Decomposition of digital signals and images into other basis or dictionaries than time or space domains is a very common approach in signal and image processing and analysis. Such a decomposition is commonly obtained using fixed transforms (e.g., Fourier or wavelet) or dictionaries learned from example databases or from the signal or image itself. In this work, we investigate in detail a new approach of constructing such a signal or image-dependent bases inspired by quantum mechanics tools, i.e., by considering the signal or image as a potential in the discretized Schroedinger equation. To illustrate the potential of the proposed decomposition, denoising results are reported in the case of Gaussian, Poisson, and speckle noise and compared to the state of the art algorithms based on wavelet shrinkage, total variation regularization or patch-wise sparse coding in learned dictionaries, non-local means image denoising, and graph signal processing.
A variety of deep neural network (DNN)-based image denoising methods have been proposed for use with medical images. Traditional measures of image quality (IQ) have been employed to optimize and evaluate these methods. However, the objective evaluation of IQ for the DNN-based denoising methods remains largely lacking. In this work, we evaluate the performance of DNN-based denoising methods by use of task-based IQ measures. Specifically, binary signal detection tasks under signal-known-exactly (SKE) with background-known-statistically (BKS) conditions are considered. The performance of the idea…
Recently, a new Signal processing method, named Semi-Classical Signal Analysis (SCSA), has been proposed for denoising Magnetic Resonance Spectroscopy (MRS) signals. It is based on the Schrödinger Operator's eigenspectrum. It allows an efficient noise reduction while preserving MRS signal's peaks. In this paper, we propose to extend this approach to different signals, in particular pulse shaped signals, by including an optimization that considers curvature constraints. The performance of the method is measured by analyzing noisy signal data and comparing with other denoising methods. Results i…
A new development in photoacoustic (PA) imaging has been the use of compact, portable and low-cost laser diodes (LDs), but LD-based PA imaging suffers from low signal intensity recorded by the conventional transducers. A common method to improve signal strength is temporal averaging, which reduces frame rate and increases laser exposure to patients. To tackle this problem, we propose a deep learning method that will denoise the PA images before beamforming with a very few frames, even one. We also present a deep learning method to automatically reconstruct point sources from noisy pre-beamform…
The main scope of this paper is to show how tools from quantum mechanics, in particular the Schroedinger equation, can be used to construct an adaptive transform suitable for signal and image processing applications. The proposed dictionary is obtained by considering the signal or image as a discrete potential in Schroedinger equation, further used to construct the Hamiltonien operator. In order to illustrate its practical interest in signal and image processing, we provide denoising results in the case of signal-dependent noise, which is the noise type the most adapted to the proposed approac…
Existing deep learning-based speech denoising approaches require clean speech signals to be available for training. This paper presents a deep learning-based approach to improve speech denoising in real-world audio environments by not requiring the availability of clean speech signals in a self-supervised manner. A fully convolutional neural network is trained by using two noisy realizations of the same speech signal, one used as the input and the other as the output of the network. Extensive experimentations are conducted to show the superiority of the developed deep speech denoising approach…
We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, and sparsity-based methods. We propose a novel approach to designing higher-order zero-phase low-pass, high-pass, and band-pass infinite impulse response filters as matrices, using spectral transformation of the state-space representation of digital filters. We also propose a proximal gradient-based technique to factorize a special class of zero-phase high-pass and band-pass digital filters so that t…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of Oklahoma（俄克拉荷马大学）；Shahid Beheshti University（沙希德·贝赫什提大学）
There are many sources of interference encountered in the electroencephalogram (EEG) recordings, specifically ocular, muscular, and cardiac artifacts. Rejection of EEG artifacts is an essential process in EEG analysis since such artifacts cause many problems in EEG signals analysis. One of the most challenging issues in EEG denoising processes is removing the ocular artifacts where Electrooculographic (EOG), and EEG signals have an overlap in both frequency and time domains. In this paper, we build and train a deep learning model to deal with this challenge and remove the ocular artifacts effe…
We propose an interpretable graph neural network framework to denoise single or multiple noisy graph signals. The proposed graph unrolling networks expand algorithm unrolling to the graph domain and provide an interpretation of the architecture design from a signal processing perspective. We unroll an iterative denoising algorithm by mapping each iteration into a single network layer where the feed-forward process is equivalent to iteratively denoising graph signals. We train the graph unrolling networks through unsupervised learning, where the input noisy graph signals are used to supervise t…
