Related papers: Continuous Boostlet Transform and Associated Uncer…

In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are - unlike more traditional transforms like wavelets -…

This work revisits a class of biomimetically inspired log-periodic waveforms first introduced by R.A. Altes in the 1970s for generalized target description. It was later observed that there is a close connection between such sonar…

In this paper, we propose Dynamic Compressive Transformer (DCT), a transformer-based framework for modeling the unbounded sequence. In contrast to the previous baselines which append every sentence representation to memory, conditionally…

An exact and general expression for the analytic wavelet transform of a real-valued signal is constructed, resolving the time-dependent effects of non-negligible amplitude and frequency modulation. The analytic signal is first locally…

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…

In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on…

In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their…

We show that continuous transform with the complex Morlet wavelet is easily performed if we replace the integration of the fast-oscillation function by the solution of the diffusion differential equations. The most important advantage of…

Cone-beam computed tomography (CBCT) is widely used for image-guided radiotherapy (IGRT). It provides real time visualization at low cost and dose. However, photon scattering and beam hindrance cause artifacts in CBCT. These include…

Periodic point sets model all solid crystalline materials (crystals) whose atoms can be considered zero-sized points with or without atomic types. This paper addresses the fundamental problem of checking whether claimed crystals are novel,…

This work presents a purely data-driven, wavelet-based framework for modal identification and reduced-order modeling of mechanical systems with assumed linear dynamics characterized by closely spaced modes with classical or non-classical…

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…

In dynamic acoustic environments with time-varying interferers, effective beamforming requires identifying stationary regions over time. The Capon beamformer, a whitened matched filter constrained to maintain unity gain in the desired…

Transformer-based architectures have advanced medical image analysis by effectively modeling long-range dependencies, yet they often struggle in 3D settings due to substantial memory overhead and insufficient capture of fine-grained local…

Modern power systems are at risk of largely reducing the inertia of generation assets and prone to experience extreme dynamics. The consequence is that, during electromechanical transients triggered by large contingencies, transmission of…

Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process…

Accurate classification of sleep stages is crucial for the diagnosis and management of sleep disorders. Conventional approaches for sleep scoring rely on manual annotation or features extracted from EEG signals in the time or frequency…

Long-term time series forecasting using transformers is hampered by the quadratic complexity of self-attention and the rigidity of uniform patching, which may be misaligned with the data's semantic structure. In this paper, we introduce the…

Objective: Cone-beam computed tomography (CBCT) provides a low-dose imaging alternative to conventional CT, but suffers from noise, scatter, and artifacts that degrade image quality. Synthetic CT (sCT) aims to translate CBCT to high-quality…

The Hilbert-Huang Transform is a novel, adaptive approach to time series analysis that does not make assumptions about the data form. Its adaptive, local character allows the decomposition of non-stationary signals with hightime-frequency…