Denoising through wavelet shrinkage: an empirical study

Fodor, Imola K.; Kamath, Chandrika

doi:10.1117/1.1525793

Cited by 128 publications

(64 citation statements)

References 27 publications

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“…We apply wavelet shrinkage, developed by Donoho & Johnstone (1994), which selects wavelet coefficients based on thresholding and uses them for reconstruction. There are two types of thresholding used in practice: hard thresholding and soft thresholding (Bruce & Gao 1996;Fodor & Kamath 2003). The output DWT coefficients W hard (k) and W sof t (k) based on these two types of thresholding with threshold η are:…”

Section: Wavelet Shrinkagementioning

confidence: 99%

Wavelet Denoising of Radio Observations of Rotating Radio Transients (RRATs): Improved Timing Parameters for Eight RRATs

Jiang

Cui

Schmid

et al. 2017

ApJ

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Rotating radio transients (RRATs) are sporadically emitting pulsars detectable only through searches for single pulses. While over 100 RRATs have been detected, only a small fraction (roughly 20%) have phase-connected timing solutions, which are critical for determining how they relate to other neutron star populations. Detecting more pulses in order to achieve solutions is a key to understanding their physical nature. Astronomical signals collected by radio telescopes contain noise from many sources, making the detection of weak pulses difficult. Applying a denoising method to raw time series prior to performing a single-pulse search typically leads to a more accurate estimation of their times of arrival (TOAs). Taking into account some features of RRAT pulses and noise, we present a denoising method based on wavelet data analysis, an image-processing technique. Assuming that the spin period of an RRAT is known, we estimate the frequency spectrum components contributing to the composition of RRAT pulses. This allows us to suppress the noise, which contributes to other frequencies. We apply the wavelet denoising method including selective wavelet reconstruction and wavelet shrinkage to the de-dispersed time series of eight RRATs with existing timing solutions. The signal-to-noise ratio (S/N) of most pulses are improved after wavelet denoising. Compared to the conventional approach, we measure 12% to 69% more TOAs for the eight RRATs. The new timing solutions for the eight RRATs show 16% to 90% smaller estimation error of most parameters. Thus, we conclude that wavelet analysis is an effective tool for denoising RRATs signal.

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Section: Wavelet Shrinkagementioning

confidence: 99%

Wavelet Denoising of Radio Observations of Rotating Radio Transients (RRATs): Improved Timing Parameters for Eight RRATs

Jiang

Cui

Schmid

et al. 2017

ApJ

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“…Because of its importance, there has been an enormous amount of research dedicated to the subject of noise removal and many methods have been proposed [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Several approaches have been proposed with the use of discrete wavelet transform (DWT) [30,31,34,35].…”

Section: Introductionmentioning

confidence: 99%

A Modified Undecimated Discrete Wavelet Transform Based Approach to Mammographic Image Denoising

et al. 2012

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In this work, the authors present an effective denoising method to attempt reducing the noise in mammographic images. The method is based on using hierarchical correlation of the coefficients of discrete stationary wavelet transforms. The features of the proposed technique include iterative use of undecimated multi-directional wavelet transforms at adjacent scales. To validate the proposed method, computer simulations were conducted, followed by its applications to clinical mammograms. Mutual information originating from information theory was used as an evaluation measure for selection of an optimal wavelet basis function. We examined the performance of the proposed method by comparing it with the conventional undecimated discrete wavelet transform (UDWT) method in terms of processing time-consuming and image quality. Our results showed that with the use of the proposed method the computation time can be reduced to approximately 1/10 of the conventional UDWT method consumed. The results of visual assessment indicated that the images processed with the proposed UDWT method showed statistically significant superior image quality over those processed with the conventional UDWT method. Our research results demonstrate the superiority and effectiveness of the proposed approach.

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“…Instead of simple techniques to reduce the grainy noise in the image, we could have used more complex techniques such as wavelet denoising or diffusion-based denoising. However, these approaches are more time consuming, require the setting of several parameters, and do not always work better than the simple techniques [19,20,2].…”

Section: Image Enhancementmentioning

confidence: 99%

Analysis of Images from Experiments Investigating Fragmentation of Materials

Kamath¹,

Hurricane²

2007

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Image processing techniques have been used extensively to identify objects of interest in image data and extract representative characteristics for these objects. However, this can be a challenge due to the presence of noise in the images and the variation across images in a dataset. When the number of images to be analyzed is large, the algorithms used must also be relatively insensitive to the choice of parameters and lend themselves to partial or full automation. This not only avoids manual analysis which can be time consuming and error-prone, but also makes the analysis reproducible, thus enabling comparisons between images which have been processed in an identical manner. In this paper, we describe our approach to extracting features for objects of interest in experimental images. Focusing on the specific problem of fragmentation of materials, we show how we can extract statistics for the fragments and the gaps between them.

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Denoising through wavelet shrinkage: an empirical study

Cited by 128 publications

References 27 publications

Wavelet Denoising of Radio Observations of Rotating Radio Transients (RRATs): Improved Timing Parameters for Eight RRATs

Wavelet Denoising of Radio Observations of Rotating Radio Transients (RRATs): Improved Timing Parameters for Eight RRATs

A Modified Undecimated Discrete Wavelet Transform Based Approach to Mammographic Image Denoising

Analysis of Images from Experiments Investigating Fragmentation of Materials

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