The discrete wavelet transform: wedding the a trous and Mallat algorithms

Shensa, M.

doi:10.1109/78.157290

Cited by 1,711 publications

(713 citation statements)

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“…Detailed mathematical description is given by Mallat (1999), Shensa (1992) and Bijaoui et al (1994). We used both of the one and two dimensional à trous transform.…”

Section: Discussionmentioning

confidence: 99%

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Improved spark and ember detection using stationary wavelet transforms

Szabó¹,

Vincze²,

Csernoch³

et al. 2010

Journal of Theoretical Biology

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Calcium sparks and embers are localized intracellular events of calcium release in muscle cells studied frequently by confocal microscopy using line-scan imaging. The large quantity of images and large number of events require automatic detection procedures based on signal processing methods. In the past decades these methods were based on thresholding procedures. Although recently wavelet transforms were also introduced, they have not become widespread. We have implemented a set of algorithms based on one and two dimensional versions of the à trous wavelet transform. The algorithms were used to perform spike filtering, denoising and detection procedures. Due to the dependence of the algorithms on user adjustable parameters, their effect on the efficiency of the algorithm was studied in detail. We give methods to avoid false positive detections which are the consequence of the background noise in confocal images. In order to establish the efficiency and reliability of the algorithms, various tests were performed on artificial and experimental images. Spark parameters (amplitude, full width at half maximum) calculated using the traditional and the wavelet methods were compared. We found that the latter method is capable of identifying more events with better accuracy on experimental images. Furthermore, we extended the wavelet based transform from calcium sparks to long-lasting small-amplitude events as calcium embers. The method not only solved their automatic detection but enabled the identification of events with small amplitude that otherwise escaped the eye, rendering the determination of their characteristic parameters more accurate.To whom it may concern, Attached please find our manuscript entitled "Improved spark and ember detection using stationary wavelet transforms" by Szabo, Vincze, Csernoch and myself for consideration for publication in the Journal of Theoretical Biology.In the manuscript we give a detailed description of a method to analyze localized calcium release events based on the à trous wavelet transform. We introduce novel algorithms to handle experimental images with large intensity pixels representing shot noise as well as methods to identify long lasting small amplitude events as calcium embers. We believe that these will solve the problem of analyzing confocal images recorded in mammalian muscle fibers.We hope that you will find our manuscript interesting for the community of both theoretical and experimental biologists and thus acceptable for publication in the Journal.Sincerely yours, Peter Szentesi Cover Letter AbstractCalcium sparks and embers are localized intracellular events of calcium release in muscle cells studied frequently by confocal microscopy using line-scan imaging.The large quantity of images and large number of events require automatic detection procedures based on signal processing methods. In the past decades these methods were based on thresholding procedures. Although recently wavelet transforms were also introduced, they have not become widespread. We ...

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“…Detailed mathematical description is given by Mallat (1999), Shensa (1992) and Bijaoui et al (1994). We used both of the one and two dimensional à trous transform.…”

Section: Discussionmentioning

confidence: 99%

“…The algorithm used here is an implementation of the à trous wavelet transform (Holschneider et al 1989, Mallat 1999, Shensa 1992. We followed the implementation that Starck (1993;Starck and Murtagh 1994) used for denoising and object detection in astronomical images.…”

Section: Implementation Of the à Trous Wavelet Transform For Spark Dementioning

confidence: 99%

Improved spark and ember detection using stationary wavelet transforms

Szabó¹,

Vincze²,

Csernoch³

et al. 2010

Journal of Theoretical Biology

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“…The ATrous wavelet transform (ATWT) [23,24] is a nonorthogonal multiresolution decomposition defined by a filter bank {h n } and {g n = δ n − h n }, with the Kronecker operator δ n denoting an all pass filter. The filter bank does not allow perfect reconstruction to be achieved if the output is decimated.…”

Section: Curvelet Transform For Fusionmentioning

confidence: 99%

Quality Assessment of Fused Image of Modis and Palsar

Kumar¹,

Singh

2010

PIER B

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Abstract-It is a current need of research to extensively use the freely available satellite images. The most commonly available satellite images are Moderate Resolution Imaging Spectroradiometer (MODIS) and Advanced Very High Resolution Radiometer (AVHRR). The problems with these images are their poor spatial resolution that restricts their use in various applications. This restriction may be minimized by application of the fusion techniques where high resolution image will be used to fuse with low resolution images. Another important aspect of fusion of different sensors data as optical and radar images (where both can provide the complimentary information), and the resultant fused image after fusion may give enhanced and useful information that may be beneficial for various applications. Therefore, in this paper an attempt has been made to fuse the full polarimetric Phased Array type L-band SAR (PALSAR) image with MODIS image and assess the quality of fused image. PALSAR image has a advantage of availability of data in four different channels. These four channels are HH (Transmitted horizontal polarization and received also in horizontal polarization), HV (Transmitted horizontal polarization and received vertical polarization), VH (Transmitted vertical polarization and received horizontal polarization) and VV (Transmitted vertical polarization and received vertical polarization), which provides various landcover information. The curvelet based fusion technique has been applied to MODIS Bands 1 and 2 and PALSAR (HH, HV and VV) bands for assessing the effect of fusion in land cover distinction. The three major land covers i.e., agriculture, urban and water are considered for evaluation of fusion of these images for the Roorkee area of India. The results are quite encouraging, and in near future 192Harish Kumar and Singh it may provide a better platform for the maximize the use of MODIS images.

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“…The most popular values for the shift and scale parameters are: a=2 j and τ=n2 j , which produce spectrum decomposition in octaves and constant-Q bandpass channels. The resulting dyadic DWT (Discrete Wavelet Transform) can be expressed by [15]:…”

Section: Some Aspects Of Discrete Wavelet Transformsmentioning

confidence: 99%

“…The most popular implementation is the a'trous algorithm [15] and an alternative is based on cycle spinning (CS) [16].…”

Section: Introducction Based On a Firm Theoretical Foundation Wavelementioning

confidence: 99%