Optimal Two-Stage Search for Sparse Targets Using Convex Criteria

Bashan, Eran; Raich, Raviv; Hero, Alfred O.

doi:10.1109/tsp.2008.929114

Cited by 39 publications

(113 citation statements)

References 12 publications

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“…The two measurements can be later combined to both detect and estimate the region of interest (ROI) and its content. In [1], we showed ARAP to be asymptotically optimal and the estimation gains were inversely proportional to the signal sparsity. In the modified version, performance continues to depend on sparsity, as well as the extent of the multi-scaling (which is directly related to the number of samples taken) and the inherent contrast of the signal.…”

Section: Introductionmentioning

confidence: 97%

“…Related problems include detection of tumors in early cancer detection and surveillance systems using agile radars. In [1], a novel cost function was introduced, and the solution of a related minimization problem yielded an asymptotically optimal adaptive resource allocation policy, namely ARAP. In this work we introduce a multi-scale modification of ARAP (M-ARAP) and show that it leads to additional performance gains in search complexity, target localization and target amplitude estimation.…”

Section: Introductionmentioning

confidence: 99%

“…Like ARAP [1], the generalized version of the distilled sensing procedure [7] applies adaptive coordinate-wise thresholding to each pixel, retaining only those pixels that exceed the threshold for consideration at the next stage. They show that there exists a sequence of thresholds and sensing energy parameters that asymptotically guarantee perfect recovery of the targets at arbitrarily small false discovery rate.…”

Section: Introductionmentioning

confidence: 99%

“…They show that there exists a sequence of thresholds and sensing energy parameters that asymptotically guarantee perfect recovery of the targets at arbitrarily small false discovery rate. While they have similarities, ARAP approaches introduced here and in [1] differ from distilled sensing approaches of [7], [9] in important ways. (1) ARAP approaches adopt a Bayesian framework and generate a posterior probability of target presence at each pixel.…”

Section: Introductionmentioning

confidence: 99%

“…In ARAP [1], we assumed independent and identical distribution (i.i.d.) of targets among pixels and presented a two stage approach for resource allocation under a fixed energy constraint.…”

Section: Introductionmentioning

confidence: 99%

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Two-Stage Multiscale Search for Sparse Targets

Bashan

Newstadt

Hero

2011

IEEE Trans. Signal Process.

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Abstract-We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multi-scale search algorithm that significantly reduces the search time of the adaptive resource allocation policy (ARAP) introduced in [Bashan et all, 2008]. Similarly to ARAP, the proposed approach scans a Q-cell partition of the search area in two stages: first the entire domain is scanned and second a subset of the domain, suspected of containing targets, is re-scanned. The search strategy of the proposed algorithm is driven by maximization of a modified version of the previously introduced ARAP objective function, which is a surrogate for energy constrained target detection performance. We analyze the performance of the proposed multistage ARAP approach and show that it can reduce mean search time with respect to ARAP for equivalent energy constrained detection performance. To illustrate the potential gains of M-ARAP, we simulate a moving target indicator (MTI) radar system and show that M-ARAP achieves an estimation performance gain of 7 dB and a 85% reduction in scan time as compared to an exhaustive search. This comes within 1 dB of the previously introduced ARAP algorithm at a fraction of its required scan time.

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Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…In ARAP [1], we assumed independent and identical distribution (i.i.d.) of targets among pixels and presented a two stage approach for resource allocation under a fixed energy constraint.…”

Section: Introductionmentioning

confidence: 99%

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Two-Stage Multiscale Search for Sparse Targets

Bashan

Newstadt

Hero

2011

IEEE Trans. Signal Process.

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Adaptive sensing for sparse recovery

Haupt¹,

Nowak²

2012

Compressed Sensing

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Sketching for large-scale learning of mixture models

Keriven

Bourrier

Gribonval

et al. 2017

Information and Inference: A Journal of the IMA

148

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Learning parameters from voluminous data can be prohibitive in terms of memory and computational requirements. We propose a "compressive learning" framework where we estimate model parameters from a sketch of the training data. This sketch is a collection of generalized moments of the underlying probability distribution of the data. It can be computed in a single pass on the training set, and is easily computable on streams or distributed datasets. The proposed framework shares similarities with compressive sensing, which aims at drastically reducing the dimension of high-dimensional signals while preserving the ability to reconstruct them. To perform the estimation task, we derive an iterative algorithm analogous to sparse reconstruction algorithms in the context of linear inverse problems. We exemplify our framework with the compressive estimation of a Gaussian Mixture Model (GMM), providing heuristics on the choice of the sketching procedure and theoretical guarantees of reconstruction. We experimentally show on synthetic data that the proposed algorithm yields results comparable to the classical Expectation-Maximization (EM) technique while requiring significantly less memory and fewer computations when the number of database elements is large. We further demonstrate the potential of the approach on real large-scale data (over 10 8 training samples) for the task of model-based speaker verification.Finally, we draw some connections between the proposed framework and approximate Hilbert space embedding of probability distributions using random features. We show that the proposed sketching operator can be seen as an innovative method to design translation-invariant kernels adapted to the analysis of GMMs. We also use this theoretical framework to derive information preservation guarantees, in the spirit of infinite-dimensional compressive sensing.

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Optimal Two-Stage Search for Sparse Targets Using Convex Criteria

Cited by 39 publications

References 12 publications

Two-Stage Multiscale Search for Sparse Targets

Two-Stage Multiscale Search for Sparse Targets

Adaptive sensing for sparse recovery

Sketching for large-scale learning of mixture models

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