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Compressive sensing achieves effective dimensionality reduction of signals, under a sparsity constraint, by means of a small number of random measurements acquired through a sensing matrix. In a signal processing system, the problem arises…
We propose a method to reconstruct and cluster incomplete high-dimensional data lying in a union of low-dimensional subspaces. Exploring the sparse representation model, we jointly estimate the missing data while imposing the intrinsic…
We present a general class of compressed sensing matrices which are then demonstrated to have associated sublinear-time sparse approximation algorithms. We then develop methods for constructing specialized matrices from this class which are…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
We perform a sparse identification of nonlinear dynamics (SINDy) for low-dimensionalized complex flow phenomena. We first apply the SINDy with two regression methods, the thresholded least square algorithm (TLSA) and the adaptive Lasso…
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…
We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over $n$ elements from given partial information; the partial information we consider is related to the group theoretic Fourier…
Growing set of optimization and regression techniques, based upon sparse representations of signals, to build models from data sets has received widespread attention recently with the advent of compressed sensing. This paper deals with the…
The goal of compressive sensing is efficient reconstruction of data from few measurements, sometimes leading to a categorical decision. If only classification is required, reconstruction can be circumvented and the measurements needed are…
Compressed sensing can decrease scanning transmission electron microscopy electron dose and scan time with minimal information loss. Traditionally, sparse scans used in compressed sensing sample a static set of probing locations. However,…
Time-frequency analysis has been applied successfully in many fields. However, the traditional methods, like short time Fourier transform and Cohen distribution, suffer from the low resolution or the interference of the cross terms. To…
In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven…
Several data compressors have been proposed in distributed optimization frameworks of network systems to reduce communication overhead in large-scale applications. In this paper, we demonstrate that effective information compression may…
A compressed sensing method consists of a rectangular measurement matrix, $M \in \mathbbm{R}^{m \times N}$ with $m \ll N$, together with an associated recovery algorithm, $\mathcal{A}: \mathbbm{R}^m \rightarrow \mathbbm{R}^N$. Compressed…
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…
Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and…
Reconstruction of unsteady vortical flow fields from limited sensor measurements is challenging. We develop machine learning methods to reconstruct flow features from sparse sensor measurements during transient vortex-airfoil wake…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
Matrix recovery from sparse observations is an extensively studied topic emerging in various applications, such as recommendation system and signal processing, which includes the matrix completion and compressed sensing models as special…
We present a dual-guided framework for reconstructing unsteady incompressible flow fields using sparse observations. The approach combines optimized sensor placement with a physics-informed guided generative model. Sensor locations are…