Two-Stage Multiscale Search for Sparse Targets

Abstract

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.

Estimation After Parameter Selection: Performance Analysis and Estimation Methods

“…The bound in (25) coincides with the conditional CRB derived in [26] for estimation after binary detection, i.e., when a binary detection step is performed before the estimation of the parameters. This observation remains valid for any non-Bayesian bound on the PSMSE, which can be derived by using the Cauchy-Schwarz inequality and the Ψ-unbiasedness, in a similar way to the derivations in [26], [43].…”

“…The problem of postdetection estimation, or estimation after data censoring, is considered by Chaumette, Larzabal, and Forster [26], [27], who derive a novel CRB on the conditional MSE, involving conditional Fisher information. It should be noted that in [26], [27], [24], [25], the selection rule selects the data to be used, while in our proposed model the parameter to be estimated is selected and all the data can be used for estimation. Selection and ranking are highly related approaches [6].…”

Adaptive search for dynamic targets under resource constraints

“…In a medical imaging application, such as early detection of breast cancer, where tumor boundaries are poorly defined, the ROI may be defined as the collection of all cells containing targets (a tumor) plus some neighboring cells. In this work, we generalize the formulation from [1], [4] to account for a time-varying ROI so that that Ψ = Ψ(t) is a function of time. Define indicator functions:…”

Performance Guarantees for Adaptive Estimation of Sparse Signals

“…Empirical results in [1], [2], [4] show that multistage adaptive sensing can lead to dramatically better estimates of nonzero signal components compared to non-adaptive sensing. However, analytical quantification of the gains in this setting has so far been lacking.…”

“…This paper studies the benefits of adaptive sensing for the estimation of nonzero signal amplitudes in a context similar to [1]. In contrast to [1]- [4] however, where the focus was on developing tractable resource allocation policies capable of large gains and on empirical validation thereof, here the focus is on theoretical certification. Specifically, the goal is to provide estimation performance guarantees for adaptive sensing policies and to analyze the key factors affecting the adaptation gain.…”