This work uses encoder-decoder networks to denoise one-dimensional signals by aligning clean and noisy signal latent representations.
problem Noise removal in one-dimensional signals, especially in medical and motion signals.
method Encoder-decoder architecture with adversarial learning to align clean and noisy signal latent representations.
result Better performance on electrocardiogram and motion signal denoising compared to learning-based and non-learning approaches.
New method optimizes matrix denoising for weighted loss functions and heterogeneous signals.
problem Estimating low-rank matrices from noisy observed matrices.
method Developed a family of weighted loss functions and derived optimal spectral denoisers.
result A new denoiser exploiting heterogeneity in signal matrices improves estimation.
This paper explains GNNs using graph signal denoising.
problem Understanding how GNNs work for node representation learning.
method Spectral graph convolutional networks and graph attention networks are analyzed from the perspective of graph signal denoising.
result GNNs implicitly solve graph signal denoising problems.
New denoisers improve signal recovery from noisy data without knowing noise distribution.
problem Denoising signals when only noise level is known, not distribution.
method Universal denoisers that shrink PY toward PX with higher-order accuracy. result Achieves O(σ4) and O(σ6) accuracy in matching generalized moments and densities. Paper presents DL models for ECG signal denoising.
problem Efficient denoising of ECG signals for wearable devices.
method CNNs, LSTM, RBM, filtering methods, wavelet-based technique.
result CNN model performs well for offline denoising.
A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, today's denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorit…
Unified method for simultaneous denoising and clustering.
problem Clustering noisy signals.
method Sparse convex wavelet clustering with fusion and group-sparse penalties.
result Unified approach that denoises and clusters simultaneously.
A new method for audio denoising using deep neural networks.
problem Improving audio quality by removing background noise.
method Combines time and time-frequency domain processing; trains a deep neural network to fit the signal.
result The method effectively disentangles clean audio from noisy signals.
Self-supervised method predicts clean signal and noise distribution from noisy images.
problem Blind denoising and noise estimation in biomedical images with limited clean data.
method Two neural networks jointly predict clean signal and noise distribution from noisy observations.
result Significantly outperforms state-of-the-art algorithms on six biomedical image datasets.
Noise2Self removes noise from data without clean signals or noise estimates.
problem Removing noise from high-dimensional data without prior signal or noise information.
method Noise independence across dimensions allows self-supervised estimation of denoising performance.
result General framework calibrates denoising algorithms from noisy data alone.
This study improves graph signal denoising for vector-valued data with non-convex penalties.
problem Denoising piecewise smooth graph signals with varying smoothness levels.
method Extended graph trend filtering with non-convex penalties and ADMM algorithm.
result Non-convex penalties outperform convex ones in recovery performance.
Efficient algorithms for adaptive signal denoising are developed.
problem Signal denoising for discrete-time signals.
method Adaptive convolution-type estimators using first-order proximal algorithms.
result Efficient implementation and computational complexity analysis of adaptive estimators.
Study uses neural networks to filter financial spillovers from noise.
problem Accurately measuring spillovers in financial markets from noise.
method Neural network-based denoising of covariance matrices.
result Developed markets are net transmitters of volatility spillovers, but can become receivers during stress.
Study improves KRR for non-i.i.d. data, with applications in denoising.
problem Kernel regression in structured non-i.i.d. settings.
method Developed a blockwise decomposition method for dependent data, deriving excess risk bounds.
result Established generalization guarantees for KRR in non-i.i.d. settings.
Method separates target signal properties from noisy mixtures.
problem Signal recovery from noisy mixtures with specific statistical properties.
method Statistical component separation method using noise samples and matching statistics.
result Method outperforms standard denoising methods in recovering target signal properties.
The paper develops a cross-validation method for improving signal denoising techniques.
problem Improving signal denoising methods for nonparametric regression.
method Develops a general cross-validation framework for signal denoising and applies it to Trend Filtering and Dyadic CART.
result Cross validated versions of Trend Filtering and Dyadic CART achieve nearly optimal convergence rates.
