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Full-Text Articles in Engineering
Performance Bounds For Grouped Incoherent Measurements In Compressive Sensing, Adam Polak, Marco Duarte, Dennis Goeckel
Performance Bounds For Grouped Incoherent Measurements In Compressive Sensing, Adam Polak, Marco Duarte, Dennis Goeckel
Marco Duarte
Compressive sensing (CS) allows for acquisition of sparse signals at sampling rates significantly lower than the Nyquist rate required for bandlimited signals. Recovery guarantees for CS are generally derived based on the assumption that measurement projections are selected independently at random. However, for many practical signal acquisition applications, including medical imaging and remote sensing, this assumption is violated as the projections must be taken in groups. In this paper, we consider such applications and derive requirements on the number of measurements needed for successful recovery of signals when groups of dependent projections are taken at random. We find a penalty …
Universality Of Wavelet-Based Non-Homogeneous Hidden Markov Chain Model Features For Hyperspectral Signatures, Siwei Feng, Marco Duarte, Mario Parente
Universality Of Wavelet-Based Non-Homogeneous Hidden Markov Chain Model Features For Hyperspectral Signatures, Siwei Feng, Marco Duarte, Mario Parente
Marco Duarte
Feature design is a crucial step in many hyperspectral signal processing applications like hyperspectral signature classification and unmixing, etc. In this paper, we describe a technique for automatically designing universal features of hyperspectral signatures. Universality is considered both in terms of the application to a multitude of classification problems and in terms of the use of specific vs. generic training datasets. The core component of our feature design is to use a non-homogeneous hidden Markov chain (NHMC) to characterize wavelet coefficients which capture the spectrum semantics (i.e., structural information) at multiple levels. Results of our simulation experiments show that the …
Compressive Parameter Estimation Via Approximate Message Passing, Marco Duarte
Compressive Parameter Estimation Via Approximate Message Passing, Marco Duarte
Marco Duarte
No abstract provided.
Image Masking Schemes For Local Manifold Learning Methods, Hamid Dadkhahi, Marco Duarte
Image Masking Schemes For Local Manifold Learning Methods, Hamid Dadkhahi, Marco Duarte
Marco Duarte
We consider the problem of selecting a subset of the dimensions of an image manifold that best preserves the underlying local structure in the original data. We have previously shown that masks which preserve the data neighborhood graph are well suited to global manifold learning algorithms. However, local manifold learning algorithms leverage a geometric structure beyond that captured by this neighborhood graph. In this paper, we present a mask selection algorithm that further preserves this additional structure by designing an extended data neighborhood graph that connects all neighbors of each data point, forming local cliques. Numerical experiments show the improvements …
Recovery From Linear Measurements With Complexity-Matching Universal Signal Estimation, Junan Zhu, Dror Baron, Marco Duarte
Recovery From Linear Measurements With Complexity-Matching Universal Signal Estimation, Junan Zhu, Dror Baron, Marco Duarte
Marco Duarte
We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity …
Conditioning Of Random Block Subdictionaries With Applications To Block-Sparse Recovery And Regression, Waheed U. Bajwa, Marco Duarte, Robert Calderbank
Conditioning Of Random Block Subdictionaries With Applications To Block-Sparse Recovery And Regression, Waheed U. Bajwa, Marco Duarte, Robert Calderbank
Marco Duarte
The linear model, in which a set of observations is assumed to be given by a linear combination of columns of a matrix (often termed a dictionary), has long been the mainstay of the statistics and signal processing literature. One particular challenge for inference under linear models is understanding the conditions on the dictionary under which reliable inference is possible. This challenge has attracted renewed attention in recent years, since many modern inference problems (e.g, high-dimensional statistics and compressed sensing) deal with the underdetermined setting, in which the number of observations is much smaller than the number of columns in …
Performance Guarantees For Sparse Regression-Based Unmixing, Yuki Itoh, Marco Duarte, Mario Parente
Performance Guarantees For Sparse Regression-Based Unmixing, Yuki Itoh, Marco Duarte, Mario Parente
Marco Duarte
Sparse regression-based unmixing has received much attention in recent years; however, its theoretical performance has not been explored in the literature. In this work, we present theoretical guarantees for the performance of a sparse regression based unmixing (in short, sparse unmixing) implemented in the form of a Lasso optimization with non-negativity constraints. We provide a sufficient condition required for the exact recovery of the endmembers and validate it both theoretically and through experiments. In cases in which the condition is not verified, we explore the performance of sparse unmixing in relation to the exact recovery coefficient (ERC).
