Image Denoising Using Wavelet Transform and Wavelet Transform with Enhanced Diversity

2011 ◽  
Vol 403-408 ◽  
pp. 866-870
Author(s):  
Vaibhav Nigam ◽  
Smriti Bhatnagar ◽  
Sajal Luthra
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Image Denoising ◽  
Wavelet Transforms ◽  
Signal To Noise Ratio ◽  
Practical Implementation ◽  
Discrete Wavelet ◽  
Maximum Output ◽  
Denoising Method ◽  
Detail Coefficient

This paper is a comparative study of image denoising using previously known wavelet transform and new type of wavelet transform, namely, Diversity enhanced discrete wavelet transform. The Discrete Wavelet Transform (DWT) has two parameters: the mother wavelet and the number of iterations. For every noisy image, there is a best pair of parameters for which we get maximum output Peak Signal to Noise Ratio, PSNR. As the denoising algorithms are sensitive to the parameters of the wavelet transform used, in this paper comparison of DEDWT to DWT has been presented. The diversity is enhanced by computing wavelet transforms with different parameters. After the filtering of each detail coefficient, the corresponding wavelet transforms are inverted and the estimated image, having a higher PSNR, is extracted. To benchmark against the best possible denoising method three thresholding techniques have been compared. In this paper we have presented a more practical, implementation oriented work.

scholarly journals An Image Steganography Algorithm using Fractional Discrete Wavelet Transform with Advanced Encryption System

2020 ◽  
Vol 9 (5) ◽  
pp. 541-546
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Mean Square Error ◽  
Signal To Noise Ratio ◽  
Image Steganography ◽  
Discrete Wavelet ◽  
Mean Square ◽  
Signal To Noise ◽  
Noise Ratio

The research constitutes a distinctive technique of steganography of image. The procedure used for the study is Fractional Random Wavelet Transform (FRWT). The contrast between wavelet transform and the aforementioned FRWT is that it comprises of all the benefits and features of the wavelet transform but with additional highlights like randomness and partial fractional value put up into it. As a consequence of the fractional value and the randomness, the algorithm will give power and a rise in the surveillance layers for steganography. The stegano image will be acquired after administrating the algorithm which contains not only the coated image but also the concealed image. Despite the overlapping of two images, any diminution in the grade of the image is not perceived. Through this steganographic process, we endeavor for expansion in surveillance and magnitude as well. After running the algorithm, various variables like Mean Square Error (MSE) and Peak Signal to Noise ratio (PSNR) are deliberated. Through the intended algorithm, a rise in the power and imperceptibility is perceived and it can also support diverse modification such as scaling, translation and rotation with algorithms which previously prevailed. The irrefutable outcome demonstrated that the algorithm which is being suggested is indeed efficacious.

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.

scholarly journals Analysis of the Quantization Noise in Discrete Wavelet Transform Filters for Image Processing

Electronics ◽  
2018 ◽  
Vol 7 (8) ◽  
pp. 135 ◽  
Author(s):  
Nikolay Chervyakov ◽  
Pavel Lyakhov ◽  
Dmitry Kaplun ◽  
Denis Butusov ◽  
Nikolay Nagornov
Keyword(s):  
Image Processing ◽  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Integrated Circuit ◽  
Filter Banks ◽  
Signal To Noise Ratio ◽  
Quantization Noise ◽  
Discrete Wavelet ◽  
Field Programmable ◽  
Application Specific Integrated Circuit

In this paper, we analyze the noise quantization effects in coefficients of discrete wavelet transform (DWT) filter banks for image processing. We propose the implementation of the DWT method, making it possible to determine the effective bit-width of the filter banks coefficients at which the quantization noise does not significantly affect the image processing results according to the peak signal-to-noise ratio (PSNR). The dependence between the PSNR of the DWT image quality on the wavelet and the bit-width of the wavelet filter coefficients is analyzed. The formulas for determining the minimal bit-width of the filter coefficients at which the processed image achieves high quality (PSNR ≥ 40 dB) are given. The obtained theoretical results were confirmed through the simulation of DWT for a test image using the calculated bit-width values. All considered algorithms operate with fixed-point numbers, which simplifies their hardware implementation on modern devices: field-programmable gate array (FPGA), application-specific integrated circuit (ASIC), etc.

