Related papers: Smoothing and Interpolating Noisy GPS Data with Sm…
Smoothing splines are twice differentiable by construction, so they cannot capture potential discontinuities in the underlying signal. In this work, we consider a special case of the weak rod model of Blake and Zisserman (1987) that allows…
Data noising is an effective technique for regularizing neural network models. While noising is widely adopted in application domains such as vision and speech, commonly used noising primitives have not been developed for discrete…
In some real world applications, such as spectrometry, functional models achieve better predictive performances if they work on the derivatives of order m of their inputs rather than on the original functions. As a consequence, the use of…
We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter''…
In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we…
We propose a novel method to determine the dissimilarity between subjects for functional data clustering. Spline smoothing or interpolation is common to deal with data of such type. Instead of estimating the best-representing curve for each…
Tracking underwater autonomous platforms is often difficult because of noisy, biased, and discretized input data. Classic filters and smoothers based on standard assumptions of Gaussian white noise break down when presented with any of…
Searches for gravitational waves crucially depend on exact signal processing of noisy strain data from gravitational wave detectors, which are known to exhibit significant non-Gaussian behavior. In this paper, we study two distinct…
In this paper, a method is proposed to solve the problem of monotone smoothing splines using general linear systems. This problem, also called monotone control theoretic splines, has been solved only when the curve generator is modeled by…
Underwater sonar imaging plays a crucial role in various applications, including autonomous navigation in murky water, marine archaeology, and environmental monitoring. However, the unique characteristics of sonar images, such as complex…
Line charts are commonly used to visualize a series of data values. When the data are noisy, smoothing is applied to make the signal more apparent. Conventional methods used to smooth line charts, e.g., using subsampling or filters, such as…
Onboard electrostatic suspension inertial sensors are important applications for gravity satellites and space gravitational wave detection missions, and it is important to suppress noise in the measurement signal. Due to the complex…
Existing dimensionality reduction methods are adept at revealing hidden underlying manifolds arising from high-dimensional data and thereby producing a low-dimensional representation. However, the smoothness of the manifolds produced by…
Global Navigation Satellite Systems (GNSS) are integrated into many devices. However, civilian GNSS signals are usually not cryptographically protected. This makes attacks that forge signals relatively easy. Considering modern devices often…
Trajectory Reconstruction (TR) is vital for accurately mapping movement patterns and validating analyses, especially in fields like robotics, biomechanics, and environmental tracking, where data might be missing or affected by outliers.…
A frequently occurring challenge in experimental and numerical observation is how to resolve features, such as spectral peaks - with center, width, height - and derivatives from measured data with unavoidable noise. Therefore, we develop a…
We discuss some details regarding the method of smoothed residuals, which has recently been used to search for anisotropic signals in low-redshift distance measurements (Supernovae). In this short note we focus on some details regarding the…
We address numerical differentiation under coarse, non-uniform sampling and Gaussian noise. A maximum-likelihood estimator with $L_2$-norm constraint on a higher-order derivative is obtained, yielding spline-based solution. We introduce a…
This work analyzes the convergence of a class of smoothing-based gradient descent methods when applied to optimization problems. In particular, Gaussian smoothing is employed to define a nonlocal gradient that reduces high-frequency noise,…
We develop a statistical analysis model of Kepler star flux data in the presence of planet transits, non-Gaussian noise, and star variability. We first develop a model for Kepler noise probability distribution in the presence of outliers,…