Related papers: Fourier-Based Spectral Analysis with Adaptive Reso…
The Fractional Fourier Transform is a ubiquitous signal processing tool in basic and applied sciences. The Fractional Fourier Transform generalizes every property and application of the Fourier Transform. Despite the practical importance of…
Can one reduce the size of a graph without significantly altering its basic properties? The graph reduction problem is hereby approached from the perspective of restricted spectral approximation, a modification of the spectral similarity…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Equations arising in General Relativity are usually too complicated to be solved analytically and one has to rely on numerical methods to solve sets of coupled partial differential equations. Among the possible choices, this paper focuses…
The average spectrum method is a promising approach for the analytic continuation of imaginary time or frequency data to the real axis. It determines the analytic continuation of noisy data from a functional average over all admissible…
The Arithmetic Fourier Transform is a numerical formulation for computing Fourier series and Taylor series coefficients. It competes with the Fast Fourier Transform in terms of speed and efficiency, requiring only addition operations and…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
The high-order accuracy of Fourier method makes it the method of choice in many large scale simulations. We discuss here the stability of Fourier method for nonlinear evolution problems, focusing on the two prototypical cases of the…
We describe a simple method for unsupervised domain adaptation, whereby the discrepancy between the source and target distributions is reduced by swapping the low-frequency spectrum of one with the other. We illustrate the method in…
Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these…
In many network problems, graphs may change by the addition of nodes, or the same problem may need to be solved in multiple similar graphs. This generates inefficiency, as analyses and systems that are not transferable have to be…
This paper presents a new approach in application of the Fourier transform to the complex error function resulting in an efficient rational approximation. Specifically, the computational test shows that with only $17$ summation terms the…
We present the Evolving Graph Fourier Transform (EFT), the first invertible spectral transform that captures evolving representations on temporal graphs. We motivate our work by the inadequacy of existing methods for capturing the evolving…
Data are represented as graphs in a wide range of applications, such as Computer Vision (e.g., images) and Graphics (e.g., 3D meshes), network analysis (e.g., social networks), and bio-informatics (e.g., molecules). In this context, our…
Within the graph learning community, conventional wisdom dictates that spectral convolutional networks may only be deployed on undirected graphs: Only there could the existence of a well-defined graph Fourier transform be guaranteed, so…
Time series forecasting typically needs to address non-stationary data with evolving trend and seasonal patterns. To address the non-stationarity, reversible instance normalization has been recently proposed to alleviate impacts from the…
Existing convolutional neural networks widely adopt spatial down-/up-sampling for multi-scale modeling. However, spatial up-sampling operators (\emph{e.g.}, interpolation, transposed convolution, and un-pooling) heavily depend on local…
X-ray scattering patterns from emerging single particle experiments have commonly many missing or contaminated pixels. This complicates different analyses including projections on Fourier or other basis functions (for noise suppression,…
Bayesian image analysis has played a large role over the last 40+ years in solving problems in image noise-reduction, de-blurring, feature enhancement, and object detection. However, these problems can be complex and lead to computational…
Bayesian inference, while foundational to probabilistic reasoning, is often hampered by the computational intractability of posterior distributions, particularly through the challenging evidence integral. Conventional approaches like Markov…