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Rotation invariance is essential for precise, object-level segmentation in UAV aerial imagery, where targets can have arbitrary orientations and exhibit fine-scale details. Conventional segmentation architectures like U-Net rely on…

In image deconvolution problems, the diagonalization of the underlying operators by means of the FFT usually yields very large speedups. When there are incomplete observations (e.g., in the case of unknown boundaries), standard…

In image reconstruction there are techniques that use analytical formulae for the Radon transform to recover an image from a continuum of data. In practice, however, one has only discrete data available. Thus one often resorts to sampling…

We present the methodology of a photon-conserving, spatially-adaptive, ray-tracing radiative transfer algorithm, designed to run on multiple parallel Graphic Processing Units (GPUs). Each GPU has thousands computing cores, making them…

The article presents a computationally effective algorithm for calculating the multiresolution discrete Fourier transform (MrDFT). The algorithm is based on the idea of reducing the computational complexity which was introduced by Wen and…

Operational Neural Networks (ONNs) have recently been proposed as a special class of artificial neural networks for grid structured data. They enable heterogenous non-linear operations to generalize the widely adopted convolution-based…

In recent years, many types of elliptical Radon transforms that integrate functions over various sets of ellipses/ellipsoids have been considered, relating to studies in bistatic synthetic aperture radar, ultrasound reflection tomography,…

Nonuniform Fourier data are routinely collected in applications such as magnetic resonance imaging, synthetic aperture radar, and synthetic imaging in radio astronomy. To acquire a fast reconstruction that does not require an online inverse…

Constructing effective image priors is critical to solving ill-posed inverse problems in image processing and imaging. Recent works proposed to exploit image non-local similarity for inverse problems by grouping similar patches and…

We present efficient algorithms to build data structures and the lists needed for fast multipole methods. The algorithms are capable of being efficiently implemented on both serial, data parallel GPU and on distributed architectures. With…

Ray tracing is increasingly utilized in wireless system simulations to estimate channel paths. In large-scale simulations with complex environments, ray tracing at high resolution can be computationally demanding. To reduce the computation,…

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative…

The study of binary pulsars enables tests of general relativity. Orbital motion in binary systems causes the apparent pulsar spin frequency to drift, reducing the sensitivity of periodicity searches. Acceleration searches are methods that…

Recently, transformer networks have outperformed traditional deep neural networks in natural language processing and show a large potential in many computer vision tasks compared to convolutional backbones. In the original transformer,…

The convolution computation is widely used in many fields, especially in CNNs. Because of the rapid growth of the training data in CNNs, GPUs have been used for the acceleration, and memory-efficient algorithms are focused because of thier…

Reconstructing an image from its Radon transform is a fundamental computed tomography (CT) task arising in applications such as X-ray scans. In many practical scenarios, a full 180-degree scan is not feasible, or there is a desire to reduce…

In this paper, an optimized efficient VLSI architecture of a pipeline Fast Fourier transform (FFT) processor capable of producing the reverse output order sequence is presented. Paper presents Radix-2 multipath delay architecture for FFT…

Hardware-based acceleration is an extensive attempt to facilitate many computationally-intensive mathematics operations. This paper proposes an FPGA-based architecture to accelerate the convolution operation - a complex and expensive…

Computed tomography (CT) has been developed as a non-destructive technique for observing minute internal images of samples. It has been difficult to obtain photo-realistic (clean or clear) CT images due to various unwanted artifacts…

The Radon transform Rf of functions f on SO(3) has recently been applied extensively in texture analysis, i.e. the analysis of preferred crystallographic orientation. In practice one has to determine the orientation probability density…