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Approximationtolerant modelbased compressive sensing
 in ACM Symp. Discrete Algorithms
, 2014
"... The goal of sparse recovery is to recover a ksparse signal x ∈ Rn from (possibly noisy) linear measurements of the form y = Ax, where A ∈ Rm×n describes the measurement process. Standard results in compressive sensing show that it is possible to recover the signal x from m = O(k log(n/k)) measureme ..."
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Cited by 10 (3 self)
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The goal of sparse recovery is to recover a ksparse signal x ∈ Rn from (possibly noisy) linear measurements of the form y = Ax, where A ∈ Rm×n describes the measurement process. Standard results in compressive sensing show that it is possible to recover the signal x from m = O(k log(n/k)) measurements, and that this bound is tight. The framework of modelbased compressive sensing [BCDH10] overcomes the lower bound and reduces the number of measurements further to O(k) by limiting the supports of x to a subsetM of the (nk) possible supports. This has led to many measurementefficient algorithms for a wide variety of signal models, including blocksparsity and treesparsity. Unfortunately, extending the framework to other, more general models has been stymied by the following obstacle: for the framework to apply, one needs an algorithm that, given a signal x, solves the following optimization problem exactly: arg min Ω∈M ‖x[n]\Ω‖2 (here x[n]\Ω denotes the projection of x on coordinates not in Ω). However, an approximation algorithm for this optimization task is not sufficient. Since many problems of this form are not known to have exact polynomialtime algorithms, this requirement poses an obstacle for extending the framework to a richer class of models. In this paper, we remove this obstacle and show how to extend the modelbased compressive sensing framework so that it requires only approximate solutions to the aforementioned optimization problems. Interestingly, our extension requires the existence of approximation algorithms for both the maximization and the minimization variants of the optimization problem. Further, we apply our framework to the Constrained Earth Mover’s Distance (CEMD) model introduced in [SHI13], obtaining a sparse recovery scheme that uses significantly less than O(k log(n/k)) measurements. This is the first nontrivial theoretical bound for this model, since the validation of the approach presented in [SHI13] was purely empirical. The result is obtained by designing a novel approximation algorithm for the maximization version of the problem and proving approximation guarantees for the minimization algorithm described in [SHI13]. 1
AUTOMATIC FAULT LOCALIZATION USING THE GENERALIZED EARTH MOVER’S DISTANCE
"... Localizing fault lines and surfaces in seismic subsurface images is a daunting challenge. Existing stateoftheart approaches usually involve visual interpretation by an expert, but this is timeconsuming, expensive and errorprone. In this paper, we propose some initial steps towards a new algorit ..."
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Localizing fault lines and surfaces in seismic subsurface images is a daunting challenge. Existing stateoftheart approaches usually involve visual interpretation by an expert, but this is timeconsuming, expensive and errorprone. In this paper, we propose some initial steps towards a new algorithmic framework for automatic fault localization. The core of our approach is a deterministic model for 2D images that we call the Constrained Generalized Earth Mover’s Distance (CGEMD) model. We propose an algorithm that returns the best approximation in the model for any given input 2D image X; the output of this algorithm is then postprocessed to reveal the locations of the faults in the image. We demonstrate the validity of this approach on a number of synthetic and realworld examples.
Fast Algorithms for Structured Sparsity (ICALP 2015 Invited Tutorial)
"... Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard ” sparsity. In many cases, we ca ..."
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Sparsity has become an important tool in many mathematical sciences such as statistics, machine learning, and signal processing. While sparsity is a good model for data in many applications, data often has additional structure that goes beyond the notion of “standard ” sparsity. In many cases, we can represent this additional information in a structured sparsity model. Recent research has shown that structured sparsity can improve the sample complexity in several applications such as compressive sensing and sparse linear regression. However, these improvements come at a computational cost, as the data needs to be “fitted ” so it satisfies the constraints specified by the sparsity model. In this survey, we introduce the concept of structured sparsity, explain the relevant algorithmic challenges, and briefly describe the best known algorithms for two sparsity models. On the way, we demonstrate that structured sparsity models are inherently combinatorial structures, and employing structured sparsity often leads to interesting algorithmic problems with strong connections to combinatorial optimization and discrete algorithms. We also state several algorithmic open problems related to structured sparsity. 1
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"... Abstract — This project enable us to calculate the weight lifted by a bulldozer. A payload monitor measures and displays payload weight for a bulldozer vehicle by sensing the hydraulic pressure. ARM KL25Z is used to calculate the payload and Graphical LCD is used to display the calculated weight. Th ..."
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Abstract — This project enable us to calculate the weight lifted by a bulldozer. A payload monitor measures and displays payload weight for a bulldozer vehicle by sensing the hydraulic pressure. ARM KL25Z is used to calculate the payload and Graphical LCD is used to display the calculated weight. The hydraulic pressure sensor is used to calculate the weight lifted by the bulldozer. It explores the payload calculation and the calculated value send to the PC or mobile [11] using GSM Module and stored using SD Card. Keywords Hydraulic Pressure Sensor, GLCD display,
Recursive Recovery of Sparse Signal Sequences from Compressive Measurements: A Review
"... In this article, we review the literature on the design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change wi ..."
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In this article, we review the literature on the design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in some dictionary. Their sparsity patterns can change with time, although in many practical applications, the changes are gradual. An important class of applications where this problem occurs is dynamic projection imaging, e.g., dynamic magnetic resonance imaging for realtime medical applications such as interventional radiology, or dynamic computed tomography.