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We give algorithms with lower arithmetic operation counts for both the Walsh-Hadamard Transform (WHT) and the Discrete Fourier Transform (DFT) on inputs of power-of-2 size $N$. For the WHT, our new algorithm has an operation count of…

Data Structures and Algorithms · Computer Science 2023-06-16 Josh Alman , Kevin Rao

The compression-complexity trade-off of lossy compression algorithms that are based on a random codebook or a random database is examined. Motivated, in part, by recent results of Gupta-Verd\'{u}-Weissman (GVW) and their underlying…

Information Theory · Computer Science 2009-04-23 Chris Gioran , Ioannis Kontoyiannis

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…

Information Theory · Computer Science 2015-09-22 Frank Ong , Sameer Pawar , Kannan Ramchandran

Discrete transforms such as the discrete Fourier transform (DFT) and the discrete Hartley transform (DHT) are important tools in numerical analysis. The successful application of transform techniques relies on the existence of efficient…

Numerical Analysis · Computer Science 2015-02-06 H. M. de Oliveira , R. J. Cintra , R. M. Campello de Souza

As a commonly-used image compression format, JPEG has been broadly applied in the transmission and storage of images. To further reduce the compression cost while maintaining the quality of JPEG images, lossless transcoding technology has…

Computer Vision and Pattern Recognition · Computer Science 2022-08-25 Xiaoshuai Fan , Xin Li , Zhibo Chen

This work explores the scope of Frequent Sequence Mining in the domain of Lossy Image Compression. The proposed work is based on the idea of clustering pixels and using the cluster identifiers in the compression. The DCT phase in JPEG is…

Image and Video Processing · Electrical Eng. & Systems 2026-01-28 Avinash Kadimisetty , Oswald C , Sivaselvan B , Alekhya Kadimisetty

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…

Numerical Analysis · Mathematics 2025-06-09 Melanie Kircheis , Daniel Potts

Due to the factors like processing power limitations and channel capabilities images are often down sampled and transmitted at low bit rates resulting in a low resolution compressed image. High resolution images can be reconstructed from…

Computer Vision and Pattern Recognition · Computer Science 2011-03-01 Liyakathunisa , C. N . Ravi Kumar

In this article, a new method is discussed for the calibration and monitoring of photomultiplier tubes (PMTs). This method is based on a Discrete Fourier Transform (DFT) and it is fast and general so that it can be used in cases where an…

Instrumentation and Detectors · Physics 2020-03-26 L. N. Kalousis , J. P. A. M. de André , E. Baussan , M. Dracos

An important component of many image alignment methods is the calculation of inner products (correlations) between an image of $n\times n$ pixels and another image translated by some shift and rotated by some angle. For robust alignment of…

Numerical Analysis · Mathematics 2020-02-19 Aaditya Rangan , Marina Spivak , Joakim Andén , Alex Barnett

Compressing images at extremely low bitrates (< 0.1 bpp) has always been a challenging task since the quality of reconstruction significantly reduces due to the strong imposed constraint on the number of bits allocated for the compressed…

Image and Video Processing · Electrical Eng. & Systems 2020-06-16 Suraj Kiran Raman , Aditya Ramesh , Vijayakrishna Naganoor , Shubham Dash , Giridharan Kumaravelu , Honglak Lee

We describe an image compression method, consisting of a nonlinear analysis transformation, a uniform quantizer, and a nonlinear synthesis transformation. The transforms are constructed in three successive stages of convolutional linear…

Computer Vision and Pattern Recognition · Computer Science 2020-07-28 Johannes Ballé , Valero Laparra , Eero P. Simoncelli

Motivated by the efficiency investigation of the Tranformer-based transform coding framework, namely SwinT-ChARM, we propose to enhance the latter, as first, with a more straightforward yet effective Tranformer-based channel-wise…

Computer Vision and Pattern Recognition · Computer Science 2023-07-13 Ahmed Ghorbel , Wassim Hamidouche , Luce Morin

We present an end-to-end image compression system based on compressive sensing. The presented system integrates the conventional scheme of compressive sampling and reconstruction with quantization and entropy coding. The compression…

Computer Vision and Pattern Recognition · Computer Science 2020-01-22 Xin Yuan , Raziel Haimi-Cohen

In this paper, we introduce low-complexity multidimensional discrete cosine transform (DCT) approximations. Three dimensional DCT (3D DCT) approximations are formalized in terms of high-order tensor theory. The formulation is extended to…

Image and Video Processing · Electrical Eng. & Systems 2023-06-21 V. A. Coutinho , R. J. Cintra , F. M. Bayer

Floating-point data is widely used across various domains. Depending on the required precision, each floating-point value can occupy several bytes. Lossless storage of this information is crucial due to its critical accuracy, as seen in…

Databases · Computer Science 2025-08-11 Samirasadat Jamalidinan , Kazem Cheshmi

We propose a fusion algorithm for haze removal that combines color information from an RGB image and edge information extracted from its corresponding NIR image using Haar wavelets. The proposed algorithm is based on the key observation…

Computer Vision and Pattern Recognition · Computer Science 2022-04-15 Sumit Laha , Ankit Sharma , Shengnan Hu , Hassan Foroosh

In recent years, the integration of advanced imaging techniques and deep learning methods has significantly advanced computer-aided diagnosis (CAD) systems for breast cancer detection and classification. Transformers, which have shown great…

Computer Vision and Pattern Recognition · Computer Science 2025-07-22 Mahtab Ranjbar , Mehdi Mohebbi , Mahdi Cherakhloo , Bijan Vosoughi. Vahdat

Non-line-of-Sight (NLOS) imaging systems collect light at a diffuse relay surface and input this measurement into computational algorithms that output a 3D volumetric reconstruction. These algorithms utilize the Fast Fourier Transform (FFT)…

Image and Video Processing · Electrical Eng. & Systems 2025-01-14 Talha Sultan , Alex Bocchieri , Chaoying Gu , Xiaochun Liu , Pavel Polynkin , Andreas Velten

Although vision transformers (ViTs) have shown promising results in various computer vision tasks recently, their high computational cost limits their practical applications. Previous approaches that prune redundant tokens have demonstrated…

Computer Vision and Pattern Recognition · Computer Science 2023-04-24 Siyuan Wei , Tianzhu Ye , Shen Zhang , Yao Tang , Jiajun Liang
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