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This article presents a novel method to sampling on manifolds based on the Dirichlet distribution. The proposed strategy allows to completely respect the underlying manifold around which data is observed, and to do massive samplings with…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
This work develops compressive sampling strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or output-projected data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It…
Line spectral estimation theory aims to estimate the off-the-grid spectral components of a time signal with optimal precision. Recent results have shown that it is possible to recover signals having sparse line spectra from few temporal…
Diffusion and flow-matching have emerged as powerful methodologies for generative modeling, with remarkable success in capturing complex data distributions and enabling flexible guidance at inference time. Many downstream applications,…
When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…
Two-dimensional, resonant scanners have been utilized in a large variety of imaging modules due to their compact form, low power consumption, large angular range, and high speed. However, resonant scanners have problems with non-optimal and…
Multiple stochastic signals possess inherent statistical correlations, yet conventional sampling methods that process each channel independently result in data redundancy. To leverage this correlation for efficient sampling, we model…
Due to the tremendous cost of seismic data acquisition, methods have been developed to reduce the amount of data acquired by designing optimal missing trace reconstruction algorithms. These technologies are designed to record as little data…
Although Monte Carlo path tracing is a simple and effective algorithm to synthesize photo-realistic images, it is often very slow to converge to noise-free results when involving complex global illumination. One of the most successful…
Among the most prevalent motion planning techniques, sampling and trajectory optimization have emerged successful due to their ability to handle tight constraints and high-dimensional systems, respectively. However, limitations in sampling…
We study the compressed sensing reconstruction problem for a broad class of random, band-diagonal sensing matrices. This construction is inspired by the idea of spatial coupling in coding theory. As demonstrated heuristically and…
This work considers distributed sensing and transmission of sporadic random samples. Lower bounds are derived for the reconstruction error of a single normally or uniformly-distributed finite-dimensional vector imperfectly measured by a…
We develop a new sampling method to estimate eigenvector centrality on incomplete networks. Our goal is to estimate this global centrality measure having at disposal a limited amount of data. This is the case in many real-world scenarios…
This paper presents an approach for instantaneous bandwidth estimation from level-crossing (LC) samples using a long short-term memory (LSTM) encoder-decoder architecture. LC sampling is a nonuniform sampling technique that is particularly…
The bootstrap is a popular data-driven method to quantify statistical uncertainty, but for modern high-dimensional problems, it could suffer from huge computational costs due to the need to repeatedly generate resamples and refit models. We…
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…
Performing k-space variable density sampling is a popular way of reducing scanning time in Magnetic Resonance Imaging (MRI). Unfortunately, given a sampling trajectory, it is not clear how to traverse it using gradient waveforms. In this…
Highly multiplexed microscopy enables rich spatial characterization of tissues at single-cell resolution, yet most analyses rely on two-dimensional sections despite inherently three-dimensional tissue organization. Acquiring dense…
Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…