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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…
This work characterizes (dyadic) wavelet frames for $L^2({\mathbb R})$ by means of spectral techniques. These techniques use decomposability properties of the frame operator in spectral representations associated to the dilation operator.…
Acoustic-resolution photoacoustic microscopy (AR-PAM) is a promising tool for microvascular imaging. In the focal region, resolution of AR-PAM is determined by the ultrasound transducer and ultimately limited by acoustic diffraction. In the…
Non-destructive characterization of multi-layered structures that can be accessed from only a single side is important for applications such as well-bore integrity inspection. Existing methods related to Synthetic Aperture Focusing…
In this paper, we introduce an innovative super resolution approach to emerging modes of near-field synthetic aperture radar (SAR) imaging. Recent research extends convolutional neural network (CNN) architectures from the optical to the…
Higher spatial resolution and larger imaging scene are always the goals pursued by advanced space-borne SAR system.High resolution and wide swath SAR imaging can provide more information about the illuminated scene of interest on one…
Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from $\mathcal{O}(n^2)$ in the number of antennas to $\mathcal{O}(n\log n)$.…
The linear frequency modulated (LFM) frequency agile radar (FAR) can synthesize a wide signal bandwidth through coherent processing while keeping the bandwidth of each pulse narrow. In this way, high range resolution profiles (HRRP) can be…
We present a framework for adapting a large pretrained latent diffusion model to high-resolution Synthetic Aperture Radar (SAR) image generation. The approach enables controllable synthesis and the creation of rare or out-of-distribution…
Amyotrophic Lateral Sclerosis (ALS) is a complex neurodegenerative disorder involving motor neuron degeneration. Significant research has begun to establish brain magnetic resonance imaging (MRI) as a potential biomarker to diagnose and…
In this paper we analyze two-dimensional wavelet reconstructions from Fourier samples within the framework of generalized sampling. For this, we consider both separable compactly-supported wavelets and boundary wavelets. We prove that the…
Data acquisition in array signal processing (ASP) is costly because achieving high angular and range resolutions necessitates large antenna apertures and wide frequency bandwidths, respectively. The data requirements for ASP problems grow…
We show that the second oversampling theorem for affine systems generates super-wavelets. These are frames generated by an affine structure on the space $L^2(\br)\oplus...\oplus L^2(\br)$.
Image super-resolution (SR) has significantly advanced through the adoption of Transformer architectures. However, conventional techniques aimed at enlarging the self-attention window to capture broader contexts come with inherent…
This paper studies the multi-reference alignment (MRA) problem of estimating a signal function from shifted, noisy observations. Our functional formulation reveals a new connection between MRA and deconvolution: the signal can be estimated…
Through-wall synthetic aperture radar (SAR) imaging is of significant interest for security purposes, in particular when using multi-static SAR systems consisting of multiple distributed radar transmitters and receivers to improve…
Several recent randomized linear algebra algorithms rely upon fast dimension reduction methods. A popular choice is the Subsampled Randomized Hadamard Transform (SRHT). In this article, we address the efficacy, in the Frobenius and spectral…
Two-point super-resolution is an important problem in many signal processing applications. In this paper, we aim to establish a resolution theory for two-point super-resolution from a single snapshot. We consider a complex two-point model…
Time-frequency representations, such as the short-time Fourier transform (STFT), are fundamental tools for analyzing non-stationary signals. However, their ability to achieve sharp localization in both time and frequency is inherently…
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…