging results and compares favourably with other image denoising filters

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Euler’s Approximations to Image Reconstruction

Cited by 4 publications

References 13 publications

Implementation of Image Denoising based on Backward Stochastic Differential Equations

Implementation of Image Denoising based on Backward Stochastic Differential Equations

Forward and backward filtering based on backward stochastic differential equations

Image Restoration Using Anisotropic Stochastic Diffusion Collaborated with Non Local Means

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