Questions tagged [scattering]
Wavelet scattering is a convolutional network formed by cascade of wavelets, modulus nonlinearities, and lowpass filters. It yields invariant, sparse, and stable representations useful for classification, generation, and other tasks. Filters are fixed, but architecture differentiable and extendable with learned layers adapted to data.
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Can finite Multi-Resolution Analysis satisfy the Littlewood-Paley Criterion (unity partition)?
Suppose we are working with a multi resolution analysis (MRA) of $L^2(\mathbb{R})$ and let $\phi$ be the corresponding scaling function and $\psi$ the derived wavelets. Using standard notation with $\...
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Littlewood-Paley Conditions, Scattering, and Multi-Resolution Analysis
So I am trying to understand the scattering transform on graphs (GST). There are many formulations but I am stuck on equation 8 in this paper. Here they give a condition on a wavelets that looks like ...
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What is "spin" for the 2D (separable) Morlet?
The 2D Morlet formed separably as product of 1D Morlets, used in JTFS, is said to have "spin":
$$
\begin{align}
\Psi_{{\mu, l, +1}}(t, \lambda)
&= \psi_\mu(t) \psi_{l}(+\lambda)
&&...
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Classification of Signals using Features Extracted from Wavelet Scattering Coefficients
I have a set of RF signal samples of 2s length each recorded at 2MHz sampling rate, such as this IQ file: https://www.dropbox.com/s/dd6fr4va4alpazj/move_x_movedist_1_speed_25k_sample_6.wav?dl=0
I can ...
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Wavelet Scattering (Kymatio) Zero Divison Error
I'm attempting to make use of wavelet scattering to analyse my signal samples.
The example IQ Wav file I am using is as follows: https://www.dropbox.com/s/dd6fr4va4alpazj/...
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Choosing a good low pass filter in the wavelet scattering transform
What's the impact of a specific filter $\phi$ when building the wavelet scattering transform? I mean, if I compute the MFCC choosing different windows, (Hamming, Blackman, etc.), the behaviour ...
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Time support for wavelets in scattering transform
In 1 they say that the energy of $\psi_\lambda(t)$ is concentrated in an interval of length $2\pi Q/\lambda$. I understand the inverse proportionality between the frequency band $\lambda/Q$ and the ...
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Building the low pass filter in the wavelet scattering transform
In 1, analyzing the equivalence between MFCC and wavelet transform, the scaled wavelets are truncated for $\lambda < 2\pi Q/T$ to fit the time spread of the wavelets within the length $T$ of the ...
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Joint Time-Frequency Scattering structure & implementation?
How does JTFS differ from wavelet time scattering in its computation graph, and how does FDTS discriminability work, at a lower level? How is it implemented in practice, and how can one visualize ...
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Joint Time-Frequency Scattering explanation?
How does JTFS work, intuitively? What are its motivations, and how's it differ from the Wavelet (time) Scattering transform? Can it be visualized?
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Wavelet Scattering time-warp equivariance
Is scattering equivariant to multiplicative time warps? Defined as
$$
x(t) \rightarrow x(\tau(t)t),\ \text{sup}|\tau'(t)| < 1
$$
This post claims it holds approximately - what are the arguments, ...
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Wavelet Scattering properties & implementation?
What are the properties of the scattering transform, besides shift invariance and warp stability? How is it implemented in practice, and how can one visualize its computational graph?
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Wavelet Scattering explanation?
How does Wavelet Scattering work, intuitively? What are its motivations, and how's it differ from the (continuous) Wavelet Transform? Can it be visualized?
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Why does each node in the wavelet scattering transform split into multiple paths?
Why does each node in the wavelet scattering transform split into multiple paths as in this figure from Deep Scattering Spectrum?
I understand roughly what’s happening along a single path, but I don’...
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