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Estimation of the Discrete-Time Fourier Transform (DTFT) at points of a finite domain arises in many imaging applications. A new approach to this task, the Golden Angle Linogram Fourier Domain (GALFD), is presented, together with a…
We report experimental implementation of discrete Fourier transformation(DFT) on a nuclear magnetic resonance(NMR) quantum computer. Experimental results agree with theoretical results. Using the pulse sequences we introduced, DFT can be…
Visual tracking usually requires an object appearance model that is robust to changing illumination, pose and other factors encountered in video. In this paper, we construct an appearance model using the 3D discrete cosine transform…
Recently, Transformers have shown promising performance in various vision tasks. To reduce the quadratic computation complexity caused by each query attending to all keys/values, various methods have constrained the range of attention…
This work presents a highly optimized computational framework for the Discrete Dipole Approximation, a numerical method for calculating the optical properties associated with a target of arbitrary geometry that is widely used in…
Graph Transformers (GTs) have emerged as powerful architectures for graph-structured data, yet remain constrained by rigid designs and lack quantifiable interpretability. Current state-of-the-art GTs commit to fixed GNN types across all…
This paper explores image modeling from the frequency space and introduces DCTdiff, an end-to-end diffusion generative paradigm that efficiently models images in the discrete cosine transform (DCT) space. We investigate the design space of…
While it is crucial to capture global information for effective image restoration (IR), integrating such cues into transformer-based methods becomes computationally expensive, especially with high input resolution. Furthermore, the…
Depth completion is crucial for many robotic tasks such as autonomous driving, 3-D reconstruction, and manipulation. Despite the significant progress, existing methods remain computationally intensive and often fail to meet the real-time…
The Quantum Fourier Transformation (QFT) is a well-known subroutine for algorithms on qubit-based universal quantum computers. In this work, the known QFT circuit is used to derive an efficient circuit for the multidimensional QFT. The…
This paper presents a general expression for a number-theoretic Hilbert transform (NHT). The transformations preserve the circulant nature of the discrete Hilbert transform (DHT) matrix together with alternating values in each row being…
A unitary shift operator (GSO) for signals on a graph is introduced, which exhibits the desired property of energy preservation over both backward and forward graph shifts. For rigour, the graph differential operator is also derived in an…
We propose a novel method, called the dimension-changing transformation (DCT), to compute one-loop Feynman integrals and recently introduced fixed-branch integrals to arbitrary orders in $\epsilon$. The DCT relates one-loop Feynman…
Exact reconstruction of an image from measurements of its Discrete Fourier Transform (DFT) typically requires all DFT coefficients to be available. However, incorporating the prior assumption that the image contains only integer values…
Binary grid mask representation is broadly used in instance segmentation. A representative instantiation is Mask R-CNN which predicts masks on a $28\times 28$ binary grid. Generally, a low-resolution grid is not sufficient to capture the…
The discrete Fourier transform and the FFT algorithm are extended from the circle to continuous graphs with equal edge lengths.
Digitally reconstructed radiographs (DRRs) are simulated 2D X-ray images generated from 3D CT volumes, widely used in preoperative settings but limited in intraoperative applications due to computational bottlenecks, especially for accurate…
Density gradient theory (DGT) allows fast and accurate determination of surface tension and density profile through a phase interface. Several algorithms have been developed to apply this theory in practical calculations. While the…
Computed tomography (CT) serves as an effective tool for lung cancer screening, diagnosis, treatment, and prognosis, providing a rich source of features to quantify temporal and spatial tumor changes. Nonetheless, the diversity of CT…
We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding…