A wavelet tour of signal processing

By Stéphane Mallat. 1998

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Citations in the corpus

Object Detection Networks on Convolutional Feature Maps (2015, methodology): “Then we adopt the “hole algorithm” [33], [34] (“Algorithme à trous” [35]) on all following layers to compensate this modification.”
Fully convolutional networks for semantic segmentation (2014, background): “Consider a layer (convolution or pooling) with input stride s , and a following convolution layer with ﬁlter weights f ij (eliding the feature dimensions, irrelevant here).”
Fully Convolutional Instance-Aware Semantic Segmentation (2016, methodology): “To reduce the feature stride and maintain the field of view, the “hole algorithm” [3, 29] (Algorithme à trous [30]) is applied.”
R-FCN: Object Detection via Region-based Fully Convolutional Networks (2016, methodology): “…and on the conv 4 stage [10] (stride=16) are unchanged; the stride=2 operations in the ﬁrst conv 5 block is modiﬁed to have stride=1, and all convolutional ﬁlters on the conv 5 stage are modiﬁed by the “hole algorithm” [16, 2] (“ Algorithme à trous ” [17]) to compensate for the reduced stride.”
NICE: Non-linear Independent Components Estimation (2014, methodology): “For example wavelets (Mallat, 1999) may provide a sparser signal to model, and normalization and whitening remove trivial scaling and correlation allowing the model to focus on more interesting structure of the data and ease the optimization process.”
Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, background): “In this context, the authors of [14, 9, 11] revisited the construction of wavelet operators on graphs.”
Deep Convolutional Networks on Graph-Structured Data (2015, background): “We then recover a classical convolution operator by noting that convolutions are by deﬁnition linear operators that diagonalize in the Fourier domain (also known as the Convolution Theorem [11]).”
Semantic Image Segmentation with Deep Convolutional Nets and Fully Connected CRFs (2014, methodology): “1 is known as the ‘hole algorithm’ (‘atrous algorithm’) and has been developed before for efﬁcient computation of the undecimated wavelet transform (Mallat, 1999).”
Fully Connected Deep Structured Networks (2015, methodology): “To take into account the skipped downsampling during subsequent convolutions we employ the ‘ ` a trous (with hole) algorithm’ [23].”
Attention to Scale: Scale-Aware Semantic Image Segmentation (2015, methodology): “DeepLab reduces it to 8 by using the à trous (with holes) algorithm [39], and employs linear interpolation to upsample by a factor of 8 the score maps of the final layer to original image resolution.”
A theory of independent mechanisms for extrapolation in generative models (2020, methodology): “We also used a discrete Haar wavelet transform of the images to isolate the contribution of each scale to the image (Mallat, 1999).”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “These kernels can be learnt efficiently by mimicking the socalled algorithme à trous [61], also referred to as dilated convolution.”
i-RevNet: Deep Invertible Networks (2018, neutral): “For example, adding constraints beyond vanishing moments in the case of a Lifting scheme is difﬁcult (Sweldens, 1998; Mallat, 1999), and this is a weakness of this method.”
Deep roto-translation scattering for object classification (2014, methodology): “Wavelet transforms can be computed with a cascade of linear filtering and sub-sampling operators, which are called multi-rate filter banks [21].”
Weakly-and Semi-Supervised Learning of a Deep Convolutional Network for Semantic Image Segmentation (2015, methodology): “Similar to [5], we also employ the ‘atrous’ algorithm [27] in the DeepLab model.”
Monocular Object Instance Segmentation and Depth Ordering with CNNs (2015, methodology): “Data subsampling can be efficiently implemented for convolutions, which has been previously discussed in work by Mallat [27], known as the ‘à trous (with hole) algorithm’ and applied to CNNs in recent work [3, 29, 32].”
Group Invariant Scattering (2011, methodology): “Numerical examples in the paper are computed with the analytic part of a cubic-spline Battle-Lemarié wavelet [13].”
Wavelets on Graphs via Spectral Graph Theory (2009, positive): “By taking separable products of one-dimensional wavelets, one can construct orthogonal families of wavelets in any dimension [21].”
Bridging Category-level and Instance-level Semantic Image Segmentation (2016, methodology): “However, Chen et al. [2] reported that the hole algorithm (or the àtrous algorithm by Mallat [22]) can be more efﬁcient.”
High-performance Semantic Segmentation Using Very Deep Fully Convolutional Networks (2016, methodology): “However, Chen et al. [2] reported that the hole algorithm (or the `atrous algorithm by Mallat [17]) can be more eﬃcient.”