Related papers: FPS-SFT: A Multi-dimensional Sparse Fourier Transf…
We unify the discrete Fourier transform (DFT), discrete cosine transform (DCT), Walsh-Hadamard, Haar wavelet, Karhunen-Lo\`eve transform, and several others along with their continuous counterparts (Fourier transform, Fourier series,…
In this paper, a novel and robust algorithm is proposed for adaptive beamforming based on the idea of reconstructing the autocorrelation sequence (ACS) of a random process from a set of measured data. This is obtained from the first column…
In distributed radar systems, when several transmitters radiate simultaneously, the reflected signals need to be distinguished at the receivers to detect various targets. If the transmit signals are in different frequency bands, they…
With the prevalence of multimodal learning, camera-LiDAR fusion has gained popularity in 3D object detection. Although multiple fusion approaches have been proposed, they can be classified into either sparse-only or dense-only fashion based…
Micro-computed tomography (micro-CT) is a widely used state-of-the-art instrument employed to study the morphological structures of objects in various fields. However, its small field-of-view (FOV) cannot meet the pressing demand for…
The extraction of information carried by light plays an increasingly important role in optical communication, imaging, and detection. However, the information can only be successfully extracted when the light pulse is comparably strong,…
A robust and streamlined method is presented for efficiently extracting spectral diffusion from two-dimensional coherent spectra by employing the projection-slice theorem. The method is based on the optical Bloch equations for a single…
The double Fourier sphere (DFS) method uses a clever trick to transform a function defined on the unit sphere to the torus and subsequently approximate it by a Fourier series, which can be evaluated efficiently via fast Fourier transforms.…
In this paper we study the performance of image reconstruction methods from incomplete samples of the 2D discrete Fourier transform. Inspired by requirements in parallel MRI, we focus on a special sampling pattern with a small number of…
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…
Compressed sensing is a novel technique where one can recover sparse signals from the undersampled measurements. This paper studies a $K \times N$ partial Fourier measurement matrix for compressed sensing which is deterministically…
This paper is to investigate the high-quality analytical reconstructions of multiple source-translation computed tomography (mSTCT) under an extended field of view (FOV). Under the larger FOVs, the previously proposed backprojection…
We present a variational Bayesian method of joint image reconstruction and point spread function (PSF) estimation when the PSF of the imaging device is only partially known. To solve this semi-blind deconvolution problem, prior…
The problem of computing the Fourier Transform of a signal whose spectrum is dominated by a small number $k$ of frequencies quickly and using a small number of samples of the signal in time domain (the Sparse FFT problem) has received…
The two-sided quaternionic Fourier transformation (QFT) was introduced in \cite{Ell:1993} for the analysis of 2D linear time-invariant partial-differential systems. In further theoretical investigations \cite{10.1007/s00006-007-0037-8,…
Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array.…
We present a novel framework to automatically learn to transform the differential cues from a stack of images densely captured with a rotational motion into spatially discriminative and view-invariant per-pixel features at each view. These…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
Forward scatter radar (FSR) has emerged as an effective imaging modality for target detection, utilizing forward scattering (FS) signals to reconstruct two-dimensional shadow profile images of objects. However, real-world FS signals are…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…