相关论文: Krylov Subspace Methods in Dynamical Sampling

The recovery of an unknown signal from its linear measurements is a fundamental problem spanning numerous scientific and engineering disciplines. Commonly, prior knowledge suggests that the underlying signal resides within a known algebraic…

Let $\xi = \{x^j\}_{j=1}^n$ be a grid of $n$ points in the $d$-cube ${\II}^d:=[0,1]^d$, and $\Phi = \{\phi_j\}_{j =1}^n$ a family of $n$ functions on ${\II}^d$. We define the linear sampling algorithm $L_n(\Phi,\xi,\cdot)$ for an…

The most general model-independent analysis of the rare $B$ decay, $\Bsll$, is presented. There are ten independent local four-Fermi interactions which may contribute to this process. The branching ratio, the forward-backward asymmetry, and…

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…

Compressed sensing provides an efficient framework for reconstructing wave signals from reduced measurements. For multi-channel buoy data, the three displacement components exhibit intrinsic correlations, as wave motion contributes…

It is well known that $\ell_1$ minimization can be used to recover sufficiently sparse unknown signals from compressed linear measurements. In fact, exact thresholds on the sparsity, as a function of the ratio between the system dimensions,…

This paper re-visits the spectral method for learning latent variable models defined in terms of observable operators. We give a new perspective on the method, showing that operators can be recovered by minimizing a loss defined on a finite…

In portable, three dimensional, and ultra-fast ultrasound imaging systems, there is an increasing demand for the reconstruction of high quality images from a limited number of radio-frequency (RF) measurements due to receiver (Rx) or…

We derive sufficient conditions for sampling with derivatives in shift-invariant spaces generated by a periodic exponential B-spline. The sufficient conditions are expressed with a new notion of measuring the gap between consecutive…

Isolating slower dynamics from fast fluctuations has proven remarkably powerful, but how do we proceed from partial observations of dynamical systems for which we lack underlying equations? Here, we construct maximally-predictive states by…

In this paper, we investigate the problem of source recovery in a dynamical system utilizing space-time samples. This is a specific issue within the broader field of dynamical sampling, which involves collecting samples from solutions to a…

Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a…

We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve…

Many complex dynamical phenomena can be effectively modeled by a system that switches among a set of conditionally linear dynamical modes. We consider two such models: the switching linear dynamical system (SLDS) and the switching vector…

State space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in…

We consider the problem of accurately recovering a matrix B of size M by M , which represents a probability distribution over M2 outcomes, given access to an observed matrix of "counts" generated by taking independent samples from the…

Suppose we wish to recover an n-dimensional real-valued vector x_0 (e.g. a digital signal or image) from incomplete and contaminated observations y = A x_0 + e; A is a n by m matrix with far fewer rows than columns (n << m) and e is an…

Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

Operator-theoretic analysis of nonlinear dynamical systems has attracted much attention in a variety of engineering and scientific fields, endowed with practical estimation methods using data such as dynamic mode decomposition. In this…

This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as…