相关论文: Wavelet Filtering with the Mellin Transform

Wavelet functions allow the sparse and efficient representation of a signal at different scales. Recently the application of wavelets to the denoising of maps of cosmic microwave background (CMB) fluctuations has been proposed. The…

This paper presents a multiscale decomposition algorithm. Unlike standard wavelet transforms, the proposed operator is both linear and shift invariant. The central idea is to obtain shift invariance by averaging the aligned wavelet…

Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…

Unsupervised deep learning has recently demonstrated the promise of producing high-quality samples. While it has tremendous potential to promote the image colorization task, the performance is limited owing to the high-dimension of data…

Masked Image Modeling (MIM) has garnered significant attention in self-supervised learning, thanks to its impressive capacity to learn scalable visual representations tailored for downstream tasks. However, images inherently contain…

While working within the spatial domain can pose problems associated with ill-conditioned scores caused by power-law decay, recent advances in diffusion-based generative models have shown that transitioning to the wavelet domain offers a…

In this paper we propose a new wavelet transform applicable to functions defined on graphs, high dimensional data and networks. The proposed method generalizes the Haar-like transform proposed in [1], and it is defined via a hierarchical…

We here use notions from the theory linear shift-invariant dynamical systems to provide an easy-to-compute characterization of all rational wavelet filters. For a given N bigger or equql to 2, the number of inputs, the construction is based…

The forward and inverse wavelet transform using the continuous Morlet basis may be symmetrized by using an appropriate normalization factor. The loss of response due to wavelet truncation is addressed through a renormalization of the…

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured…

This correspondence presents an efficient method for reconstructing a band-limited signal in the discrete domain from its crossings with a sine wave. The method makes it possible to design A/D converters that only deliver the crossing…

The application of the continuous wavelet transform to study of a wide class of physical processes with oscillatory dynamics is restricted by large central frequencies due to the admissibility condition. We propose an alternative…

Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately,…

This article describes a series of new results outlining equivalences between certain "rewirings" of filterbank system block diagrams, and the corresponding actions of convolution, modulation, and downsampling operators. This gives rise to…

The wavelet transform, a family of orthonormal bases, is introduced as a technique for performing multiresolution analysis in statistical mechanics. The wavelet transform is a hierarchical technique designed to separate data sets into sets…

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the…

In analogy with steerable wavelets, we present a general construction of adaptable tight wavelet frames, with an emphasis on scaling operations. In particular, the derived wavelets can be "dilated" by a procedure comparable to the operation…

This paper develops a threshold model with a time-varying threshold, represented using a wavelet series expansion. The model adequately captures irregular and abrupt variations, as well as smooth changes in the threshold parameter, allowing…

Wavelet analysis and compression tools are reviewed and different applications to study MHD and plasma turbulence are presented. We introduce the continuous and the orthogonal wavelet transform and detail several statistical diagnostics…

We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…