Study improves denoising score matching under relaxed manifold assumptions.
problem Improving denoising score matching under relaxed manifold assumptions.
method Model density with nonparametric Gaussian mixtures, relax manifold assumption, derive non-asymptotic bounds.
result Non-asymptotic bounds on approximation and generalization errors, rates of convergence determined by intrinsic dimension.
We propose a new framework for manifold denoising based on processing in the graph Fourier frequency domain, derived from the spectral decomposition of the discrete graph Laplacian. Our approach uses the Spectral Graph Wavelet transform in order to per- form non-iterative denoising directly in the graph frequency domai…
Nonparametric empirical Bayes denoising on Riemannian manifolds
problem Denoising measurements on compact Riemannian manifolds
method Using a surrogate oracle denoiser based on the marginal distribution of measurements
result Achieving nearly the Bayes risk in a low-noise regime
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.
Proposes a new method for efficient manifold denoising robust to high dimensional noise.
problem Efficiently denoise manifolds in high dimensional spaces with complicated noise.
method Landmark diffusion and optimal shrinkage under high dimensional noise and compact manifold setup.
result Systematic comparison with other algorithms on simulated and real datasets shows superior performance.
Simplifies denoising score matching for manifold learning.
problem Learning distributions on manifolds is computationally intensive.
method Modifies denoising score matching to implicitly account for the manifold.
result Reduces computational burden while maintaining efficiency.
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.
Chart autoencoders learn latent features preserving manifold topology and geometry, with robust denoising capabilities.
problem Learning low-dimensional latent features of high-dimensional data sampled near a manifold.
method Chart autoencoders encode data into latent features on charts, preserving manifold topology and geometry.
result Chart autoencoders achieve a squared generalization error of n−d+22log4n under proper network architectures. Proximal algorithms applied to current deformation into cycles.
problem Deformation of de Rham currents into cycles.
method Proximal algorithms, total variation denoising for differential forms.
result Calibrated cycles constructed in calibrated manifolds.
PNDMs accelerate DDPMs by treating them as differential equations on manifolds.
problem Accelerate DDPMs while maintaining sample quality.
method Propose pseudo numerical methods (PNDMs) to solve differential equations on manifolds.
result PNDMs generate higher quality images with only 50 steps compared to 1000-step DDIMs (20x speedup).
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.
FHDMs achieve optimal convergence in spherically supported data.
problem Statistical convergence properties of FHDMs for spherical data.
method FHDMs leverage random generation time and Doob's h-transform to optimize convergence rate.
result Achieve minimax optimal convergence rate in total variation for spherically supported Sobolev smooth data.
Paper proves diffusion models work on manifolds.
problem Current diffusion models assume densities are w.r.t. Lebesgue measure, limiting their applicability.
method Introduced convergence results for diffusion models on more general target distributions.
result Quantitative bounds on Wasserstein distance for target and generated distributions.
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.
Local averaging accurately distills manifold structure from noisy data.
problem Tackles the challenge of uncovering manifold structure from noisy data.
method Two-round mini-batch local averaging method applied to noisy samples.
result Achieves accuracy bound of $d(\hat{\mathbf q}, \mathcal M) \leq σ\sqrt{d\left(1+\frac{κ\mathrm{diam}(\mathcal {M})}{\log(D)}
ight)}$.
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 score matching method estimates local intrinsic dimension efficiently.
problem Quantifying the local intrinsic dimension of complex data.
method Denoising score matching loss and equivalent implicit score matching loss.
result Denoising score matching loss is a highly competitive and scalable LID estimator.
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.
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.
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 wit…
Image denoising is an important pre-processing step in medical image analysis. Different algorithms have been proposed in past three decades with varying denoising performances. More recently, having outperformed all conventional methods, deep learning based models have shown a great promise. These methods are however …
Robust method learns nonlinear structures robustly to noise.
problem Learning nonlinear structures in noisy data.
method Robust Non-Linear Matrix Factorization (RNLMF).
result RNLMF achieves noticeable improvements in denoising and clustering.
DSM on manifolds removes singularities and computes small-noise expansions.
problem DSM on manifolds with singular noise.
method Rao-Blackwellized score matching, nearest-point projection, intrinsic Riemannian score.
result Canonical target equals intrinsic Riemannian score up to a small correction.
