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This paper elaborates on a sieving technique that has first been applied in 2018 for improving bounds on deterministic integer factorization. We will generalize the sieve in order to obtain a polynomial-time reduction from integer…
Machine learning-based analysis of medical images often faces several hurdles, such as the lack of training data, the curse of dimensionality problem, and the generalization issues. One of the main difficulties is that there exists…
We propose a special computational device which uses light rays for solving the subset-sum problem. The device has a graph-like representation and the light is traversing it by following the routes given by the connections between nodes.…
Image filters are fast, lightweight and effective, which make these conventional wisdoms preferable as basic tools in vision tasks. In practical scenarios, users have to tweak parameters multiple times to obtain satisfied results. This…
The generalized Morse wavelets are shown to constitute a superfamily that essentially encompasses all other commonly used analytic wavelets, subsuming eight apparently distinct types of analysis filters into a single common form. This…
Diffusion models have emerged as the leading approach for image synthesis, demonstrating exceptional photorealism and diversity. However, training diffusion models at high resolutions remains computationally prohibitive, and existing…
This work proposes a learnable filterbank based on a multi-channel masking framework for multi-channel source separation. The learnable filterbank is a 1D Conv layer, which transforms the raw waveform into a 2D representation. In contrast…
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…
Existing parallel algorithms for wavelet tree construction have a work complexity of $O(n\log\sigma)$. This paper presents parallel algorithms for the problem with improved work complexity. Our first algorithm is based on parallel integer…
The meshless/meshfree radial basis function (RBF) method is a powerful technique for interpolating scattered data. But, solving large RBF interpolation problems without fast summation methods is computationally expensive. For RBF…
In this paper, we investigate a cell-free massive multiple-input multiple-output system with both access points and user equipments equipped with multiple antennas over the Weichselberger Rayleigh fading channel. We study the uplink…
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partial Differential Equations (PDEs). However, applying these…
This paper presents algorithms for the included-sums and excluded-sums problems used by scientific computing applications such as the fast multipole method. These problems are defined in terms of a $d$-dimensional array of $N$ elements and…
Multiresolution Matrix Factorization (MMF) is unusual amongst fast matrix factorization algorithms in that it does not make a low rank assumption. This makes MMF especially well suited to modeling certain types of graphs with complex…
In this paper, we study the synthesis of Gegenbauer processes using the wavelet packets transform. In order to simulate a 1-factor Gegenbauer process, we introduce an original algorithm, inspired by the one proposed by Coifman and…
Even though convolutional neural networks have become the method of choice in many fields of computer vision, they still lack interpretability and are usually designed manually in a cumbersome trial-and-error process. This paper aims at…
The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…
The wavelet scattering transform creates geometric invariants and deformation stability. In multiple signal domains, it has been shown to yield more discriminative representations compared to other non-learned representations and to…
Wavelet estimators for a probability density f enjoy many good properties, however they are not "shape-preserving" in the sense that the final estimate may not be non-negative or integrate to unity. A solution to negativity issues may be to…
The discrete wavelet transform can be found at the heart of many image-processing algorithms. Until now, the transform on general-purpose processors (CPUs) was mostly computed using a separable lifting scheme. As the lifting scheme consists…