scholarly journals Fast Compressed Sensing MRI Based on Complex Double-Density Dual-Tree Discrete Wavelet Transform

2017 ◽  
Vol 2017 ◽  
pp. 1-13
Author(s):  
Shanshan Chen ◽  
Bensheng Qiu ◽  
Feng Zhao ◽  
Chao Li ◽  
Hongwei Du
Keyword(s):  
Wavelet Transform ◽  
Compressed Sensing ◽  
Discrete Wavelet Transform ◽  
Signal To Noise Ratio ◽  
Similarity Index ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Signal To Noise ◽  
Reconstruction Methods ◽  
Noise Ratio

Compressed sensing (CS) has been applied to accelerate magnetic resonance imaging (MRI) for many years. Due to the lack of translation invariance of the wavelet basis, undersampled MRI reconstruction based on discrete wavelet transform may result in serious artifacts. In this paper, we propose a CS-based reconstruction scheme, which combines complex double-density dual-tree discrete wavelet transform (CDDDT-DWT) with fast iterative shrinkage/soft thresholding algorithm (FISTA) to efficiently reduce such visual artifacts. The CDDDT-DWT has the characteristics of shift invariance, high degree, and a good directional selectivity. In addition, FISTA has an excellent convergence rate, and the design of FISTA is simple. Compared with conventional CS-based reconstruction methods, the experimental results demonstrate that this novel approach achieves higher peak signal-to-noise ratio (PSNR), larger signal-to-noise ratio (SNR), better structural similarity index (SSIM), and lower relative error.

scholarly journals Denoising of Heavily Contaminated Partial Discharge signals in High-Voltage Cables Using Maximal Overlap Discrete Wavelet Transform

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6540
Author(s):  
Mohammed A. Shams ◽  
Hussein I. Anis ◽  
Mohammed El-Shahat
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
High Voltage ◽  
Signal To Noise Ratio ◽  
Partial Discharge ◽  
Gaussian White Noise ◽  
Discrete Wavelet ◽  
Power Cable ◽  
Power Cables ◽  
Algorithm Performance

Online detection of partial discharges (PD) is imperative for condition monitoring of high voltage equipment as well as power cables. However, heavily contaminated sites often burden the signals with various types of noise that can be challenging to remove (denoise). This paper proposes an algorithm based on the maximal overlap discrete wavelet transform (MODWT) to denoise PD signals originating from defects in power cables contaminated with various levels of noises. The three most common noise types, namely, Gaussian white noise (GWN), discrete spectral interference (DSI), and stochastic pulse shaped interference (SPI) are considered. The algorithm is applied to an experimentally acquired void-produced partial discharge in a power cable. The MODWT-based algorithm achieved a good improvement in the signal-to-noise ratio (SNR) and in the normalized correlation coefficient (NCC) for the three types of noises. The MODWT-based algorithm performance was also compared to that of the empirical Bayesian wavelet transform (EBWT) algorithm, in which the former showed superior results in denoising SPI and DSI, as well as comparable results in denoising GWN. Finally, the algorithm performance was tested on a PD signal contaminated with the three type of noises simultaneously in which the results were also superior.

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.

PERFECT-TRANSLATION-INVARIANT CUSTOMIZABLE COMPLEX DISCRETE WAVELET TRANSFORM

2013 ◽  
Vol 11 (04) ◽  
pp. 1360003 ◽  
Author(s):  
HIROSHI TODA ◽  
ZHONG ZHANG ◽  
TAKASHI IMAMURA
Keyword(s):  
Wavelet Transform ◽  
Discrete Wavelet Transform ◽  
Frequency Domain ◽  
Wavelet Transforms ◽  
Wavelet Packet ◽  
Variable Density ◽  
Discrete Wavelet ◽  
Translation Invariance ◽  
Translation Invariant ◽  
High Degree

The theorems, giving the condition of perfect translation invariance for discrete wavelet transforms, have already been proven. Based on these theorems, the dual-tree complex discrete wavelet transform, the 2-dimensional discrete wavelet transform, the complex wavelet packet transform, the variable-density complex discrete wavelet transform and the real-valued discrete wavelet transform, having perfect translation invariance, were proposed. However, their customizability of wavelets in the frequency domain is limited. In this paper, also based on these theorems, a new type of complex discrete wavelet transform is proposed, which achieves perfect translation invariance with high degree of customizability of wavelets in the frequency domain.

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