Related papers: Robust flow field reconstruction from limited meas…
Successful applications of sparse models in computer vision and machine learning imply that in many real-world applications, high dimensional data is distributed in a union of low dimensional subspaces. Nevertheless, the underlying…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
The role of sparse representations in the context of structured noise filtering is discussed. A strategy, especially conceived so as to address problems of an ill posed nature, is presented. The proposed approach revises and extends the…
Identifying damage of structural systems is typically characterized as an inverse problem which might be ill-conditioned due to aleatory and epistemic uncertainties induced by measurement noise and modeling error. Sparse representation can…
We propose and analyze an online algorithm for reconstructing a sequence of signals from a limited number of linear measurements. The signals are assumed sparse, with unknown support, and evolve over time according to a generic nonlinear…
Optical flow is the pattern of apparent motion of objects in a scene. The computation of optical flow is a critical component in numerous computer vision tasks such as object detection, visual object tracking, and activity recognition.…
Sparse coding refers to the pursuit of the sparsest representation of a signal in a typically overcomplete dictionary. From a Bayesian perspective, sparse coding provides a Maximum a Posteriori (MAP) estimate of the unknown vector under a…
The rapid development of 3D technology and computer vision applications have motivated a thrust of methodologies for depth acquisition and estimation. However, most existing hardware and software methods have limited performance due to poor…
It is now well understood that (1) it is possible to reconstruct sparse signals exactly from what appear to be highly incomplete sets of linear measurements and (2) that this can be done by constrained L1 minimization. In this paper, we…
Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…
We use compressed sensing to demonstrate theoretically the reconstruction of sub-wavelength features from measured far-field, and provide experimental proof-of-concept. The methods can be applied to non-optical microscopes, provided the…
Signals sparse in a transformation domain can be recovered from a reduced set of randomly positioned samples by using compressive sensing algorithms. Simple re- construction algorithms are presented in the first part of the paper. The…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…
A super-resolution (SR) method for the reconstruction of Navier-Stokes (NS) flows from noisy observations is presented. In the SR method, first the observation data is averaged over a coarse grid to reduce the noise at the expense of losing…
Recent results from compressive sampling (CS) have demonstrated that accurate reconstruction of sparse signals often requires far fewer samples than suggested by the classical Nyquist--Shannon sampling theorem. Typically, signal…
We report a novel physics-informed neural framework for reconstructing unsteady fluid-structure interactions (FSI) from sparse, single-phase observations of the flow. Our approach combines a modal surface model with coordinate neural…
The recovery of sparsest overcomplete representation has recently attracted intensive research activities owe to its important potential in the many applied fields such as signal processing, medical imaging, communication, and so on. This…
The sparse representation of signals defined on Euclidean domains has been successfully applied in signal processing. Bringing the power of sparse representations to non-regular domains is still a challenge, but promising approaches have…
We present a fast and accurate method for dense depth reconstruction from sparsely sampled light fields obtained using a synchronized camera array. In our method, the source images are over-segmented into non-overlapping compact superpixels…
Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the…