We develop a data-driven approach for signal denoising that utilizes variational mode decomposition (VMD) algorithm and Cramer Von Misses (CVM) statistic. In comparison with the classical empirical mode decomposition (EMD), VMD enjoys superior mathematical and theoretical framework that makes it robust to noise and mode mixing. These desirable properties of VMD materialize in segregation of a major part of noise into a few final modes while majority of the signal content is distributed among the earlier ones. To exploit this representation for denoising purpose, we propose to estimate the dist…
Least-Squares Adaptive Filter-Based Cohen's Class Time-Frequency Distribution for Signal Denoising
Nanjing University of Information Science and Technology（南京信息工程大学）；Hubei University（湖北大学）；Shanghai Jiao Tong University（上海交通大学）；Nanjing Institute of Technology（南京工程学院）
Technische Universität München（慕尼黑工业大学）；Universität Ulm（乌尔姆大学）
The presence of noise is common in signal processing regardless the signal type. Deep neural networks have shown good performance in noise removal, especially on the image domain. In this work, we consider deep neural networks as a denoising tool where our focus is on one dimensional signals. We introduce an encoder-decoder architecture to denoise signals, represented by a sequence of measurements. Instead of relying only on the standard reconstruction error to train the encoder-decoder network, we treat the task of denoising as distribution alignment between the clean and noisy signals. Then,…
Acoustic monitoring has recently shown great potential in the diagnosis of infrastructure condition. However, due to the severe noise interference in acoustic signals, meaningful features tend to be difficult to infer. It creates a considerable obstacle for an extensive application of acoustic monitoring. To tackle this problem, we propose an acceleration-guided acoustic signal denoising framework (AG-ASDF) based on learnable wavelet transform to automatically denoise the acoustic signal and extract the relevant features based on the acceleration signal. This denoising framework requires the a…
This paper presents a non-contact fault diagnostic method for ball bearing using adaptive wavelet denoising, statistical-spectral acoustic features, and one-dimensional (1D) convolutional neural networks (CNN). The health conditions of the ball bearing are monitored by microphone under noisy conditions. To eliminate noise, adaptive wavelet denoising method based on kurtosis-entropy (KE) index is proposed. Multiple acoustic features are extracted base on expert knowledge. The 1D ResNet is used to classify the health conditions of the bearings. Case study is presented to examine the proposed met…
King Juan Carlos University（胡安·卡洛斯国王大学）；Rice University（莱斯大学）；Technical University of Munich（慕尼黑工业大学）
A fundamental problem in signal processing is to denoise a signal. While there are many well-performing methods for denoising signals defined on regular supports, such as images defined on two-dimensional grids of pixels, many important classes of signals are defined over irregular domains such as graphs. This paper introduces two untrained graph neural network architectures for graph signal denoising, provides theoretical guarantees for their denoising capabilities in a simple setup, and numerically validates the theoretical results in more general scenarios. The two architectures differ on h…
Optimal Wiener-Filter Solutions for Denoising of Graph Signals on Directed Graphs
Neuro-X Institute, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院神经-X研究所）；Department of Radiology and Medical Informatics, University of Geneva（日内瓦大学放射学与医学信息学系）
Denoising and filtering are widely used in routine seismic-data-processing to improve the signal-to-noise ratio (SNR) of recorded signals and by doing so to improve subsequent analyses. In this paper we develop a new denoising/decomposition method, DeepDenoiser, based on a deep neural network. This network is able to learn simultaneously a sparse representation of data in the time-frequency domain and a non-linear function that maps this representation into masks that decompose input data into a signal of interest and noise (defined as any non-seismic signal). We show that DeepDenoiser achieve…
We consider the problem of estimating a low-rank matrix from a noisy observed matrix. Previous work has shown that the optimal method depends crucially on the choice of loss function. In this paper, we use a family of weighted loss functions, which arise naturally for problems such as submatrix denoising, denoising with heteroscedastic noise, and denoising with missing data. However, weighted loss functions are challenging to analyze because they are not orthogonally-invariant. We derive optimal spectral denoisers for these weighted loss functions. By combining different weights, we then use t…
Electrocardiographic signal is a subject to multiple noises, caused by various factors. It is therefore a standard practice to denoise such signal before further analysis. With advances of new branch of machine learning, called deep learning, new methods are available that promises state-of-the-art performance for this task. We present a novel approach to denoise electrocardiographic signals with deep recurrent denoising neural networks. We utilize a transfer learning technique by pretraining the network using synthetic data, generated by a dynamic ECG model, and fine-tuning it with a real dat…
