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Sigma-Delta modulation is a popular method for analog-to-digital conversion of bandlimited signals that employs coarse quantization coupled with oversampling. The standard mathematical model for the error analysis of the method measures the…

Information Theory · Computer Science 2010-01-29 Percy Deift , C. Sinan Güntürk , Felix Krahmer

Several analog-to-digital conversion methods for bandlimited signals used in applications, such as Sigma Delta quantization schemes, employ coarse quantization coupled with oversampling. The standard mathematical model for the error accrued…

Information Theory · Computer Science 2010-04-21 Felix Krahmer , Rachel Ward

In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…

Information Theory · Computer Science 2019-11-14 Kung-Ching Lin

Adversarial examples contain carefully crafted perturbations that can fool deep neural networks (DNNs) into making wrong predictions. Enhancing the adversarial robustness of DNNs has gained considerable interest in recent years. Although…

Computer Vision and Pattern Recognition · Computer Science 2021-07-27 Shao-Yuan Lo , Vishal M. Patel

The evolution of image halftoning, from its analog roots to contemporary digital methodologies, encapsulates a fascinating journey marked by technological advancements and creative innovations. Yet the theoretical understanding of…

Image and Video Processing · Electrical Eng. & Systems 2024-06-19 Felix Krahmer , Anna Veselovska

Compared to the error diffusion, dot diffusion provides an additional pixel-level parallelism for digital halftoning. However, even though its periodic and blocking artifacts had been eased by previous works, it was still far from…

Multimedia · Computer Science 2015-10-28 Yun-Fu Liu , Jing-Ming Guo

In signal quantization, it is well-known that introducing adaptivity to quantization schemes can improve their stability and accuracy in quantizing bandlimited signals. However, adaptive quantization has only been designed for…

Information Theory · Computer Science 2022-02-07 He Lyu , Rongrong Wang

Halftoning aims to reproduce a continuous-tone image with pixels whose intensities are constrained to two discrete levels. This technique has been deployed on every printer, and the majority of them adopt fast methods (e.g., ordered…

Computer Vision and Pattern Recognition · Computer Science 2023-10-16 Haitian Jiang , Dongliang Xiong , Xiaowen Jiang , Li Ding , Liang Chen , Kai Huang

Coarsely quantized MIMO signalling methods have gained popularity in the recent developments of massive MIMO as they open up opportunities for massive MIMO implementation using cheap and power-efficient radio-frequency front-ends. This…

Information Theory · Computer Science 2020-01-08 Mingjie Shao , Wing-Kin Ma , Qiang Li , Lee Swindlehurst

Diffuse optical imaging (DOI) offers valuable insights into scattering mediums, but the quest for high-resolution imaging often requires dense sampling strategies, leading to higher imaging errors and lengthy acquisition times. This work…

Optics · Physics 2025-04-07 Ben Wiesel , Shlomi Arnon

We study Sigma-Delta ($\Sigma\Delta$) quantization of oversampled bandlimited functions. We prove that digitally integrating blocks of bits and then down-sampling, a process known as decimation, can efficiently encode the associated…

Information Theory · Computer Science 2023-07-19 Ingrid Daubechies , Rayan Saab

Manifold models in data analysis and signal processing have become more prominent in recent years. In this paper, we will look at one of the main tasks of modern signal processing, namely, at analog-to-digital (A/D) conversion in connection…

Signal Processing · Electrical Eng. & Systems 2019-11-19 Olga Graf , Felix Krahmer , Sara Krause-Solberg

We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…

Machine Learning · Computer Science 2022-04-14 Jinjie Zhang , Harish Kannan , Alexander Cloninger , Rayan Saab

We propose a unified diffusion model-based correction and super-resolution method to enhance the fidelity and resolution of diverse low-quality data through a two-step pipeline. First, the correction step employs a novel enhanced stochastic…

Numerical Analysis · Mathematics 2025-05-15 Wuzhe Xu , Yulong Lu , Sifan Wang , Tong-Rui Liu

In Analog-to-digital (A/D) conversion, signal decimation has been proven to greatly improve the efficiency of data storage while maintaining high accuracy. When one couples signal decimation with the $\Sigma\Delta$ quantization scheme, the…

Information Theory · Computer Science 2020-02-06 Kung-Ching Lin

Diffusion models demonstrate impressive image generation performance with text guidance. Inspired by the learning process of diffusion, existing images can be edited according to text by DDIM inversion. However, the vanilla DDIM inversion…

Computer Vision and Pattern Recognition · Computer Science 2024-09-17 Qi Qian , Haiyang Xu , Ming Yan , Juhua Hu

Diffusion models excel at image restoration via probabilistic modeling of forward noise addition and reverse denoising, and their ability to handle complex noise while preserving fine details makes them well-suited for Low-Light Image…

Computer Vision and Pattern Recognition · Computer Science 2026-04-08 Ying Liu , Junchao Zhang , Caiyun Wu

Sampling above the Nyquist rate is at the heart of sigma-delta modulation, where the increase in sampling rate is translated to a reduction in the overall (mean-squared-error) reconstruction distortion. This is attained by using a feedback…

Information Theory · Computer Science 2015-06-10 Or Ordentlich , Uri Erez

We consider the problem of digital halftoning from the view point of statistical mechanics. The digital halftoning is a sort of image processing, namely, representing each grayscale in terms of black and white binary dots. The digital…

Disordered Systems and Neural Networks · Physics 2010-11-09 Jun-ichi Inoue , Yohei Saika , Masato Okada

This paper considers the context of multiuser massive MIMO downlink precoding with low-resolution digital-to-analog converters (DACs) at the transmitter. This subject is motivated by the consideration that it is expensive to employ…

Signal Processing · Electrical Eng. & Systems 2024-02-28 Wai-Yiu Keung , Wing-Kin Ma
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