Variational Image Denoising with Adaptive Constraint Sets

In recent twenty years, image denoising method which is based on partial differential equations (PDE) has been developed rapidly. Due to its scientific and strong theoretical foundation, it owns accurate and stable results which can be got by efficient algorithms. But it still leaves some problems which need to be solved. The staircase effect is one of the most basic problems in the classical TV (Total Variation) model. This problem can be effectively solved by high-order model proposed in this paper. A fast and efficient numerical algorithm is designed to solve minimization problems related to the high-order model and its applications to variational image denoising are shown. The performance of the proposed model is compared with TV model and other high-order models. The algorithm used for the proposed model is also compared with Split Bregman algorithm. Some numerical experiments validate the model proposed and the algorithm designed in this paper.

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A new iterative algorithm for mean curvature-based variational image denoising

BIT Numerical Mathematics ◽

10.1007/s10543-013-0448-y ◽

2013 ◽

Vol 54 (2) ◽

pp. 523-553 ◽

Cited By ~ 9

Author(s):

Li Sun ◽

Ke Chen

Keyword(s):

Image Denoising ◽

Iterative Algorithm ◽

Mean Curvature ◽

Variational Image

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THE CONSTRUCTION OF MULTIWAVELET BI-FRAMES AND APPLICATIONS TO VARIATIONAL IMAGE DENOISING

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691310003560 ◽

2010 ◽

Vol 08 (03) ◽

pp. 431-455 ◽

Cited By ~ 15

Author(s):

MARTIN EHLER ◽

KARSTEN KOCH

Keyword(s):

Variational Problem ◽

Image Denoising ◽

Wavelet Basis ◽

Parameter Choice ◽

Orthonormal Wavelet ◽

Wavelet Bases ◽

Flexible Tool ◽

Curve Method ◽

Discretization Technique ◽

Variational Image

We remove noise from images by solving a parameter depending variational problem. The choice of the parameter is essential for the success of the approach, and in order to compute a solution, the problem must be discretized. It is commonly known that the parameter choice according to the H-curve criterion performs well in combination with discretizations derived from a dyadic orthonormal wavelet basis. However, the concept of orthonormal wavelet bases is restrictive and bears limitations. In order to have a more flexible tool, we construct new nondyadic wavelet bi-frames by convolving scalar wavelets with wavelet vectors. We discretize the variational problem by these new bi-frames, and we verify that the H-curve method performs well for this much more flexible discretization technique.

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Variational Image Denoising Approach with Diffusion Porous Media Flow

Abstract and Applied Analysis ◽

10.1155/2013/856876 ◽

2013 ◽

Vol 2013 ◽

pp. 1-8 ◽

Cited By ~ 22

Author(s):

Tudor Barbu

Keyword(s):

Porous Media ◽

Image Denoising ◽

Nonlinear Filter ◽

Porous Media Flow ◽

Porous Media Equation ◽

Diffusion Flow ◽

Image Noise Reduction ◽

Variational Image ◽

Image Edges ◽

Degraded Images

A novel PDE-based image denoising approach is proposed in this paper. One designs here a nonlinear filter for image noise reduction based on the diffusion flow generated by the porous media equation∂u/∂t=Δβ(u), whereβis a nonlinear continuous function of the formβ(u)=λum,0<m<1. With respect to standard 2D Gaussian smoothing and some nonlinear PDE-based filters, this one is more efficient to remove noise from degraded images and also to reduce “staircasing” effects and preserve the image edges.

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