Sparse recovery for Earth Mover Distance

Gupta, Rishi; Indyk, Piotr; Price, Eric

doi:10.1109/allerton.2010.5707127

Cited by 10 publications

(11 citation statements)

References 18 publications

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“…Limiting the error in sparsely recovered images to l p norms is quite inconvenient because they do not accurately represent perceptual differences between images. 43,44 Intuitively, given two images, the EMD reflects the minimal amount of work that must be performed to transform one image into the other. Thus, the EMD Journal of Electronic Imaging 021003-11 Apr-Jun 2013/Vol.…”

Section: Simulation Resultsmentioning

confidence: 99%

Determining building interior structures using compressive sensing

Lagunas

Amin

Ahmad

et al. 2013

J. Electron. Imaging

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Abstract. We consider imaging of the building interior structures using compressive sensing (CS) with applications to through-thewall imaging and urban sensing. We consider a monostatic synthetic aperture radar imaging system employing stepped frequency waveform. The proposed approach exploits prior information of building construction practices to form an appropriate sparse representation of the building interior layout. We devise a dictionary of possible wall locations, which is consistent with the fact that interior walls are typically parallel or perpendicular to the front wall. The dictionary accounts for the dominant normal angle reflections from exterior and interior walls for the monostatic imaging system. CS is applied to a reduced set of observations to recover the true positions of the walls. Additional information about interior walls can be obtained using a dictionary of possible corner reflectors, which is the response of the junction of two walls. Supporting results based on simulation and laboratory experiments are provided. It is shown that the proposed sparsifying basis outperforms the conventional through-thewall CS model, the wavelet sparsifying basis, and the block sparse model for building interior layout detection.

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Section: Simulation Resultsmentioning

confidence: 99%

Determining building interior structures using compressive sensing

Lagunas

Amin

Ahmad

et al. 2013

J. Electron. Imaging

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“…where c, α and β collect the trigonometric coefficients from the individual approximations (14). The resulting coefficients to the equation (16) α and β yield an estimate of the frequencies via the bijective relation…”

Section: Polar Interpolationmentioning

confidence: 99%

“…We recently introduced an approach to compressive parameter estimation that relies on the earth mover's distance (EMD) to measure the error in the coefficient vector (i.e., the distance between the estimated and the true coefficient vectors) in terms of similarity between the values and locations of their nonzero entries. The EMD between two vectors is obtained by optimizing the flow of mass among the entries of one vector to make it match with the other [13,14]. Let p and q be two K-sparse coefficient vectors with nonzero entries, and let I, J ⊂ 0, 1, .…”

Section: Compressive Parameter Estimation Via Clusteringmentioning

confidence: 99%

Compressive line spectrum estimation with clustering and interpolation

Duarte

2016

2016 Annual Conference on Information Science and Systems (CISS)

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We consider the standard line spectral estimation problem when the number of observed samples is significantly lower than that prescribed by the Nyquist rate. Two families of sparsity-based methods have recently been proposed for this problem. The first one uses an atomic norm minimization algorithm where the atoms correspond to complex exponentials of varying frequencies. The second one defines the sparse coefficient vectors for the signals of interest by designing parametric dictionaries that can be leveraged by sparse approximation algorithms involving clustering and interpolation. This paper compares the performance of these two algorithm families. Experiments show their advantages and disadvantages in terms of precision and complexity.

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“…Alternatively, the earth mover's distance (EMD) has recently been used in CS to measure the distance between coefficient vectors in terms of the similarity between their supports [21,22]. In particular, the EMD between two vectors with the same 1 norm optimizes the work of the flow (i.e., the amount of the flow and the distance of flow) applied to one vector in order to obtain the other vector.…”

Section: Parametric Dictionariesmentioning

confidence: 99%

“…Additionally, the guarantees of bounded error between the true and the estimated PD coefficient vectors, measured via the Euclidean distance in almost all existing methods, have very limited impact on the performance of compressive parameter estimation given that the Euclidean distance does not relate to the parameter estimation error. In contrast, the earth mover's distance (EMD) [20][21][22] is a very attractive option due to the fact that the EMD of two sparse PD coefficient vectors is indicative of the parameter estimation error when the elements of the PD are sorted in increasing order of the values of the corresponding parameters.…”

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confidence: 99%

Compressive parameter estimation via K-median clustering

Duarte

2018

Signal Processing

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Compressive sensing (CS) has attracted significant attention in parameter estimation tasks, where parametric dictionaries (PDs) collect signal observations for a sampling of the parameter space and yield sparse representations for signals of interest when the sampling is dense. While this sampling also leads to high dictionary coherence, one can leverage structured sparsity models to prevent highly coherent dictionary elements from appearing simultaneously in the recovered signal. However, the resulting approaches depend heavily on the careful setting of the maximum allowable coherence; furthermore, their guarantees are not concerned with general parameter estimation performance. We propose the use of earth mover's distance (EMD), as applied to a pair of true and estimated PD coefficient vectors, to measure the parameter estimation error. We formally analyze the connection between the EMD and the parameter estimation error and show that the EMD provides a better-suited metric for parameter estimation performance than the Euclidean distance. Additionally, we analyze the previously described relationship between K-median clustering and EMD-optimal sparse approximation and leverage it to develop improved PD-based parameter estimation algorithms. Finally, our numerical experiments verify our theoretical results and show that the proposed compressive parameter estimation algorithms have similar performance as the state-of-the-art algorithms while featuring simpler implementation and broader applicability.

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Sparse recovery for Earth Mover Distance

Cited by 10 publications

References 18 publications

Determining building interior structures using compressive sensing

Determining building interior structures using compressive sensing

Compressive line spectrum estimation with clustering and interpolation

Compressive parameter estimation via K-median clustering

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