The Undecimated Wavelet Decomposition and its Reconstruction

Starck, Jean-Luc; Fadili, Jalal M.; Murtagh, Fionn

doi:10.1109/tip.2006.887733

Cited by 447 publications

(254 citation statements)

References 36 publications

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“…However, it will not work effectively for some extended sources such as galaxies, gas emission, and nebulae. Fortunately, in these cases, a sparse representation of the signal can be achieved by using some dictionary functions such as the wavelet transform and the undecimated wavelet transform (Starck et al 2007). …”

Section: Compressive Sensing-based Deconvolution Methodsmentioning

confidence: 99%

“…In this paper, we introduce a CS-based deconvolution method that deals with extended emission without assuming Gaussian shapes. This method adopts the isotropic undecimated wavelet transform (IUWT) (Starck et al 2007) as a basis function. Our motivation for adopting the IUWT is based upon the work of Starck et al, who found that the IUWT can decompose a wide range of astronomical images into a sparse isotropic representation (Starck et al 2007).…”

Section: Introductionmentioning

confidence: 99%

“…This method adopts the isotropic undecimated wavelet transform (IUWT) (Starck et al 2007) as a basis function. Our motivation for adopting the IUWT is based upon the work of Starck et al, who found that the IUWT can decompose a wide range of astronomical images into a sparse isotropic representation (Starck et al 2007). We compare the performance of the resulting deconvolution method with Högbom CLEAN, the multiscale CLEAN (Cornwell 2008), and another CS-based method.…”

Section: Introductionmentioning

confidence: 99%

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The application of compressive sampling to radio astronomy

Cornwell

Hoog

2011

A&A

114

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Compressive sampling is a new paradigm for sampling, based on sparseness of signals or signal representations. It is much less restrictive than Nyquist-Shannon sampling theory and thus explains and systematises the widespread experience that methods such as the Högbom CLEAN can violate the Nyquist-Shannon sampling requirements. In this paper, a CS-based deconvolution method for extended sources is introduced. This method can reconstruct both point sources and extended sources (using the isotropic undecimated wavelet transform as a basis function for the reconstruction step). We compare this CS-based deconvolution method with two CLEANbased deconvolution methods: the Högbom CLEAN and the multiscale CLEAN. This new method shows the best performance in deconvolving extended sources for both uniform and natural weighting of the sampled visibilities. Both visual and numerical results of the comparison are provided.

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Section: Compressive Sensing-based Deconvolution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The application of compressive sampling to radio astronomy

Cornwell

Hoog

2011

A&A

114

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“…1 (upper left) is a waveletfiltered image, computed in the 0.5-2.5 keV energy band. To generate this image, we corrected the photon map for effective exposure and soft-thresholded its undecimated B3-spline wavelet coefficients (Starck et al 2007) to a 3 σ level. In this procedure, significance thresholds have been directly computed from the raw (Poisson distributed) photon map, following the multi-scale variance stabilisation scheme introduced in Zhang et al (2008).…”

Section: Xmm-newton Observation and Data Reductionmentioning

confidence: 99%

Planckintermediate results

Ade

Aghanim

Arnaud

et al. 2013

A&A

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The survey of galaxy clusters performed by Planck through the Sunyaev-Zeldovich effect has already discovered many interesting objects, thanks to its full sky coverage. One of the SZ candidates detected in the early months of the mission near to the signal-to-noise threshold, PLCKG214.6+37.0, was later revealed by XMM-Newton to be a triple system of galaxy clusters. We present the results from a deep XMM-Newton re-observation of PLCKG214.6+37.0, part of a multi-wavelength programme to investigate Planck discovered superclusters. The characterisation of the physical properties of the three components has allowed us to build a template model to extract the total SZ signal of this system with Planck data. We have partly reconciled the discrepancy between the expected SZ signal derived from X-rays and the observed one, which are now consistent within 1.2σ. We measured the redshift of the three components with the iron lines in the X-ray spectrum, and confirm that the three clumps are likely part of the same supercluster structure. The analysis of the dynamical state of the three components, as well as the absence of detectable excess X-ray emission, suggests that we are witnessing the formation of a massive cluster at an early phase of interaction.

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“…Thus its denoising performance can change drastically if the starting position of the signal is shifted. In order to achieve the shift invariance and to get more complete characteristic of the analyzed signal, the undecimated DWT (UDWT) has been proposed [36][37][38][39]. Mencattini et al developed methods for the reduction of noise in mammographic images, based on UDWT using subband noise variance computation both for homoscedastic and heteroscedastic noise [40,41].…”

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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The Undecimated Wavelet Decomposition and its Reconstruction

Cited by 447 publications

References 36 publications

The application of compressive sampling to radio astronomy

The application of compressive sampling to radio astronomy

Planckintermediate results

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

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