Related papers: Nonstationary Gabor Frames - Approximately Dual Fr…
One of a key problems in signal reconstruction process with the use of frames is to find a dual frame. Typically, a canonical dual frame is used. However, there are many applications where this choice appears to be unfortunate. Due to that…
We develop sub-Nyquist sampling systems for analog signals comprised of several, possibly overlapping, finite duration pulses with unknown shapes and time positions. Efficient sampling schemes when either the pulse shape or the locations of…
In computed tomography (CT), the forward model consists of a linear Radon transform followed by an exponential nonlinearity based on the attenuation of light according to the Beer-Lambert Law. Conventional reconstruction often involves…
We propose NonStGM, a general nonparametric graphical modeling framework for studying dynamic associations among the components of a nonstationary multivariate time series. It builds on the framework of Gaussian Graphical Models (GGM) and…
We extend the Gabor analysis in \cite{GaSa} to a broad class of modulation spaces, allowing more general mixed quasi-norm estimates and weights in the definition of the modulation space quasi-norm. For such spaces we deduce invariance and…
We propose two-channel critically-sampled filter banks for signals on undirected graphs that utilize spectral domain sampling. Unlike conventional approaches based on vertex domain sampling, our transforms have the following desirable…
We consider stochastic gradient methods under the interpolation regime where a perfect fit can be obtained (minimum loss at each observation). While previous work highlighted the implicit regularization of such algorithms, we consider an…
Consider the problem of simultaneous estimation and support recovery of the coefficient vector in a linear data model with additive Gaussian noise. We study the problem of estimating the model coefficients based on a recently proposed…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
We develop a versatile framework for statistical learning in non-stationary environments. In each time period, our approach applies a stability principle to select a look-back window that maximizes the utilization of historical data while…
Wavelet phase is a critical parameter in seismic processing, where zero-phase wavelets are essential for maximizing temporal resolution and ensuring accurate interpretation of subsurface structures. In practice, however, the seismic wavelet…
This paper develops new theory and algorithms to recover signals that are approximately sparse in some general dictionary (i.e., a basis, frame, or over-/incomplete matrix) but corrupted by a combination of interference having a sparse…
Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process…
Many physical datasets are generated by collections of instruments that make measurements at regular time intervals. For such regular monitoring data, we extend the framework of half-spectral covariance functions to the case of…
The motion of planar ground vehicles is often non-holonomic, and as a result may be modelled by the 2 DoF Ackermann steering model. We analyse the feasibility of estimating such motion with a downward facing camera that exerts…
Functions or distributions used to sample and to reconstruct signals often occur in different domains, like the Dirac delta and a band-limited bump function in classical sampling. Oblique dual frames generalize this phenomenon. In this…
Fusion frames are collection of subspaces which provide a redundant representation of signal spaces. They generalize classical frames by replacing frame vectors with frame subspaces. This paper considers the sparse recovery of a signal from…
The ability to perform mathematical computations using metastructures is an emergent paradigm that carries the potential of wave-based analog computing to the realm of near-speed-of-light, low-loss, compact devices. We theoretically…
The recent work [Kurz et al., Numer. Math., 147 (2021)] proposed functional a posteriori error estimates for boundary element methods (BEMs) together with a related adaptive mesh-refinement strategy. Unlike most a posteriori BEM error…
Modeling data with non-stationary covariance structure is important to represent heterogeneity in geophysical and other environmental spatial processes. In this work, we investigate a multistage approach to modeling non-stationary…