We propose a novel deep learning based denoising filter selection algorithm for noisy Electrocardiograph (ECG) signal preprocessing. ECG signals measured under clinical conditions, such as those acquired using skin contact devices in hospitals, often contain baseline signal disturbances and unwanted artefacts; indeed for signals obtained outside of a clinical environment, such as heart rate signatures recorded using non-contact radar systems, the measurements contain greater levels of noise than those acquired under clinical conditions. In this paper, we focus on heart rate signals acquired us…
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Denoising of time domain data is a crucial task for many applications such as communication, translation, virtual assistants etc. For this task, a combination of a recurrent neural net (RNNs) with a Denoising Auto-Encoder (DAEs) has shown promising results. However, this combined model is challenged when operating with low signal-to-noise ratio (SNR) data embedded in non-Gaussian and non-stationary noise. To address this issue, we design a novel model, referred to as 'Enhanced Deep Recurrent Denoising Auto-Encoder' (EDRDAE), that incorporates a signal amplifier layer, and applies curriculum le…
In order to improve the transmission effect of low-power communication signal of Internet of things and compress the enhancement time of low-power communication signal, this paper designs a low-power communication signal enhancement method of Internet of things based on nonlocal mean denoising. Firstly, the residual of one-dimensional communication layer is pre processed by convolution core to obtain the residual of one-dimensional communication layer; Then, according to the two classification recognition method, the noise reduction signal feature recognition of the low-power communication sig…
Noise originating from several sources in a RF environment degrades the performance of communication systems. In wideband systems, such as cognitive radios, noise at the receiver can originate from non-linearity present in the RF front end, time-varying thermal noise within the receiver radio system, and noise from adjacent network nodes. Several denoising techniques have been proposed for cognitive radios, some of which are applied during spectrum sensing and others to received noisy signal during communication. Examples of some of these techniques used for noise cancellation in received sign…
Monitoring of electrocardiogram (ECG) provides vital information as well as any cardiovascular anomalies. Recent advances in the technology of wearable electronics have enabled compact devices to acquire personal physiological signals in the home setting; however, signals are usually contaminated with high level noise. Thus, an efficient ECG filtering scheme is a dire need. In this paper, a novel method using Ensemble Kalman Filter (EnKF) is developed for denoising ECG signals. We also intensively explore various filtering algorithms, including Savitzky-Golay (SG) filter, Ensemble Empirical mo…
One of the fundamental challenges affecting the performance of communication systems is the undesired impact of noise on a signal. Noise distorts the signal and originates due to several sources including, system non-linearity and noise interference from adjacent environment. Conventional communication systems use filters to cancel noise in a received signal. In the case of cognitive radio systems, denoising a signal is important during the spectrum sensing period, and also during communication with other network nodes. Based on our findings, few surveys are found that only review particular d…
EEGDnet: Fusing Non-Local and Local Self-Similarity for 1-D EEG Signal Denoising with 2-D Transformer
School of Computer Science and Engineering, University of Electronic Science and Technology of China（电子科技大学计算机科学与工程学院）；Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）
Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
In many scientific applications, measured time series are corrupted by noise or distortions. Traditional denoising techniques often fail to recover the signal of interest, particularly when the signal-to-noise ratio is low or when certain assumptions on the signal and noise are violated. In this work, we demonstrate that deep learning-based denoising methods can outperform traditional techniques while exhibiting greater robustness to variation in noise and signal characteristics. Our motivating example is magnetic resonance spectroscopy, in which a primary goal is to detect the presence of sho…
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…
Generative Adversarial Networks (GAN) are known to produce synthetic data that are difficult to discern from real ones by humans. In this paper we present an approach to use GAN to produce realistically looking ECG signals. We utilize them to train and evaluate a denoising autoencoder that achieves state-of-the-art filtering quality for ECG signals. It is demonstrated that generated data improves the model performance compared to the model trained on real data only. We also investigate an effect of transfer learning by reusing trained discriminator network for denoising model.
