Related papers: Stochastic Parameterization using Compressed Sensi…

In this study we investigate a data-driven stochastic methodology to parameterize small-scale features in a prototype multiscale dynamical system, the Lorenz '96 (L96) model. We propose to model the small-scale features using a vector…

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…

We consider faithfully combining phase retrieval with classical compressed sensing. Inspired by the recent novel formulation for phase retrieval called PhaseMax, we present and analyze SparsePhaseMax, a linear program for phaseless…

Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…

We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…

We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

Compressed sensing provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many…

There is an urgent need to build models to tackle Indoor Air Quality issue. Since the model should be accurate and fast, Reduced Order Modelling technique is used to reduce the dimensionality of the problem. The accuracy of the model, that…

Deep learning is a powerful tool to represent subgrid processes in climate models, but many application cases have so far used idealized settings and deterministic approaches. Here, we develop stochastic parameterizations with calibrated…

We present a novel method for the classification and reconstruction of time dependent, high-dimensional data using sparse measurements, and apply it to the flow around a cylinder. Assuming the data lies near a low dimensional manifold…

The sparse modeling is an evident manifestation capturing the parsimony principle just described, and sparse models are widespread in statistics, physics, information sciences, neuroscience, computational mathematics, and so on. In…

We consider the problem of the recovery of a k-sparse vector from compressed linear measurements when data are corrupted by a quantization noise. When the number of measurements is not sufficiently large, different $k$-sparse solutions may…

Compressive sensing (CS) is a new methodology to capture signals at lower rate than the Nyquist sampling rate when the signals are sparse or sparse in some domain. The performance of CS estimators is analyzed in this paper using tools from…

We consider the problem of reconstructing time sequences of spatially sparse signals (with unknown and time-varying sparsity patterns) from a limited number of linear "incoherent" measurements, in real-time. The signals are sparse in some…

In this paper, we consider a compressed sensing problem of reconstructing a sparse signal from an undersampled set of noisy linear measurements. The regularized least squares or least absolute shrinkage and selection operator (LASSO)…

This paper extends the sample complexity theory for ill-posed inverse problems developed in a recent work by the authors [`Compressed sensing for inverse problems and the sample complexity of the sparse Radon transform', J. Eur. Math. Soc.,…

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…

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…

Compressive sensing is a technique to sample signals well below the Nyquist rate using linear measurement operators. In this paper we present an algorithm for signal reconstruction given such a set of measurements. This algorithm…