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Compressed sensing has shown great potential in reducing data acquisition time in magnetic resonance imaging (MRI). Recently, a spread spectrum compressed sensing MRI method modulates an image with a quadratic phase. It performs better than…
Magnetic Resonance Fingerprinting (MRF) is an emerging technology with the potential to revolutionize radiology and medical diagnostics. In comparison to traditional magnetic resonance imaging (MRI), MRF enables the rapid, simultaneous,…
Graph signal processing (GSP) leverages the inherent signal structure within graphs to extract high-dimensional data without relying on translation invariance. It has emerged as a crucial tool across multiple fields, including learning and…
Phase retrieval from phaseless short-time Fourier transform (STFT) measurements is known to be inherently unstable when measurements are taken with respect to a single window. While an explicit inversion formula exists, it is useless in…
Fourier representation (FR) is an indispensable mathematical formulation for modeling and analysis of physical phenomenon, engineering systems and signals in numerous applications. In this study, we present the generalized Fourier…
To analyze signals with rapid frequency variations or transient components, the time-reassigned synchrosqueezing transform (TSST) and its variants have been recently proposed. Unlike the traditional synchrosqueezing transform, TSST squeezes…
Via chirp functions from fractional Fourier transforms, the authors introduce fractional Riesz potentials related to chirp functions, establish their relations with fractional Fourier transforms, fractional Laplace operators related to…
Vertex-frequency analysis, particularly the windowed graph Fourier transform (WGFT), is a significant challenge in graph signal processing. Tight frame theories is known for its low computational complexity in signal reconstruction, while…
The fundamentals of Fourier Transform are presented, with analytical solutions derived for Continuous Fourier Transform (CFT) of truncated signals, to benchmark against Fast Fourier Transform (FFT). Certain artifacts from FFT were…
Transformers have exhibited promising performance in computer vision tasks including image super-resolution (SR). However, popular transformer-based SR methods often employ window self-attention with quadratic computational complexity to…
In this paper, we study the convolution structure in the special affine Fourier domain to combine the advantages of the well known special affine Fourier and wavelet transforms into a novel integral transform coined as special affine…
Gaussian Splatting (GS) has emerged as a dominating technique for image rendering and has quickly been adapted for the X-ray Computed Tomography (CT) reconstruction task. However, despite being on par or better than many of its…
Vision Transformers have shown superior performance to the traditional convolutional-based frameworks in many vision applications, including but not limited to the segmentation of 3D medical images. To further advance this area, this study…
Computed tomography perfusion (CTP) and magnetic resonance perfusion (MRP) are widely used in acute ischemic stroke assessment and other cerebrovascular conditions to generate quantitative maps of cerebral hemodynamics. While commercial…
Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing.…
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,…
Many multi-dimensional signals appear in the real world, such as digital images and data that has spatial and temporal dimensions. How to show the spectrum of these multi-dimensional signals correctly is a key challenge in the field of…
This work is concerned with applying iterative image reconstruction, based on constrained total-variation minimization, to low-intensity X-ray CT systems that have a high sampling rate. Such systems pose a challenge for iterative image…
X-Ray based computed tomography (CT) is a well-established technique for determining the three-dimensional structure of an object from its two-dimensional projections. In the past few decades, there have been significant advancements in the…
Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate enhancement in resolution of a non-periodical object…