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.
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.
SUNLayer framework improves image denoising stability.
problem Stable denoising of images and other inverse problems.
method Introduces SUNLayer framework based on spherical harmonics to analyze generative models.
result Demonstrates stable denoising performance of SUNLayer on various activation functions.
Proves exact relationship between optimal denoising and data distribution.
problem Understanding the relationship between denoising and data distribution.
method Analyzes additive Gaussian noise to prove exact relationship.
result Generalizes known relationship to non-small noise conditions.
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
This paper tackles denoising of complex measures using optimal transport and curvature analysis.
problem Denoising of complex, possibly non-log-concave measures.
method Score function and optimal transport theory to revert Langevin diffusion chains.
result The difficulty of denoising depends on the curvature complexity of the initial measure at specific SNR scales.
The paper characterizes functions of shallow ReLU NN denoisers under minimal norm constraints.
problem Understanding the theoretical success of neural network denoisers.
method Characterization of functions realized by shallow ReLU NN denoisers under minimal norm constraints.
result The functions realized by shallow ReLU NN denoisers are contractive toward clean data points and generalize better than the empirical MMSE estimator at low noise levels.
Novel DLSC framework improves high-res tfMRI connectivity.
problem Denoising high-resolution tfMRI data for precise connectivity analysis.
method Dictionary Learning and Sparse Coding (DLSC) with task-specific prior knowledge.
result Significant improvement in prominent connectivity patterns compared to other methods.
Heuristic weighting improves denoising score matching without requiring noise distribution assumptions.
problem Improving denoising score matching without assuming noise distribution.
method Demonstrated heteroskedasticity, derived optimal weighting functions, and provided theoretical and empirical comparisons.
result Heuristical weighting function can achieve lower variance than optimal weighting, facilitating more stable and efficient training.
Improved self-supervised denoising for Poisson-Gaussian noise.
problem Handling Poisson-Gaussian noise in self-supervised denoising.
method Extended blindspot model, improved training scheme without hyperparameters.
result Improved denoising performance on microscope image benchmarks.
In this paper, we study how the mean shift algorithm can be used to denoise a dataset. We introduce a new framework to analyze the mean shift algorithm as a denoising approach by viewing the algorithm as an operator on a distribution function. We investigate how the mean shift algorithm changes the distribution and sho…
Estimates drift functions in SDEs using denoising diffusion models.
problem Estimating time-homogeneous drift functions in multivariate SDEs.
method Formulates drift estimation as a denoising problem, trains a conditional diffusion model.
result Proposed estimator matches classical methods in low dimensions and remains competitive in higher dimensions.
New TVD estimator adapts to piecewise constant functions, improving performance.
problem Improving TVD estimator performance for piecewise constant functions.
method Investigates adaptivity of TVD estimator to piecewise constant functions and proposes a data-driven tuning parameter.
result The ideally tuned TVD estimator performs better than in the worst case for piecewise constant functions.
Novel algorithm accelerates PnP methods for image deblurring and super-resolution.
problem Efficiently solving inverse problems and imaging with provable convergence guarantees.
method Incorporates quasi-Newton steps into provable PnP framework based on proximal denoisers.
result 2--8x faster convergence compared to other provable PnP methods with similar quality.
New method for mesh denoising using TGV of normal vector field.
problem Improving mesh quality by removing noise.
method Proposes a novel TGV formulation for normal vector fields on triangular meshes.
result New method outperforms existing techniques in mesh denoising experiments.
Improved score matching methods for estimating score functions and Hessians without high dimensionality.
problem Estimating score functions and Hessians efficiently in high-dimensional data.
method Implicit score matching and denoising score matching, leveraging Gagliardo-Nirenberg inequalities.
result Achieves convergence rates similar to denoising score matching and estimates Hessians without dimensionality issues.
U-Nets use belief propagation for efficient image denoising and classification.
problem Efficiently denoise and classify images using generative hierarchical models.
method Interpreted U-Nets as implementing belief propagation in tree-structured models.
result U-Nets can efficiently approximate denoising functions with sample complexity bounds.
Proposes DeGLIF to denoise graph data for label noise robustness.
problem Label noise in graph data makes node classification challenging.
method Uses leave-one-out influence function to denoise graph data.
result DeGLIF improves accuracy in node classification on noisy datasets.
New inequalities for unbounded functions improve denoising score matching.
problem Statistical error bounds for denoising score matching with unbounded objective functions.
method Derive new concentration inequalities using McDiarmid's inequality and Rademacher complexity bounds.
result Improved statistical error bounds for denoising score matching.
Diffusion models improve creativity by smoothing the score function, leading to interpolated data.
problem Improving creativity in diffusion models.
method Analyzing the effect of score smoothing on diffusion model dynamics.
result Score smoothing causes diffusion models to generate data that interpolate the training set.
The paper interprets diffusion models as gradient descent and proposes a new sampler.
problem Improving the efficiency and quality of diffusion models.
method Interprets diffusion models as gradient descent and proposes a new sampler.
result The new sampler achieves state-of-the-art FID scores and generates high quality samples.
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 algorithm targets nonsmooth constraints for robust data interpolation and denoising.
problem Robust data interpolation and denoising with large outliers and varying amplitudes.
method Flexible algorithmic framework targeting nonsmooth level-set constraints (L1, Linf, L0 norms).
result Improved robustness to large outliers and significant amplitude variations in seismic data.