New adaptive signal denoising method mimics oracle with better statistical properties.
problem Adaptive discrete-time signal denoising with linear oracle structure.
method Minimizes the ℓ2-norm of the estimation residual, proving oracle inequalities for ℓ2-loss. result Improved statistical properties over ℓ∞-fit estimators, especially in ℓ2- and pointwise losses. Paper proposes a self-supervised method to denoise autoregressive signals with heavy-tailed noise.
problem Denoising autoregressive signals corrupted by heavy-tailed noise.
method Self-supervised learning approach without requiring full noise distribution knowledge.
result Strong denoising performance compared to baseline methods, especially for impulsive noise.
Nyström approximation for scalable operator learning
problem Scalability of operator learning for large datasets
method Nyström subsampling with operator learning
result Minimax-optimal convergence rates for functional outputs
Paper proposes GAN frameworks for learning clean signals from superposed structured components.
problem Learning clean signals from superposed structured components when clean samples are not available.
method Proposes denoising-GAN and demixing-GAN frameworks to learn the structure of components.
result Demonstrates competitive performance in tasks like denoising, demixing, and compressive sensing.
New method denoises graph signals using wavelets, scalable for large graphs.
problem Denoising graph signals with overcomplete tight frames and correlated noise.
method Data-driven wavelet tight frame, Stein's unbiased risk estimate, Chebyshev-Jackson polynomial approximations, Monte-Carlo strategy.
result Method scales to large graphs and finds applications in differential privacy.
Bayesian method optimizes Potts model regularization for 1D signal denoising.
problem Automated selection of Potts model regularization parameter.
method Combines hierarchical Bayesian and l2-Potts formulations.
result Automatically tunes regularization parameter with efficiency.
DDGM generates realistic ECG signals for clinical use.
problem Generating accurate ECG signals from noisy data.
method Bayesian ECG reconstruction using DDGM trained on healthy ECG data.
result DDGM successfully generates realistic ECG signals for clinical applications.
GDiff tackles blind denoising with Gibbs sampling and Monte Carlo inference.
problem Blind denoising of signals with unknown noise parameters.
method Gibbs Diffusion (GDiff) method that alternates sampling steps from a conditional diffusion model and a Monte Carlo sampler.
result GDiff achieves blind denoising of natural images and cosmic microwave background data.
The paper analyzes Laplacian pyramids for extending and denoising discrete functions.
problem Analyzing conditions for convergence and stability of Laplacian pyramids.
method Investigates Laplacian pyramids for extension and denoising, providing convergence conditions and stability bounds.
result Mild conditions are provided under which the Laplacian pyramids algorithm converges and stability bounds are proven.
These notes review six lectures given by Prof. Andrea Montanari on the topic of statistical estimation for linear models. The first two lectures cover the principles of signal recovery from linear measurements in terms of minimax risk. Subsequent lectures demonstrate the application of these principles to several pract…
A new distance metric derived from information theory and estimation theory.
problem Developing a robust distance metric for complex signal distributions.
method Information-Estimation Metric (IEM) derived from continuous probability density and denoising errors.
result The IEM is a valid global distance metric that adapts to the geometry of complex distributions.
A new Dantzig Selector with an optimal denoising matrix for reinforcement learning.
problem Improving Dantzig Selector's performance in sparse signal recovery and reinforcement learning.
method Defining an optimal denoising matrix through minimax optimization and proposing an approximate algorithm to estimate it.
result Empirical validation of the proposed ODDS algorithm's superior performance in reinforcement learning.
Unified view of GNNs as graph signal denoising.
problem Understanding and improving GNNs for graph data.
method Established GNNs as graph denoising problems with smoothness assumptions.
result Unified framework UGNN for adaptive smoothness graphs.
New analysis improves denoising of modulo signals on graphs.
problem Robustly unwrapping noisy modulo samples of smooth functions.
method Analyzing sphere-relaxation and unconstrained relaxation of a QCQP on a graph.
result Proves denoising of modulo observations w.r.t the ℓ2 norm in Gaussian noise. New algorithms improve rank one signal estimation from noisy data.
problem Estimating a rank one signal matrix from corrupted data with rotationally invariant noise.
method Developed approximate message-passing algorithms exploiting eigenvalues and iterates denoisers.
result Achieves optimal asymptotic estimation error among iterative algorithms.
MLShrink integrates machine learning with wavelet shrinkage for denoising.
problem Denoising signals with uncertain magnitudes
method Combines wavelet shrinkage with machine learning
result Preserves simplicity for signal coefficients while allowing data-adaptive decisions for ambiguous coefficients
Improves CNN stability by translating classical signal denoising methods.
problem Stability of CNNs is poorly understood.
method Interprets classical signal denoising methods as ResNet architectures.
result Translates diffusivities, shrinkage functions, and regularizers into CNN activation functions.
