De-noising by soft-thresholding

Donoho, David L.

doi:10.1109/18.382009

Cited by 8,308 publications

(4,483 citation statements)

References 28 publications

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“…Denoising is carried out in both dimensions using discrete wavelet transform with interval dependent thresholding 32 (cmddenoise function in Matlab). Set thresholds are based on Donoho thresholds, 33 and for denoising, the maximum number of intervals are set to 6 and 3 in the IM and RT dimensions, respectively, with levels set to 5 and 2 in the IM and RT dimensions, respectively. Daubechies 8 wavelet and hard thresholding is used in denoising for both dimensions.…”

Section: ■ Theorymentioning

confidence: 99%

Data Size Reduction Strategy for the Classification of Breath and Air Samples Using Multicapillary Column-Ion Mobility Spectrometry

et al. 2015

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Ion mobility spectrometry combined with multicapillary column separation (MCC-IMS) is a wellknown technology for detecting volatile organic compounds (VOCs) in gaseous samples. Due to their large data size, processing of MCC-IMS spectra is still the main bottleneck of data analysis, and there is an increasing need for data analysis strategies in which the size of MCC-IMS data is reduced to enable further analysis. In our study, the first untargeted chemometric strategy is developed and employed in the analysis of MCC-IMS spectra from 264 breath and ambient air samples. This strategy does not comprise identification of compounds as a primary step but includes several preprocessing steps and a discriminant analysis. Data size is significantly reduced in three steps. Wavelet transform, mask construction, and sparse-partial least squares-discriminant analysis (s-PLS-DA) allow data size reduction with down to 50 variables relevant to the goal of analysis. The influence and compatibility of the data reduction tools are studied by applying different settings of the developed strategy. Loss of information after preprocessing is evaluated, e.g., by comparing the performance of classification models for different classes of samples. Finally, the interpretability of the classification models is evaluated, and regions of spectra that are related to the identification of potential analytical biomarkers are successfully determined. This work will greatly enable the standardization of analytical procedures across different instrumentation types promoting the adoption of MCC-IMS technology in a wide range of diverse application fields.

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Section: ■ Theorymentioning

confidence: 99%

Data Size Reduction Strategy for the Classification of Breath and Air Samples Using Multicapillary Column-Ion Mobility Spectrometry

et al. 2015

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“…Finally, figure 14 shows a comparison between the proposed method and other image denoising algorithms: Donoho's digital wavelet (DWT) [17,18] and discrete cosine transform (DCT) based methods [19]. The proposed method has given the best results since it has been developed in order to reduce this specific noise pattern, achieving an improvement in Jaccard similarity coefficient of 0.2649 versus 0.1296 and 0.028 obtained by DWT and DCT methods respectively.…”

Section: Structuring Element Size Selectionmentioning

confidence: 99%

Metal artifact reduction in dental CT images using polar mathematical morphology

Naranjo

Llorens

Alcañíz

et al. 2011

Computer Methods and Programs in Biomedicine

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ElsevierNaranjo Ornedo, V.; Lloréns Rodríguez, R.; Alcañiz Raya, ML.; López-Mir, F. (2011). Metal artifact reduction in dental CT images using polar mathematical morphology. Computer Methods and Programs in Biomedicine. 102 (1) AbstractMost dental implant planning systems use a 3D representation of the CT scan of the patient under study as it provides a more intuitive view of the human jaw. The presence of metallic objects in human jaws, such as amalgam or gold fillings, provokes several artifacts like streaking and beam hardening which makes the reconstruction process difficult. In order to reduce these artifacts, several methods have been proposed using the raw data, directly obtained from the tomographs, in different ways. However, in DICOM-based applications this information is not available, and thus the need of a new method that handles this task in the DICOM domain. The presented method performs a morphological filtering in the polar domain yielding output images less affected by artifacts (even in cases of multiple metallic objects) without causing significant smoothing of the anatomic structures, which allows a great improvement in the 3D reconstruction. The algorithm has been automated and compared to other image denoising methods with successful results.

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“…In terms of minimum mean-square error, wavelets generally outperform or at worst match conventional denoising or estimation techniques depending on the local smoothness properties of the underlying signal. Donoho (1995) noted that with ''overwhelming probability'', one can hope to recover a function that is at least as smooth as the true function, and that this observation holds across a wide range of smoothness classes. In the wavelet domain, this is equivalent to stating that noise has a high likelihood of disappearing from the recovered signal, which in turn leads us to have high confidence in the zeroed wavelet coefficients.…”

Section: P Value Interpretation Of Wavelet Thresholdingmentioning

confidence: 99%

Spatiotemporal wavelet analysis for functional MRI

et al. 2004

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Characterizing the spatiotemporal behavior of the BOLD signal in functional Magnetic Resonance Imaging (fMRI) is a central issue in understanding brain function. While the nature of functional activation clusters is fundamentally heterogeneous, many current analysis approaches use spatially invariant models that can degrade anatomic boundaries and distort the underlying spatiotemporal signal. Furthermore, few analysis approaches use true spatiotemporal continuity in their statistical formulations. To address these issues, we present a novel spatiotemporal wavelet procedure that uses a stimulus-convolved hemodynamic signal plus correlated noise model. The wavelet fits, computed by spatially constrained maximum-likelihood estimation, provide efficient multiscale representations of heterogeneous brain structures and give well-identified, parsimonious spatial activation estimates that are modulated by the temporal fMRI dynamics. In a study of both simulated data and actual fMRI memory task experiments, our new method gave lower mean-squared error and seemed to result in more localized fMRI activation maps compared to models using standard wavelet or smoothing techniques. Our spatiotemporal wavelet framework suggests a useful tool for the analysis of fMRI studies. D

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De-noising by soft-thresholding

Cited by 8,308 publications

References 28 publications

Data Size Reduction Strategy for the Classification of Breath and Air Samples Using Multicapillary Column-Ion Mobility Spectrometry

Data Size Reduction Strategy for the Classification of Breath and Air Samples Using Multicapillary Column-Ion Mobility Spectrometry

Metal artifact reduction in dental CT images using polar mathematical morphology

Spatiotemporal wavelet analysis for functional MRI

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