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We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
Synchrosqueezing transform (SST) is a useful tool for vibration signal analysis due to its high time-frequency (TF) concentration and reconstruction properties. However, existing SST requires much processing time for large-scale data. In…
In this paper, we describe the principle of a multi-aperture interferometer that uses a phase-shifting technique and is suitable for quick, snapshot imaging of astrophysical objects at extreme angular resolution through Fourier inversion. A…
Starting from the observation that the correlation coefficient defined by the scattered field data tested by two adjacent antennas decreases with the noise, it turns out that the imaging performance can be improved by adding non-redundant…
Signal extrapolation tasks arise in miscellaneous manners in the field of image and video signal processing. But, due to the widespread use of low-power and mobile devices, the computational complexity of an algorithm plays a crucial role…
Digital filters for recursively computing the discrete Fourier transform (DFT) and estimating the frequency spectrum of sampled signals are examined, with an emphasis on magnitude-response and numerical stability. In this tutorial-style…
This summary of the doctoral thesis provides a comprehensive formulation of the Extended Discrete Fourier Transform (EDFT), derived directly from the Fourier integral and its orthogonality properties. The method is obtained by solving…
Image Fusion, a technique which combines complimentary information from different images of the same scene so that the fused image is more suitable for segmentation, feature extraction, object recognition and Human Visual System. In this…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
As the medical usage of computed tomography (CT) continues to grow, the radiation dose should remain at a low level to reduce the health risks. Therefore, there is an increasing need for algorithms that can reconstruct high-quality images…
In this article, we develop comprehensive frequency domain methods for estimating and inferring the second-order structure of spatial point processes. The main element here is on utilizing the discrete Fourier transform (DFT) of the point…
Signal decomposition is an effective tool to assist the identification of modal information in time-domain signals. Two signal decomposition methods, including the empirical wavelet transform (EWT) and Fourier decomposition method (FDM),…
This project is aimed at designing the fast forward projection algorithm and also the backprojection algorithm for cone beam CT imaging systems with circular X-ray source trajectory. The principle of the designs is based on utilizing the…
The pseudo-polar Fourier transform is a specialized non-equally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid, known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other…
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…
Video frame interpolation is an important low-level vision task, which can increase frame rate for more fluent visual experience. Existing methods have achieved great success by employing advanced motion models and synthesis networks.…
By viewing the nonuniform discrete Fourier transform (NUDFT) as a perturbed version of a uniform discrete Fourier transform, we propose a fast, stable, and simple algorithm for computing the NUDFT that costs $\mathcal{O}(N\log…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
Various applications such as MRI, solution of PDEs, etc. need to perform an inverse nonequispaced fast Fourier transform (NFFT), i. e., compute $M$ Fourier coefficients from given $N$ nonequispaced data. In the present paper we consider…
A simple scheme for all-optical time interpolation using spectral interferometry is put forward that is in principle capable of single-shot measurements. In this method, the arrival time of optical timing pulses is encoded into the spectrum…