Gen-CUDE is a neural network for denoising noisy channels.
problem Denoising in finite-input, general-output noisy channels.
method Unsupervised neural network trained on noisy data.
result Gen-CUDE achieves better denoising results than other methods.
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.
A natural way to characterize the cluster structure of a dataset is by finding regions containing a high density of data. This can be done in a nonparametric way with a kernel density estimate, whose modes and hence clusters can be found using mean-shift algorithms. We describe the theory and practice behind clustering…
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.
While it is believed that denoising is not always necessary in many big data applications, we show in this paper that denoising is helpful in urban traffic analysis by applying the method of bounded total variation denoising to the urban road traffic prediction and clustering problem. We propose two easy-to-implement m…
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.
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. New model reduces sampling cost in diffusion models, making them faster and applicable to real-world applications.
problem Challenges in generating high-quality samples, mode coverage, and fast sampling in deep generative models.
method Proposes denoising diffusion GANs that model each denoising step using a multimodal conditional GAN to reduce sampling cost.
result Demonstrates 2000imes faster sampling on CIFAR-10 dataset while maintaining competitive sample quality and diversity. 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
UDVD uses deep learning to denoise videos without supervision.
problem Lack of clean video data for training deep learning models.
method UDVD is a CNN trained solely on noisy video data, adapting to local motion.
result UDVD performs as well as supervised methods, even with limited training data.
Unified framework for denoising models across various spaces.
problem Improving generative models and approximate posterior simulation.
method Generalizing denoising diffusions to a broader class of spaces using a new extension of score matching.
result Unified models for denoising and posterior simulation.
We study the theoretical properties of image denoising via total variation penalized least-squares. We define the total vatiation in terms of the two-dimensional total discrete derivative of the image and show that it gives rise to denoised images that are piecewise constant on rectangular sets. We prove that, if the t…
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.
Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained a…
New method quantifies uncertainty in denoising models.
problem Uncertainty quantification in denoising models.
method Derives a relation between posterior moments and derivatives, uses it for efficient uncertainty quantification.
result Efficient computation of principal components and full marginal distributions of the posterior.
New method improves image denoising with fewer parameters and less data.
problem Image denoising requires large datasets and supervised settings, limiting practical applications.
method Self-supervised framework using Tucker low-rank tensor approximation.
result Improves model generalizability and reduces data acquisition costs.
Physics-informed denoising improves sensor data accuracy without needing clean data.
problem Noise in real-life sensor data affects system performance and reliability.
method Physics-informed denoising model that uses algebraic relationships between sensor measurements governed by physical laws.
result Achieved state-of-the-art performance in various real-world applications.
Fluorescence microscopy has enabled a dramatic development in modern biology. Due to its inherently weak signal, fluorescence microscopy is not only much noisier than photography, but also presented with Poisson-Gaussian noise where Poisson noise, or shot noise, is the dominating noise source. To get clean fluorescence…
Image denoising based on a probabilistic model of local image patches has been employed by various researchers, and recently a deep (denoising) autoencoder has been proposed by Burger et al. [2012] and Xie et al. [2012] as a good model for this. In this paper, we propose that another popular family of models in the fie…
Noise2Inverse removes artifacts in noisy CT images without needing clean data.
problem Removing artifacts in noisy CT images.
method Noise2Inverse uses a deep CNN trained on multiple statistically independent reconstructions of the same noisy data.
result Noise2Inverse improves peak signal-to-noise ratio and structural similarity index compared to existing methods.
Paper analyzes self-supervised image denoising with denatured data.
problem Understanding the performance of self-supervised image denoising with denatured data.
method Theoretical analysis and numerical experiments on a denoising algorithm.
result Theoretical analysis shows the algorithm finds desired solutions to the optimization problem.
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…
New method denoises images without clean reference using Tweedie distributions.
problem Image denoising without clean reference images.
method Combining Tweedie distributions, Noise2Score, and saddle point approximation.
result General closed-form denoising formula for various noise distributions.
Paper optimizes diffusion models for denoising tasks with theoretical guarantees.
problem Lack of theoretical understanding of MSE optimality in diffusion models.
method Inspired by MSE-optimal CME, proposes a novel denoising strategy for diffusion models.
result Demonstrates polynomial-time convergence to the CME under mild conditions.