Proposes SVR-based image denoising using natural image relations.
problem Image denoising with arbitrary noise sources.
method Support Vector Regression (SVR) in wavelet domain, enforcing natural image relations.
result Outperforms conventional methods and is similar to state-of-the-art methods for Gaussian noise.
Paper uses diffusion model to denoise financial time series data.
problem Low signal-to-noise ratio in financial time series data.
method Conditional diffusion model for progressive noise addition and removal.
result Denoised financial time series improve future return classification and trading performance.
New method extracts radio signal features for automatic modulation classification.
problem Challenges in automatic modulation classification without expert-defined features.
method Biologically-inspired regularized stacked sparse denoising autoencoders (SSDAs).
result Correct classification rates > 99% at 7.5 dB SNR and > 92% at 0 dB SNR.
Self-training in linear models shows a U-shaped test-risk curve due to signal forgetting and denoising.
problem Understanding the dynamics of iterative self-training in high-dimensional linear regression.
method Derivation of deterministic-equivalent recursions for prediction risk and effective noise, analysis of signal forgetting and denoising effects.
result An optimal early-stopping time is determined, and a U-shaped test-risk curve is observed.
Convolutional denoising autoencoders improve medical image denoising with small sample sizes.
problem Efficient denoising of medical images with limited training data.
method Convolutional denoising autoencoders trained on small datasets.
result Simple autoencoders can denoise images with high noise levels indistinguishable to humans.
The paper extends stationarity to graph signals, providing new estimation methods.
problem Developing flexible models for signals on graphs.
method Generalizing stationarity to graph signals, introducing graph localization operator and Power Spectral Density.
result Stationary graph signals have a well-defined Power Spectral Density that can be efficiently estimated.
We solve matrix denoising with both row and column correlations, setting limits and designing optimal methods.
problem Matrix denoising with doubly heteroscedastic noise (both row and column correlations).
method Established information-theoretic and algorithmic limits, designed a novel spectral estimator with optimality guarantees.
result The novel spectral estimator achieves positive correlation with the signal and Bayes-optimal error under one-sided heteroscedasticity.
New method uses SURE to denoise signals, outperforming NPMLE.
problem Learning to optimally denoise signals corrupted by Gaussian noise.
method Hyvärinen's score matching (SM) is shown equivalent to SURE minimization.
result SURE achieves nearly parametric rates of convergence in empirical Bayes settings.
A parallel algorithm learns efficient Kronecker product dictionaries.
problem Sparse representation of 2D signals like images and hyperspectral data.
method Highly parallelizable algorithm for learning separable dictionaries.
result Competitive sparse representations at lower computational cost.
Graph-based denoising framework for smooth manifolds.
problem Denoising of signals on smooth manifolds.
method Spectral Graph Wavelet transform applied to the graph Fourier frequency domain.
result Significantly outperforms state-of-the-art denoising methods.
Recently, the deep-belief-networks (DBN) based voice activity detection (VAD) has been proposed. It is powerful in fusing the advantages of multiple features, and achieves the state-of-the-art performance. However, the deep layers of the DBN-based VAD do not show an apparent superiority to the shallower layers. In this…
New method unifies and formalizes data partitioning using a single vector.
problem Data partitioning and clustering methods.
method Rank-one matrix factorization and denoising of piecewise constant signals.
result Demonstrates robustness of denoising step in partitioning.
End-to-end denoising framework improves SDR and PESQ metrics.
problem Spectrum and metric mismatches in speech enhancement networks.
method Optimizes network on time-domain signals after ISTFT and uses improved loss functions.
result Significantly improved SDR and PESQ performance.
Nonparametric density deconvolution and denoising using simulation-based inference
problem Learning latent signals and their distributions in the presence of measurement noise
method Convolutional maximum mean discrepancy (convMMD) loss and likelihood-free framework
result Learn a latent generative model matching observed data distribution
CNNs improve InSAR image denoising and coherence estimation.
problem Noise in InSAR imagery corrupts ground movement estimates.
method Autoencoder CNN architectures for denoising and preprocessing.
result Proposed method outperforms four established methods.