Textural Image Denoising Using Gumbel Random Vectors in Gaussian Noise

2017 ◽  
Vol 17 (01) ◽  
pp. 1750003 ◽  
Author(s):  
P. Kittisuwan
Keyword(s):  
Wavelet Transform ◽  
Gaussian Noise ◽  
Discrete Wavelet ◽  
Wavelet Domain ◽  
Wavelet Coefficients ◽  
Random Vectors ◽  
Bayesian Techniques ◽  
Pearson Type ◽  
Gaussian Density ◽  
Non Gaussian

Gaussian noise is an important problem in computer vision. The novel methods that become popular in recent years for Gaussian noise reduction are Bayesian techniques in wavelet domain. In wavelet domain, the Bayesian techniques require a prior distribution of wavelet coefficients. In general case, the wavelet coefficients might be better modeled by non-Gaussian density such as Laplacian, two-sided gamma, and Pearson type VII densities. However, statistical analysis of textural image is Gaussian model. So, we require flexible model between non-Gaussian and Gaussian models. Indeed, Gumbel density is a suitable model. So, we present new Bayesian estimator for Gumbel random vectors in AWGN (additive white Gaussian noise). The proposed method is applied to dual-tree complex wavelet transform (DT-CWT) as well as orthogonal discrete wavelet transform (DWT). The simulation results show that our proposed methods outperform the state-of-the-art methods qualitatively and quantitatively.

Multifocus image fusion based on coefficient significance of redundant discrete wavelet transform

2019 ◽  
Vol 46 (3) ◽  
pp. 377-383
Author(s):  
Jianhua Liu ◽  
Peng Geng ◽  
Hongtao Ma
Keyword(s):  
Wavelet Transform ◽  
Image Fusion ◽  
Discrete Wavelet Transform ◽  
Fusion Rule ◽  
Discrete Wavelet ◽  
Wavelet Domain ◽  
Content Type ◽  
Ripplet Transform ◽  
Detail Coefficient ◽  
Redundant Discrete Wavelet Transform

Purpose This study aims to obtain the more precise decision map to fuse the source images by Coefficient significance method. In the area of multifocus image fusion, the better decision map is very important the fusion results. In the processing of distinguishing the well-focus part with blur part in an image, the edge between the parts is more difficult to be processed. Coefficient significance is very effective in generating the better decision map to fuse the multifocus images. Design/methodology/approach The energy of Laplacian is used in the approximation coefficients of redundant discrete wavelet transform. On the other side, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient. Findings Due to the shift-variance of the redundant discrete wavelet and the effectiveness of fusion rule, the presented fusion method is superior to the region energy in harmonic cosine wavelet domain, pixel significance with the cross bilateral filter and multiscale geometry analysis method of Ripplet transform. Originality/value In redundant discrete wavelet domain, the coefficient significance based on statistic property of covariance is proposed to merge the detail coefficient of source images.

Low-complexity image denoising based on mixture model and simple form of MMSE estimation

2018 ◽  
Vol 16 (06) ◽  
pp. 1850052 ◽  
Author(s):  
Pichid Kittisuwan
Keyword(s):  
Em Algorithm ◽  
Noise Reduction ◽  
Closed Form ◽  
Mixture Model ◽  
Gaussian Noise ◽  
Good Efficiency ◽  
Mixture Density ◽  
Pearson Type ◽  
Gaussian Density ◽  
Mmse Estimation

In order to enhance efficiency of artificial intelligence (AI) tools such as classification or pattern recognition, it is important to have noise-free data to be processed with AI tools. Therefore, the study of algorithms used for reducing noise is also very significant. In thermal condition, Gaussian noise is important problem in analog circuit and image processing. Therefore, this paper focuses on the study of an algorithm for Gaussian noise reduction. In recent year, Bayesian with wavelet-based methods provides good efficiency in noise reduction and spends short time in processing. In Bayesian method, mixture density is more flexible than non-mixture density. Therefore, we proposed novel form of minimum mean square error (MMSE) estimation for mixture model, Pearson type VII and logistic densities, in Gaussian noise. The expectation-maximization (EM) algorithm is most deeply used for computing statistical parameters of mixture model. However, the EM estimator for the proposed method does not have the closed-form. Numerical methods are required to implement an EM algorithm. Therefore, we employ maximum a posteriori (MAP) estimation to compute local noisy variances with half-normal distribution prior for local noisy variances and Gaussian density for noisy wavelet coefficients. Here, the proposed method is expressed in closed-form. The denoising results present that our proposed algorithm outperforms the state-of-the-art method qualitatively and quantitatively.