This paper tackles noise in raw datasets to improve representation learning efficiency.
problem Noise in real-world datasets degrades representation learning quality.
method Proposes denoising Cosine-Similarity (dCS) loss to learn robust representations.
result Empirical results show the dCS loss outperforms baseline objective functions.
Unified framework denoises data and abstains from uncertain predictions.
problem Data quality and predictive uncertainty in deep neural networks.
method Unified filtering framework leveraging data density.
result Framework outperforms state-of-the-art techniques in denoising and abstaining.
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.
New PnP algorithm converges with relaxed proximal gradient descent.
problem Convergence issues in PnP methods with deep denoisers.
method Relaxed proximal gradient descent for PnP with weakly convex regularization.
result Proposed PnP-αPGD converges for a wider range of regularization parameters. Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
Consensus NN learns from noisy data only for medical image denoising.
problem Lack of clean training data for medical image denoising.
method Trains neural network using only noisy data by splitting and combining subsets.
result Improved performance on denoising medical images compared to existing methods.
New method DDVI improves posterior inference for deep Gaussian processes.
problem Inference of inducing points in DGPs is challenging and biased.
method DDVI uses denoising diffusion SDE and score matching for posterior approximation.
result Empirically shows DDVI outperforms baseline methods in inducing point inference.
A method for noise reduction in functional time series using FPCA.
problem Noise contamination in functional time series.
method Extending FPCA to separate signal and noise components.
result Optimal projection minimizes mean integrated squared error.
This paper improves change-point detection for complex data streams using denoising score matching.
problem Timely identification of distributional shifts in high-dimensional, complex data streams.
method Score-based CUSUM change-point detection with denoising score matching.
result Denoising score matching enhances detection power by effectively controlling noise scale.
Bias-free CNNs outperform biased ones in blind image denoising.
problem Deep learning methods often require bias terms, leading to overfitting and poor performance outside training noise levels.
method Developed a bias-free convolutional neural network architecture by removing additive constant terms in every layer, including batch normalization.
result Bias-free CNNs generalize robustly across noise levels, preserving state-of-the-art performance within the training range.
A new EBM trained with multi-scale denoising score matching outperforms GANs in high-dimensional data synthesis.
problem Training EBMs in high-dimensional spaces is slow and challenging.
method Multi-scale denoising score matching to train EBMs.
result The proposed EBM achieves comparable performance to GANs in high-dimensional data synthesis.
A new method approximates the exact posterior score for diffusion models.
problem Training-free guidance of diffusion models for image restoration and inverse problems.
method Presented a novel expression for the exact posterior score, leveraging it to compute step sizes on the fly.
result Demonstrated competitive performance with fewer time steps compared to state-of-the-art techniques.
Paper compares optimal denoising methods for generative models, finding different results based on data regularity.
problem Optimizing denoising in score-based generative models for various data types.
method Comparison of full-denoising and half-denoising approaches, analyzing performance in terms of distribution distances.
result Different denoising methods perform better under different data regularity conditions.
Optimizes data-driven design problems on implicit manifolds using score functions.
problem Optimizing over implicit low-dimensional manifolds in high-dimensional data.
method Introduces a link function connecting data distribution to manifold operations, enabling efficient optimization.
result Establishes theoretical guarantees for feasibility and optimality of proposed algorithms.
L2R learns to denoise images without needing noise distribution knowledge.
problem Traditional denoising methods require noise distribution knowledge, limiting their applicability.
method L2R uses a learnable monotonic neural network to learn recorruption without distribution knowledge.
result L2R achieves state-of-the-art performance across various noise distributions.
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.
We show how a deep denoising autoencoder with lateral connections can be used as an auxiliary unsupervised learning task to support supervised learning. The proposed model is trained to minimize simultaneously the sum of supervised and unsupervised cost functions by back-propagation, avoiding the need for layer-wise pr…
Generative models use DAE or DSM to estimate score, then Langevin sampling for sampling.
problem Estimating the score function of complex distributions for sampling.
method DAE or DSM for score estimation, Langevin sampling for sampling.
result Finite-sample bounds in Wasserstein distance for the sampling scheme.
Paper tackles sampling from non-log-concave distributions using denoising diffusion.
problem Sampling from non-log-concave distributions efficiently.
method DDMC framework, Zeroth-Order Diffusion Monte Carlo (ZOD-MC) algorithm.
result ZOD-MC achieves inverse polynomial dependence on sampling accuracy, efficient for low dimensions.
The paper tackles denoising of function samples modulo 1.
problem Recover smooth estimates of a function's modulo 1 samples from noisy data.
method Formulates and solves a quadratically constrained quadratic program relaxation.
result Demonstrates robustness of the approach to noise.
DDS samples from noisy data by reversing diffusion, providing theoretical guarantees.
problem Sampling from unnormalized densities.
method Denoising diffusion process, score matching, optimal control, Schrödinger bridges.
result DDS provides theoretical guarantees for sampling.
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.
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.
DDPD separates generation into planning and denoising for improved efficiency.
problem Efficiently denoise corrupted data during generation.
method Separates generation into a planner and denoiser, selecting denoising positions based on corruption severity.
result DDPD outperforms traditional methods on language and image generation benchmarks.
Bounded total variation denoising improves traffic analysis accuracy.
problem Improving traffic prediction and clustering accuracy in urban areas.
method Applying bounded total variation denoising to GPS traffic data and clustering analysis.
result Significant improvement in predicting and clustering accuracy after denoising.