Electrocardiogram (ECG) signal is an important physiological signal which contains cardiac information and is the basis to diagnosis cardiac related diseases. In this paper, several innovative and efficient methods based on adaptive filter and empirical mode decomposition (EMD) to denoise ECG signal contaminated by various kinds of noise, including baseline wander (BW), power line interference (PLI), electrode motion artifact (EM) and muscle artifact (MA), are proposed. We first present a novel method based on EMD and adaptive filter for the removal of BW and PLI in ECG signal. We then extend …
A multivariate signal denoising method is proposed which employs a novel multivariate goodness of fit (GoF) test that is applied at multiple data scales obtained from discrete wavelet transform (DWT). In the proposed multivariate GoF test, we first utilize squared Mahalanobis distance (MD) measure to transform input multivariate data residing in M-dimensional space $\mathcal{R}^M$ to a single-dimensional space of positive real numbers $\mathcal{R}_+$, i.e., $\mathcal{R}^M \rightarrow \mathcal{R}_+$, where $M > 1$. Owing to the properties of the MD measure, the transformed data in $\mathcal{R}_…
ADVA Optical Networking SE（ADVA光网络公司）；Kiel University (CAU)（基尔大学（克里斯蒂安-阿尔布雷希茨大学））
Optical time-domain reflectometry (OTDR) has been widely used for characterizing fiber optical links and for detecting and locating fiber faults. OTDR traces are prone to be distorted by different kinds of noise, causing blurring of the backscattered signals, and thereby leading to a misleading interpretation and a more cumbersome event detection task. To address this problem, a novel method combining a denoising convolutional autoencoder (DCAE) and a bidirectional long short-term memory (BiLSTM) is proposed, whereby the former is used for noise removal of OTDR signals and the latter for fault…
Click-evoked otoacoustic emissions (CEOAEs) are clinically used as an objective way to infer whether cochlear functions are normal. However, because the sound pressure level of CEOAEs is typically much lower than the background noise, it usually takes hundreds, if not thousands of repetitions to estimate the signal with sufficient accuracy. In this paper, we propose to improve the signal-to-noise ratio (SNR) of CEOAE signals within limited measurement time by optimal shrinkage (OS) in two different settings: the covariance-based OS (cOS) and the singular value decomposition (SVD)-based OS (sOS…
School of Electrical and Electronics Engineering（电气与电子工程学院）；University of Manchester（曼彻斯特大学）
Effective and powerful methods for denoising real electrocardiogram (ECG) signals are important for wearable sensors and devices. Deep Learning (DL) models have been used extensively in image processing and other domains with great success but only very recently have been used in processing ECG signals. This paper presents several DL models namely Convolutional Neural Networks (CNNs), Long Short-Term Memory (LSTM), Restricted Boltzmann Machine (RBM) together with the more conventional filtering methods (low pass filtering, high pass filtering, Notch filtering) and the standard wavelet-based te…
Robust Photoplethysmography Signal Denoising via Mamba Networks
National Taiwan University（国立台湾大学）；Research Center for Information Technology Innovation, Academia Sinica（学术院资讯科技创新研究中心）；Graduate Institute of Communication Engineering, National Taiwan University（国立台湾大学通信工程研究所）；Department of Electrical Engineering, National Taiwan University（国立台湾大学电机工程系）
Queens College, City University of New York（纽约市立大学皇后学院）；University of Michigan（密歇根大学）；Northeastern University（东北大学）
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with attendant noise. Under the additive noise model and with the assumption that the underlying clean tensor has low rank, many denoising methods have been created that utilize tensor decomposition to effect denoising through low rank tensor approximation. However, all such decomposition methods require estimating the tensor rank, or related measures such as the tensor…