Compressive Parameter Estimation For Sparse Translation-Invariant Signals Using Polar Interpolation, Karsten Fyhn, Marco Duarte, Søren Holdt Jensen
Compressive Parameter Estimation For Sparse Translation-Invariant Signals Using Polar Interpolation, Karsten Fyhn, Marco Duarte, Søren Holdt Jensen
Marco Duarte
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in two aspects: (i) we extend the formulation from real non-negative amplitude parameters to arbitrary complex ones, and (ii) we allow for mismatch between the manifold described by the parameters and its polar approximation. To quantify the improvements afforded by the proposed extensions, we evaluate six algorithms for estimation of parameters in sparse translation-invariant signals, exemplified with the time delay estimation problem. The evaluation is based on three performance metrics: …
Masking Schemes For Image Manifolds, Hamid Dadkhahi, Marco Duarte
Masking Schemes For Image Manifolds, Hamid Dadkhahi, Marco Duarte
Marco Duarte
We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the dimensions of the image space that preserves the manifold structure present in the original data. Such masking implements a form of compressed sensing that reduces power consumption in emerging imaging sensor platforms. Our goal is for the manifold learned from masked images to resemble the manifold learned from full images as closely as possible. We show that the process of finding the optimal masking pattern can be cast as a binary integer program, which is computationally expensive but can be approximated …
Complexity-Adaptive Universal Signal Estimation For Compressed Sensing, Junan Zhu, Dror Baron, Marco Duarte
Complexity-Adaptive Universal Signal Estimation For Compressed Sensing, Junan Zhu, Dror Baron, Marco Duarte
Marco Duarte
We study the compressed sensing (CS) signal estimation problem where a signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the signal during estimation, additional signal structure that can be leveraged is often not known a priori. For signals with independent and identically distributed (i.i.d.) entries, existing CS algorithms achieve optimal or near optimal estimation error without knowing the statistics of the signal. This paper addresses estimating stationary ergodic non-i.i.d. signals with unknown statistics. We have previously proposed a universal CS approach to simultaneously estimate the statistics of a …
Average Case Analysis Of High-Dimensional Block-Sparse Recovery And Regression For Arbitrary Designs, Waheed U. Bajwa, Marco Duarte, Robert Calderbank
Average Case Analysis Of High-Dimensional Block-Sparse Recovery And Regression For Arbitrary Designs, Waheed U. Bajwa, Marco Duarte, Robert Calderbank
Marco Duarte
This paper studies conditions for highdimensional inference when the set of observations is given by a linear combination of a small number of groups of columns of a design matrix, termed the \block-sparse" case. In this regard, it rst speci es conditions on the design matrix under which most of its block submatrices are well conditioned. It then leverages this result for average-case analysis of high-dimensional block-sparse recovery and regression. In contrast to earlier works: (i) this paper provides conditions on arbitrary designs that can be explicitly computed in polynomial time, (ii) the provided conditions translate into near-optimal scaling of …
Sparsity And Structure In Hyperspectral Imaging: Sensing, Reconstruction, And Target Detection, Rebecca M. Willett, Marco Duarte, Mark A. Davenport, Richard G. Baraniuk
Sparsity And Structure In Hyperspectral Imaging: Sensing, Reconstruction, And Target Detection, Rebecca M. Willett, Marco Duarte, Mark A. Davenport, Richard G. Baraniuk
Marco Duarte
Hyperspectral imaging is a powerful technology for remotely inferring the material properties of the objects in a scene of interest. Hyperspectral images consist of spatial maps of light intensity variation across a large number of spectral bands or wavelengths; alternatively, they can be thought of as a measurement of the spectrum of light transmitted or reflected from each spatial location in a scene. Because chemical elements have unique spectral signatures, observing the spectra at a high spatial and spectral resolution provides information about the material properties of the scene with much more accuracy than is possible with conventional three-color images. …
Tailoring Non-Homogeneous Markov Chain Models For Hyperspectral Signature Classification, Siwei Feng, Yuki Itoh, Mario Parente, Marco Duarte
Tailoring Non-Homogeneous Markov Chain Models For Hyperspectral Signature Classification, Siwei Feng, Yuki Itoh, Mario Parente, Marco Duarte
Marco Duarte
We consider the application of non-homogeneous hidden Markov chain (NHMC) models to the problem of hyperspectral signature classification. It has been previously shown that the NHMC model enables the detection of several semantic structural features of hyperspectral signatures. However, there are some aspects of the spectral data that are not fully captured by the proposed NHMC models such as the relatively smooth but fluctuating regions and the fluctuation orientations. In order to address these limitations, we propose an improved NHMC model based on Daubechies-1 wavelets in conjunction with an increased the model complexity. Experimental results show that the revised approach …