An Implementation of the “algorithme à trous” to Compute the Wavelet Transform

By P. Dutilleux. 1989

Subfields: Computer Vision and Pattern Recognition, Speech & Audio

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Citations in the corpus

WaveNet: A Generative Model for Raw Audio (2016, methodology): “Dilated convolutions have previously been used in various contexts, e.g. signal processing (Holschneider et al., 1989; Dutilleux, 1989), and image segmentation (Chen et al., 2015; Yu & Koltun, 2016).”
Monte-Carlo Sure: A Black-Box Optimization of Regularization Parameters for General Denoising Algorithms (2008, methodology): “iii) The Haar-RSWST method; it is implemented using the algorithm à trous [41] which, for , requires a total of computations.”
Compressed Sensing with Coherent and Redundant Dictionaries (2010, unknown): “The UWT lacks the downsamplers and upsamplers in the DWT but upsamples the ﬁlter co-eﬃcients by a factor of 2 m at the ( m − 1)st level – hence it is overcomplete.”
A new intensity-hue-saturation fusion approach to image fusion with a tradeoff parameter (2006, background): “Recently, some studies have shown that the use of a redundant DWT (such as an undecimated à trous wavelet transform [19]) produces a satisfactory spatial resolution [7]–[11].”
The redundant discrete wavelet transform and additive noise (2005, methodology): “The RDWT1 has a long history, having been independently discovered a number of times and given a number of different names, including the algorithme a trous [4], [ 5 ], the undecimated DWT (UDWT) [6], the overcomplete DWT (ODWT) [7], the shift-invariant DWT (SIDWT) [8], and discrete wavelet frames (”
The Undecimated Wavelet Decomposition and its Reconstruction (2007, background): “For other applications where a reconstruction is needed, some researchers have chosen an intermediate approach, which consists of keeping the filter bank construction with fast and dyadic algorithms, but eliminating the decimation step in the orthogonal wavelet transform [8], [9].”
Error‐correction methods and evaluation of an ensemble based hydrological forecasting system for the Upper Danube catchment (2008, methodology): “Especially, the package called DSE (developed by Gilbert [1995]), which focus on various aspects of multivariate ARMAX models, state-space modeling and Kalman filtering, has been applied.”
Image fusion—the ARSIS concept and some successful implementation schemes (2003, background): “The term “à trous” ("with holes") was introduced by Dutilleux (1989) and relates to the fact that the even coefficients of the used scaling function (and the associated wavelet function), except the central one, are zero.”
Multiresolution Tree Networks for 3D Point Cloud Processing (2018, methodology): “Our tree network builds on the ideas of multiscale [18,27], mutligrid [22] and dilated [46] or atrous filters [11,8] effective for a number of image recognition tasks.”
A comparative analysis of image fusion methods (2005, unknown): “The term “à trous” was originally introduced in [35].”
Identification of Intermittent Electrical and Mechanical Faults in Permanent-Magnet AC Drives Based on Time–Frequency Analysis (2007, unknown): “This is known as the “Algorithme à Trous” [20], [21].”