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Graph signal processing (GSP) advances spectral analysis on irregular domains. However, existing two-dimensional graph fractional Fourier transform (2D-GFRFT) employs a single fractional order for both factor graphs, thereby limiting its…
Deep Convolutional Neural Networks (DCNNs) are capable of obtaining powerful image representations, which have attracted great attentions in image recognition. However, they are limited in modeling orientation transformation by the internal…
We implement an efficient method of computation of two dimensional Fourier-type integrals based on approximation of the integrand by Gaussian radial basis functions, which constitute a standard tool in approximation theory. As a result, we…
Extracting and using class-discriminative features is critical for fine-grained recognition. Existing works have demonstrated the possibility of applying deep CNNs to exploit features that distinguish similar classes. However, CNNs suffer…
This paper introduces a design method for densergraph-frequency graph Fourier frames (DGFFs) to enhance graph signal processing and analysis. The graph Fourier transform (GFT) enables us to analyze graph signals in the graph spectral domain…
This work proposes a new precoded filter bank (FB) system via a two-dimensional (2D) fast Fourier transform (2D-FFT). Its structure is similar to Orthogonal Time Frequency Space (OTFS) systems, where the OFDM transmitter is changed to a…
As generative models become increasingly capable of producing high-fidelity visual content, the demand for efficient, interpretable, and editable image representations has grown substantially. Recent advances in 2D Gaussian Splatting (2DGS)…
Recent advances in 2D Gaussian Splatting (2DGS) have demonstrated its potential as a compact image representation with millisecond-level decoding. However, existing 2DGS-based pipelines allocate representation capacity and parameter…
We discuss efficient algorithms for the accurate forward and reverse evaluation of the discrete Fourier-Bessel transform (dFBT) as numerical tools to assist in the 2D polar convolution of two radially symmetric functions, relevant, e.g., to…
Computational complexity of the brute-force implementation of the bilateral filter (BF) depends on its filter kernel size. To achieve the constant-time BF whose complexity is irrelevant to the kernel size, many techniques have been…
We present a novel algorithm, named the 2D-FFAST, to compute a sparse 2D-Discrete Fourier Transform (2D-DFT) featuring both low sample complexity and low computational complexity. The proposed algorithm is based on mixed concepts from…
Extremely large-scale array (XL-array) has emerged as one promising technology to improve the spectral efficiency and spatial resolution of future sixth generation (6G) wireless systems.The upsurge in the antenna number antennas renders…
This paper introduces an efficient edge detection method based on Gabor filter and rough clustering. The input image is smoothed by Gabor function, and the concept of rough clustering is used to focus on edge detection with soft…
We describe a massively parallel implementation of the recently developed discontinuous Galerkin density functional theory (DGDFT) [J. Comput. Phys. 2012, 231, 2140] method, for efficient large-scale Kohn-Sham DFT based electronic structure…
3D Gaussian Splatting (3DGS) has recently revolutionized radiance field reconstruction, achieving high quality novel view synthesis and fast rendering speed without baking. However, 3DGS fails to accurately represent surfaces due to the…
Steerable properties dominate the design of traditional filters, e.g., Gabor filters, and endow features the capability of dealing with spatial transformations. However, such excellent properties have not been well explored in the popular…
3D Gaussian Splatting (3DGS) has emerged as a mainstream solution for novel view synthesis and 3D reconstruction. By explicitly encoding a 3D scene using a collection of Gaussian kernels, 3DGS achieves high-quality rendering with superior…
This paper presents a simple and efficient method to convolve an image with a Gaussian kernel. The computation is performed in a constant number of operations per pixel using running sums along the image rows and columns. We investigate the…
In this paper we characterize and construct novel oversampled filter banks implementing fusion frames. A fusion frame is a sequence of orthogonal projection operators whose sum can be inverted in a numerically stable way. When properly…
A method for constructing non-uniform filter banks is presented. Starting from a uniform system of translates, generated by a prototype filter, a non-uniform covering of the frequency axis is obtained by composition with a warping function.…