Efficient and Adaptive Rotation Invariant Wavelet Transform

2003 ◽  
Vol 01 (03) ◽  
pp. 353-372
Author(s):  
Chi-Man Pun
Keyword(s):  
Wavelet Transform ◽  
Texture Classification ◽  
Wavelet Packet ◽  
Sampling Rate ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Information Cost ◽  
Image Size ◽  
Rotation Invariant ◽  
Adaptive Wavelet

It is well known that the sensitivity to translations and orientations is a major drawback in 2D discrete wavelet transform (DWT). In this paper, we have proposed an effective scheme for rotation invariant adaptive wavelet packet transform. During decomposition, the wavelet coefficients are obtained by applying a polar transform (PT) followed by a row-shift invariant wavelet packet decomposition (RSIWPD). In the first stage, the polar transform generates a row-shifted image and is adaptive to the image size to achieve complete and minimum sampling rate. In the second stage, the RSIWPD is applied to the row-shifted image to generate rotation invariant but over completed subbands of wavelet coefficients. In order to reduce the redundancy and computational complexity, we adaptively select some subbands to decompose and form a best basis representation with minimal information cost with respect to an appropriate information cost function. With this best basis representation, the original image can be reconstructed easily by applying a row-shift invariant wavelet packet reconstruction (RSIWPR) followed by an inverse polar transform (IPT). In the experiments, we study the application of this representation for texture classification and achieve 96.5% classification accuracy.

M-Ary Alpha-Stable Noise Modulation in Spread-Spectrum Communication

2015 ◽  
Vol 14 (03) ◽  
pp. 1550022 ◽  
Author(s):  
Mehmet Emre Cek
Keyword(s):  
Gaussian Noise ◽  
Spread Spectrum ◽  
Additive White Gaussian Noise ◽  
Characteristic Exponent ◽  
Random Signal ◽  
Spread Spectrum Communication ◽  
Order Moment ◽  
Gaussian Density ◽  
Shift Keying ◽  
Non Gaussian

In this paper, a spread-spectrum communication system based on a random carrier is proposed which transmits M-ary information. The random signal is considered as a single realization of a random process taken from prescribed symmetric α-stable (SαS) distribution that carries digital M-ary information to be transmitted. Considering the noise model in the channel as additive white Gaussian noise (AWGN), the transmitter sends the information carrying random signal from non-Gaussian density. Alpha-stable distribution is used to encode the M-ary message. Inspired by the chaos shift keying techniques, the proposed method is called M-ary symmetric alpha-stable differential shift keying (M-ary SαS-DSK). The main purpose of preferring non-Gaussian noise instead of conventional pseudo-noise (PN) sequence is to overcome the drawback of self-repeating noise-like sequences which are detectable due to the periodic behavior of the autocorrelation function of PN sequences. Having infinite second order moment in α-stable random carrier offers secrecy of the information due to the non-constant autocorrelation behavior. The bit error rate (BER) performance of the proposed method is illustrated by Monte Carlo simulations with respect to various characteristic exponent values and different data length.

scholarly journals Errata: Estimation of non-Gaussian noise parameters in the wavelet domain using the moment-generating function

2012 ◽  
Vol 21 (3) ◽  
pp. 039802-1
Author(s):  
Jan Švihlík ◽  
Karel Fliegel ◽  
Jaromír Kukal ◽  
Eva Jerhotová ◽  
Petr Páta ◽  
...  
Keyword(s):  
Generating Function ◽  
Gaussian Noise ◽  
Moment Generating Function ◽  
Wavelet Domain ◽  
Noise Parameters ◽  
The Moment ◽  
Non Gaussian

Simultaneous Least Squares Wavelet Decomposition for Multidimensional Irregularly Spaced Data

2012 ◽  
Vol 239-240 ◽  
pp. 1213-1218 ◽  
Author(s):  
Mehdi Shahbazian ◽  
Saeed Shahbazian
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Wavelet Decomposition ◽  
Least Square ◽  
Multidimensional Case ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Sampled Data ◽  
Irregularly Sampled Data

The multidimensional Discrete Wavelet Transform (DWT) has been widely used in signal and image processing for regularly sampled data. For irregularly sampled data, however, other techniques should be used including the Least Square Wavelet Decomposition (LSWD). The commonly used level by level (sequential) wavelet decomposition, which calculates the wavelet coefficients in each resolution separately, may result in a gross interpolation error. To overcome this drawback, a different approach called the Simultaneous Least Square Wavelet Decomposition, which computes all wavelet coefficients simultaneously, have been proposed by the authors. In this paper, we extend the simultaneous LSWD approach to the multidimensional case and show that this method has excellent reconstruction property for two dimensional irregularly spaced data.

scholarly journals Image enhancement in wavelet domain based on histogram equalization and median filter

