An input signal x is filtered by a collection of dilated band-pass wavelets obtained from ψ, followed by a modulus and finally averaged by a dilation of φ. The wavelets we chose decompose the signal in a …

In the context of deriving rotationally invariant representations, the Fourier Transform is particularly appealing since it exhibits invariance to rotational deformations up to phase (a truly invariant …

The scattering transform, proposed in [29], is a cascade of wavelets and complex modulus nonlinearities, which can be seen as a convolutional neural network (CNN) with fixed, predetermined …

ScatNet [5] cascades wavelet transfor- m with nonlinear modulus and average pooling, to extract a translation invariant feature robust to deformations and preserve high-frequency information for …

In the case of a wavelet transform obtained by rotation of a mother wavelet, it is possible to recover a new subgroup of symmetry after a modulus non-linearity, the ro-tation SO2, and the group of …

For instance, while an individual CNT has an elastic modulus of around 1 TPa, a CNT forest’s compressive elastic modulus are frequently on the order of 1-10 MPa [26], akin to nat-ural rubber.

They instead take the modulus of the response to a bank of discretely rotated and scaled wavelets, repeatedly in a deep fashion. This is perhaps the most successful version of a handcrafted deep …

Unlike typical CNNs: 1) regarding the architecture, convolutional layers are defined by fixed wavelet filters, with modulus-based nonlinearity, but without subsequent pooling; 2) regarding the …

Applying a modulus removes this variability. As a classical result of signal theory, ob-serve also that an averaged rectified signal is approximately equal to the average of its complex envelope [18].

For PCF, kuk1 = | denotes the vector L1 norm and γ i=1 is a corre- Pd sponding weight, while for EPCF, |u| = (|u1|, ..., |ud|)⊤ denotes the component-wise modulus and γ ∈ IRd is a cor-responding weight …