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1

Bivariate Hahn moments for image reconstruction

Wu H., Yan S.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 2

417--428

EN

This paper presents a new set of bivariate discrete orthogonal moments which are based on bivariate Hahn polynomials with non-separable basis. The polynomials are scaled to ensure numerical stability. Their computational aspects are discussed in detail. The principle of parameter selection is established by analyzing several plots of polynomials with different kinds of parameters. Appropriate parameters of binary images and a grayscale image are obtained through experimental results. The performance of the proposed moments in describing images is investigated through several image reconstruction experiments, including noisy and noise-free conditions. Comparisons with existing discrete orthogonal moments are also presented. The experimental results show that the proposed moments outperform slightly separable Hahn moments for higher orders.

2

An efficient algorithm for adaptive total variation based image decomposition and restoration

Liu X., Huang L.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 2

405--415

EN

With the aim to better preserve sharp edges and important structure features in the recovered image, this article researches an improved adaptive total variation regularization and H-1 norm fidelity based strategy for image decomposition and restoration. Computationally, for minimizing the proposed energy functional, we investigate an efficient numerical algorithm—the split Bregman method, and briefly prove its convergence. In addition, comparisons are also made with the classical OSV (Osher–Sole–Vese) model (Osher et al., 2003) and the TV-Gabor model (Aujol et al., 2006), in terms of the edge-preserving capability and the recovered results. Numerical experiments markedly demonstrate that our novel scheme yields significantly better outcomes in image decomposition and denoising than the existing models.

3

Application of the partitioning method to specific Toeplitz matrices

Stanimirović P., Miladinović M., Stojanović I., Miljković S.

International Journal of Applied Mathematics and Computer Science

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2013

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Vol. 23, no. 4

809--821

EN

We propose an adaptation of the partitioning method for determination of the Moore–Penrose inverse of a matrix augmented by a block-column matrix. A simplified implementation of the partitioning method on specific Toeplitz matrices is obtained. The idea for observing this type of Toeplitz matrices lies in the fact that they appear in the linear motion blur models in which blurring matrices (representing the convolution kernels) are known in advance. The advantage of the introduced method is a significant reduction in the computational time required to calculate the Moore–Penrose inverse of specific Toeplitz matrices of an arbitrary size. The method is implemented in MATLAB, and illustrative examples are presented.

4

A well-posed multiscale regularization scheme for digital image denoising

Prasath V. B. S.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 4

769-777

EN

We propose an edge adaptive digital image denoising and restoration scheme based on space dependent regularization. Traditional gradient based schemes use an edge map computed from gradients alone to drive the regularization. This may lead to the oversmoothing of the input image, and noise along edges can be amplified. To avoid these drawbacks, we make use of a multiscale descriptor given by a contextual edge detector obtained from local variances. Using a smooth transition from the computed edges, the proposed scheme removes noise in flat regions and preserves edges without oscillations. By incorporating a space dependent adaptive regularization parameter, image smoothing is driven along probable edges and not across them. The well-posedness of the corresponding minimization problem is proved in the space of functions of bounded variation. The corresponding gradient descent scheme is implemented and further numerical results illustrate the advantages of using the adaptive parameter in the regularization scheme. Compared with similar edge preserving regularization schemes, the proposed adaptive weight based scheme provides a better multiscale edge map, which in turn produces better restoration.

5

Application of the adaptive noise removal technique to the enhancement of cDNA microarray images

Smolka B., Bieda R.

Journal of Medical Informatics & Technologies

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2005

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Vol. 9

131--142

EN

In this paper a novel class of filters designed for the removal of impulsive noise in colour images is presented. The proposed filter family is based on the kernel function which controls the noise suppression properties of the new filtering scheme. The comparison of the new filtering method with the standard techniques used for impulsive noise removal indicates its superior noise removal capabilities and excellent structure preserving properties. The proposed filtering scheme has been successfully applied to the denoising of the cDNA microarray images. Experimental results proved that the new filter is capable of removing efficiently the impulses present in multichannel images, while preserving their textural features.

6

Nonparametric design of impulsive noise removal in colour images

Smolka B., Budzan S., Lukač R.

Journal of Medical Informatics & Technologies

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2004

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Vol. 7

MIP3--12

EN

In this paper the problem of nonparametric impulsive noise removal in multichannel images is addressed. The proposed filter class is based on the nonparametric estimation of the density probability function in a sliding filter window. The obtained results show good noise removal capabilities and excellent structure preserving properties of the new impulsive noise removal technique.