2021 ◽  
Author(s):  
Haval Sulaiman Abdullah ◽  
◽  
Firas Mahmood Mustafa ◽  
Atilla Elci ◽  
◽  
...  
Keyword(s):  
Wavelet Transform ◽  
Noise Reduction ◽  
Discrete Wavelet Transform ◽  
Image Enhancement ◽  
Median Filter ◽  
Histogram Equalization ◽  
Image Noise ◽  
Discrete Wavelet ◽  
Wavelet Domain ◽  
Image Noise Reduction

During the acquisition of a new digital image, noise may be introduced as a result of the production process. Image enhancement is used to alleviate problems caused by noise. In this work, the purpose is to propose, apply, and evaluate enhancement approaches to images by selecting suitable filters to produce improved quality and performance results. The new method proposed for image noise reduction as an enhancement process employs threshold and histogram equalization implemented in the wavelet domain. Different types of wavelet filters were tested to obtain the best results for the image noise reduction process. Also, the effect of canceling one or more of the high-frequency bands in the wavelet domain was tested. The mean square error and peak signal to noise ratio are used for measuring the improvement in image noise reduction. A comparison made with two related works shows the superiority of the methods proposed and implemented in this research. The proposed methods of applying the median filter before and after the histogram equalization methods produce improvement in performance and efficiency compared to the case of using discrete wavelet transform only, even with the cases of multiresolution discrete wavelet transform and the cancellation step.

scholarly journals Restoration of Noisy Blurred Images Using MFPIA and Discrete Wavelet Transform

2013 ◽  
Vol 9 (1) ◽  
pp. 1-15
Author(s):  
Dunia Tahir
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Gaussian Noise ◽  
Motion Blur ◽  
Discrete Wavelet ◽  
Wavelet Thresholding ◽  
Fixed Phase ◽  
Approximation Coefficients ◽  
Blurred Images ◽  
Deblurring And Denoising

In this paper, image deblurring and denoising are presented. The used images were blurred either with Gaussian or motion blur and corrupted either by Gaussian noise or by salt & pepper noise. In our algorithm, the modified fixed-phase iterative algorithm (MFPIA) is used to reduce the blur. Then a discrete wavelet transform is used to divide the image into two parts. The first part represents the approximation coefficients. While the second part represents the detail coefficients, that a noise is removed by using the BayesShrink wavelet thresholding method.

scholarly journals The Improvement of Discrete Wavelet Transform

2021 ◽  
Author(s):  
Zhihua Zhang
Keyword(s):  
Wavelet Transform ◽  
Decay Rate ◽  
Discrete Wavelet Transform ◽  
Wavelet Transforms ◽  
Polynomial Interpolation ◽  
Discrete Wavelet ◽  
Two Dimensional ◽  
Wavelet Coefficients ◽  
Periodic Wavelet ◽  
Improved Algorithm

Discrete wavelet transform and discrete periodic wavelet transform have been widely used in image compression and data approximation. Due to discontinuity on the boundary of original data, the decay rate of the obtained wavelet coefficients is slow. In this study, we use the combination of polynomial interpolation and one-dimensional/two-dimensional discrete periodic wavelet transforms to mitigate boundary effects. The decay rate of the obtained wavelet coefficients in our improved algorithm is faster than that of traditional two-dimensional discrete wavelet transform. Moreover, our improved algorithm can be extended naturally to the higher-dimensional case.

Text Categorisation Through Dimensionality Reduction Using Wavelet Transform

2020 ◽  
Vol 19 (04) ◽  
pp. 2050039
Author(s):  
Jorge Chamorro-Padial ◽  
Rosa Rodríguez-Sánchez
Keyword(s):  
Wavelet Transform ◽  
Dimensionality Reduction ◽  
Text Classification ◽  
High Energy ◽  
Discrete Wavelet ◽  
Wavelet Coefficients ◽  
Vertical Orientation ◽  
Method Of Dimensionality Reduction ◽  
Horizontal Orientation ◽  
Relevant Level

This paper proposes a new method of dimensionality reduction when performing Text Classification, by applying the discrete wavelet transform to the document-term frequencies matrix. We analyse the features provided by the wavelet coefficients from the different orientations: (1) The high energy coefficients in the horizontal orientation correspond to relevant terms in a single document. (2) The high energy coefficients in the vertical orientation correspond to relevant terms for a single document, but not for the others. (3) The high energy coefficients in the diagonal orientation correspond to relevant terms in a document in comparison to other terms. If we filter using the wavelet coefficients and fulfil these three conditions simultaneously, we can obtain a reduced vocabulary of the corpus, with less dimensions than in the original one. To test the success of the reduced vocabulary, we recoded the corpus with the new reduced vocabulary and we obtained a statistically relevant level of accuracy for document classification.

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