Related papers: Fourier-Based Spectral Analysis with Adaptive Reso…
Many signals on Cartesian product graphs appear in the real world, such as digital images, sensor observation time series, and movie ratings on Netflix. These signals are "multi-dimensional" and have directional characteristics along each…
This article is written to serve as an introduction and survey of imaging with synthetic aperture radar (SAR). The reader will benefit from having some familiarity with harmonic analysis, electromagnetic radiation, and inverse problems.…
Computer vision models normally witness degraded performance when deployed in real-world scenarios, due to unexpected changes in inputs that were not accounted for during training. Data augmentation is commonly used to address this issue,…
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is…
The recovery of a signal from the magnitude of its Fourier transform, also known as phase retrieval, is of fundamental importance in many scientific fields. It is well known that due to the loss of Fourier phase the problem in 1D is…
In Fourier ptychography, multiple low resolution images are captured and subsequently combined computationally into a high-resolution, large-field of view micrograph. A theoretical image-formation model based on the assumption of plane-wave…
The classical Fourier transform is, in essence, a way to take data and extract components (in the form of complex exponentials) which are invariant under cyclic shifts. We consider a case in which the components must instead be invariant…
A brief survey of the theory of soliton perturbations is presented. The focus is on the usefulness of the so-called Generalised Fourier Transform (GFT). This is a method that involves expansions over the complete basis of `squared olutions`…
Spectral imaging is a fundamental diagnostic technique with widespread application. Conventional spectral imaging approaches have intrinsic limitations on spatial and spectral resolutions due to the physical components they rely on. To…
We study the volatility functional inference by Fourier transforms. This spectral framework is advantageous in that it harnesses the power of harmonic analysis to handle missing data and asynchronous observations without any artificial time…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
The graph fractional Fourier transform (GFRFT) applies a single global fractional order to all graph frequencies, which restricts its adaptability to diverse signal characteristics across the spectral domain. To address this limitation, in…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…
Spatial variables can be observed in many different forms, such as regularly sampled random fields (lattice data), point processes, and randomly sampled spatial processes. Joint analysis of such collections of observations is clearly…
We propose a decomposition method for the spectral peaks in an observed frequency spectrum, which is efficiently acquired by utilizing the Fast Fourier Transform. In contrast to the traditional methods of waveform fitting on the spectrum,…
Source-free domain adaptation (SFDA) is compelling because it allows adapting an off-the-shelf model to a new domain using only unlabelled data. In this work, we apply existing SFDA techniques to a challenging set of naturally-occurring…
A novel approach to 3D surface imaging is proposed, allowing for the continuous sampling of 3D surfaces to extract localized perspective transformation coefficients from Fourier spectrum analysis of projected patterns. The mathematical…
Signal processing on directed graphs (digraphs) is problematic, since the graph shift, and thus associated filters, are in general not diagonalizable. Furthermore, the Fourier transform in this case is now obtained from the Jordan…
Foundation models (FMs) have emerged as a transformative paradigm in medical image analysis, offering the potential to provide generalizable, task-agnostic solutions across a wide range of clinical tasks and imaging modalities. Their…