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Spectrum denoising is an important procedure for large-scale spectroscopical surveys. This work proposes a novel stellar spectrum denoising method based on deep Bayesian modeling. The construction of our model includes a prior distribution…

Appropriate preprocessing is a fundamental prerequisite for analyzing a noisy dataset. The purpose of this paper is to apply a nonparametric preprocessing method, called Singular Spectrum Analysis (SSA), to a variety of datasets which are…

With the rapid growth of data, how to extract effective information from data is one of the most fundamental problems. In this paper, based on Tikhonov regularization, we propose an effective method for reconstructing the function and its…

Reducing noise caused by the instrumentation in observational data is a crucial step in data post-processing. A method is searched for that conserves most of the instrumental resolution and introduces as few methodical artefacts as…

Point cloud source data for surface reconstruction is usually contaminated with noise and outliers. To overcome this deficiency, a density-based point cloud denoising method is presented to remove outliers and noisy points. First,…

Attaining reliable profile gradients is of utmost relevance for many physical systems. In most situations, the estimation of gradient can be inaccurate due to noise. It is common practice to first estimate the underlying system and then…

We present a method of reliably extracting the flux of individual sources from sky maps in the presence of noise and a source population in which number counts are a steeply falling function of flux. The method is an extension of a standard…

Lack of training data presents a grand challenge to scaling out spoken language understanding (SLU) to low-resource languages. Although various data augmentation approaches have been proposed to synthesize training data in low-resource…

Tunneling spectroscopy is an important tool for the study of both real-space and momentum-space electronic structure of correlated electron systems. However, such measurements often yield noisy data. Machine learning provides techniques to…

In this paper we introduce a new method for automatically selecting knots in spline regression. The approach consists in setting a large number of initial knots and fitting the spline regression through a penalized likelihood procedure…

A new efficient orthogonalization of the B-spline basis is proposed and contrasted with some previous orthogonalized methods. The resulting orthogonal basis of splines is best visualized as a net of functions rather than a sequence of them.…

Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…

Gaussian smoothing combined with a probabilistic framework for denoising via the empirical Bayes formalism, i.e., the Tweedie-Miyasawa formula (TMF), are the two key ingredients in the success of score-based generative models in Euclidean…

In this paper we analyse the pathwise approximation of stochastic differential equations by polynomial splines with free knots. The pathwise distance between the solution and its approximation is measured globally on the unit interval in…

We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is…

Explaining the output of a deep network remains a challenge. In the case of an image classifier, one type of explanation is to identify pixels that strongly influence the final decision. A starting point for this strategy is the gradient of…

Dynamic speckle method is an effective tool for estimation of speed of processes. Speed distribution is encoded in a map built by statistical pointwise processing of time-correlated speckle patterns. For industrial inspection,the outdoor…

In this paper, we propose a new method for Salt-and-Pepper noise removal from images. Whereas most of the existing methods are based on Ordered Statistics filters, our method is based on the growing theory of Sparse Signal Processing. In…

I point out the mathematical correspondence between an incoherent imaging model proposed by my group in the study of quantum-inspired superresolution [Tsang, Nair, and Lu, Physical Review X 6, 031033 (2016)] and a noise spectroscopy model…

Spin noise spectroscopy has become a widespread technique to extract information on spin dynamics in atomic and solid-state systems, in a potentially non-invasive way, through the optical probing of spin fluctuations. Here we experimentally…