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We present a novel method for training score-based generative models which uses nonlinear noising dynamics to improve learning of structured distributions. Generalizing to a nonlinear drift allows for additional structure to be incorporated…
We develop a data-driven optimal shrinkage algorithm for matrix denoising in the presence of high-dimensional noise with a separable covariance structure; that is, the noise is colored and dependent across samples. The algorithm, coined…
The first order derivative of a data density can be estimated efficiently by denoising score matching, and has become an important component in many applications, such as image generation and audio synthesis. Higher order derivatives…
Motivated by recent work on atomic norms in inverse problems, we propose a new approach to line spectral estimation that provides theoretical guarantees for the mean-squared-error (MSE) performance in the presence of noise and without…
Learning-based methods commonly treat state estimation in robotics as a sequence modeling problem. While this paradigm can be effective at maximizing end-to-end performance, models are often difficult to interpret and expensive to train,…
Score matching enables the estimation of the gradient of a data distribution, a key component in denoising diffusion models used to recover clean data from corrupted inputs. In prior work, a heuristic weighting function has been used for…
In the study of condensed matter physics, spectral information plays an important role for understand the mechanism of materials. However, it is difficult to obtain the spectrum directly through experiments or simulation. For example, the…
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…
A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional…
The ultimate aim of image restoration like denoising is to find an exact correlation between the noisy and clear image domains. But the optimization of end-to-end denoising learning like pixel-wise losses is performed in a sample-to-sample…
In observational astronomy, noise obscures signals of interest. Large-scale astronomical surveys are growing in size and complexity, which will produce more data and increase the workload of data processing. Developing automated tools, such…
How to efficiently utilize the temporal features is crucial, yet challenging, for video restoration. The temporal features usually contain various noisy and uncorrelated information, and they may interfere with the restoration of the…
The localized nature of curvelet functions, together with their frequency and dip characteristics, makes the curvelet transform an excellent choice for processing seismic data. In this work, a denoising method is proposed based on a…
Denoising and score estimation have long been known to be linked via the classical Tweedie's formula. In this work, we first extend the latter to a wider range of distributions often called "energy models" and denoted elliptical…
Cosmology places the strongest current limits on the sum of neutrino masses. Future observations will further improve the sensitivity and this will require accurate cosmological simulations to quantify possible systematic uncertainties and…
Image classification and denoising suffer from complementary issues of lack of robustness or partially ignoring conditioning information. We argue that they can be alleviated by unifying both tasks through a model of the joint probability…
In this paper, we propose a novel image denoising algorithm exploiting features from both spatial as well as transformed domain. We implement intensity-invariance based improved grouping for collaborative support-agnostic sparse…
Denoising algorithms play a crucial role in medical image processing and analysis. However, classical denoising algorithms often ignore explanatory and critical medical features preservation, which may lead to misdiagnosis and legal…
We propose a data-dependent denoising procedure to restore noisy images. Different from existing denoising algorithms which search for patches from either the noisy image or a generic database, the new algorithm finds patches from a…
When it comes to image compression in digital cameras, denoising is traditionally performed prior to compression. However, there are applications where image noise may be necessary to demonstrate the trustworthiness of the image, such as…