Adaptive transform via quantum signal processing: application to signal and image denoising

Low-dimensional Denoising Embedding Transformer for ECG Classification

The transformer based model (e.g., FusingTF) has been employed recently for Electrocardiogram (ECG) signal classification. However, the high-dimensional embedding obtained via 1-D convolution and positional encoding can lead to the loss of the signal's own temporal information and a large amount of training parameters. In this paper, we propose a new method for ECG classification, called low-dimensional denoising embedding transformer (LDTF), which contains two components, i.e., low-dimensional denoising embedding (LDE) and transformer learning. In the LDE component, a low-dimensional represen…

基于多尺度补丁嵌入和Transformer的心电信号去噪

ECG Signal Denoising Using Multi-scale Patch Embedding and Transformers

本文提出一种结合一维卷积层和Transformer的深度学习方法，通过多尺度补丁嵌入增强去噪能力，以提高ECG信号信噪比，用于心血管监测。

超短TDoA测量的高质量去噪以实现5G-NR无人机定位

Quality-Aware Denoising of Ultra-Short TDoA Measurements for 5G-NR UAV Localization

本文提出AGES算法，通过结合指数加权平均与3GPP测量质量报告，有效降低定位误差，仅需3-5次重复测量即可实现亚米精度，保持5G-NR基础设施兼容性。

Blind Denoising Autoencoder

The term blind denoising refers to the fact that the basis used for denoising is learnt from the noisy sample itself during denoising. Dictionary learning and transform learning based formulations for blind denoising are well known. But there has been no autoencoder based solution for the said blind denoising approach. So far autoencoder based denoising formulations have learnt the model on a separate training data and have used the learnt model to denoise test samples. Such a methodology fails when the test image (to denoise) is not of the same kind as the models learnt with. This will be fir…

一种高性能的无训练管道用于通过自适应小波去噪和贝叶斯数字化方法实现鲁棒的随机 Telegraph 信号特性分析

A High-Performance Training-Free Pipeline for Robust Random Telegraph Signal Characterization via Adaptive Wavelet-Based Denoising and Bayesian Digitization Methods

本文提出一种无训练信号处理管道，结合自适应双树复小波变换去噪和轻量级贝叶斯数字化方法，提高多级结构信号和背景噪声下的RTS分析性能，实现高准确度和速度提升。

Data-driven Thresholding in Denoising with Spectral Graph Wavelet Transform

This paper is devoted to adaptive signal denoising in the context of Graph Signal Processing (GSP) using Spectral Graph Wavelet Transform (SGWT). This issue is addressed \emph{via} a data-driven thresholding process in the transformed domain by optimizing the parameters in the sense of the Mean Square Error (MSE) using the Stein's Unbiased Risk Estimator (SURE). The SGWT considered is built upon a partition of unity making the transform semi-orthogonal so that the optimization can be performed in the transformed domain. However, since the SGWT is over-complete, the divergence term in the SURE …

The Role of Redundant Bases and Shrinkage Functions in Image Denoising

Wavelet denoising is a classical and effective approach for reducing noise in images and signals. Suggested in 1994, this approach is carried out by rectifying the coefficients of a noisy image in the transform domain, using a set of scalar shrinkage function (SFs). A plethora of papers deals with the optimal shape of the SFs and the transform used, where it is known that applying the SFs in redundant bases provides improved results. This paper provides a complete picture of the interrelations between the transform used, the optimal shrinkage functions, and the domains in which they are optimi…

迭代执行离散和反向离散傅里叶变换及其在信号去噪中的应用

Iterative execution of discrete and inverse discrete Fourier transforms with applications for signal denoising via sparsification

本文提出了一种迭代算法家族，通过反复执行离散和反向离散傅里叶变换，利用稀疏化操作在时域和频域数据中实现信号去噪，特别是在高斯噪声中恢复周期性尖峰信号。

量子信号去噪算法

Quantum Algorithm for Signal Denoising

本文提出一种基于振幅放大和自适应阈值的量子信号去噪算法，可处理经典与量子信号，速度更快，且在去除量子噪声方面显著优于现有量子算法。

去噪扩散概率模型在未知低维性下最优适应

Denoising diffusion probabilistic models are optimally adaptive to unknown low dimensionality

该研究证明了DDPM在未知低维数据下具有最优适应性，其迭代复杂度与内在维度线性相关，且与KL散度度量一致。