Related papers: Parametric Scattering Networks
In graph signal processing, one of the most important subjects is the study of filters, i.e., linear transformations that capture relations between graph signals. One of the most important families of filters is the space of shift invariant…
In Image Compression, the researchers' aim is to reduce the number of bits required to represent an image by removing the spatial and spectral redundancies. Recently discrete wavelet transform and wavelet packet has emerged as popular…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
Waveform evaluation for sixth generation (6G) networks has largely relied on sparse and quasi-stationary channel models that enabled mathematical tractability, diversity gains, and Doppler robustness. However, such models obscure the…
In recent years, the underwater image formation model has found extensive use in the generation of synthetic underwater data. Although many approaches focus on scenes primarily affected by discoloration, they often overlook the model's…
This paper introduces an adaptive filtering process based on shrinking wavelet coefficients from the corresponding signal wavelet representation. The filtering procedure considers a threshold method determined by an iterative algorithm…
Normalized wave packets express particles in nature. Their sizes are determined by their interactions with matter, and depend on environments. Nevertheless, these characterize scatterings processes in realistic situations, and govern the…
What makes waveform-based deep learning so hard? Despite numerous attempts at training convolutional neural networks (convnets) for filterbank design, they often fail to outperform hand-crafted baselines. These baselines are linear…
Factorization of matrices of Laurent polynomials plays an important role in mathematics and engineering such as wavelet frame construction and filter bank design. Wavelet frames (a.k.a. framelets) are useful in applications such as signal…
The tradeoff between receptive field size and efficiency is a crucial issue in low level vision. Plain convolutional networks (CNNs) generally enlarge the receptive field at the expense of computational cost. Recently, dilated filtering has…
The underlying mathematics of the wavelet formalism is a representation of the inhomogeneous Lorentz group or the affine group. Within the framework of wavelets, it is possible to define the ``window'' which allows us to introduce a…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…
Filters in convolutional networks are typically parameterized in a pixel basis, that does not take prior knowledge about the visual world into account. We investigate the generalized notion of frames designed with image properties in mind,…
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers we may be able to accurately classify signals, however that accuracy may decline if using a reduced…
This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of…
In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
With the aim of constructing a biologically plausible model of machine listening, we study the representation of a multicomponent stationary signal by a wavelet scattering network. First, we show that renormalizing second-order nodes by…
Conventionally, convolutional neural networks (CNNs) process different images with the same set of filters. However, the variations in images pose a challenge to this fashion. In this paper, we propose to generate sample-specific filters…
Time series are ubiquitous in many applications that involve forecasting, classification and causal inference tasks, such as healthcare, finance, audio signal processing and climate sciences. Still, large, high-quality time series datasets…