Eran Bashan

Optimal Two-Stage Search for Sparse Targets Using Convex Criteria

We consider the problem of estimating and detecting sparse signals over a large area of an image or other medium. We introduce a novel cost function that captures the tradeoff between allocating energy to signal regions, called regions of interest (ROI), versus exploration of other regions. We show that minimizing our cost guarantees reduction of both the error probability over the unknown ROI and the mean square error (MSE) in estimating the ROI content. Two solutions to the resource allocation problem, subject to a total resource constraint, are derived. Asymptotic analysis shows that the estimated ROI converges to the true ROI. We show that our adaptive sampling method outperforms exhaustive search and are nearly optimal in terms of MSE performance. An illustrative example of our method in radar imaging is given.

Two-Stage Multiscale Search for Sparse Targets

We consider the problem of energy constrained and noise-limited search for targets that are sparsely distributed over a large area. We propose a multiscale search algorithm that significantly reduces the search time of the adaptive resource allocation policy (ARAP) introduced in [Bashan 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 rescanned. 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 near "Zero Information" points: angle-of-arrival near the endfire

We examine large-sample properties of the maximum- likelihood estimator (MLE) in the vicinity of points where the Fisher information measure (FIM) equals zero. Under mild regularity conditions the MLE is asymptotically efficient and therefore lower bounded by the Cramer-Rao lower bound (CRLB) [5], which diverges for such points. When a linear sensor array is used for angle-of-arrival (AOA) estimation, the CRLB diverges as the AOA approaches pi/2. We provide new results characterizing the MLE performance in the AOA problem.

Adaptive search for dynamic targets under resource constraints

Previous work on resource constrained adaptive search for sparse static targets has produced two-stage allocation policies with desirable properties. For example, for large asymptotic SNR, such policies converge to the true region of interest (ROI) and attain optimal energy allocations relative to exhaustive search. This work investigates the problem of extending previous allocation policies to T ≫ 2 stages, with particular emphasis on cases where the SNR for any particular stage is considerably less than the asymptotic SNR. Furthermore, a new formulation is given that can account for non-static targets, including a dynamic transition model for target location and a population model to account for targets that leave or enter the scene. Under this formulation, a dynamic adaptive resource allocation policy (D-ARAP) is proposed that performs well and has low computational cost. It is shown that this policy provides significant gains over an exhaustive search policy in both static and dynamic target cases with near optimal performance as T → ∞. Moreover, D-ARAP is shown to be more robust than a greedy (myopic) policy when there are outliers or when targets may be obscured for periods of time.

A novel approach to optimise glycaemic control in insulin users

Insulin therapy has been available for almost a century. However, its success rate is still disappointing where the majority of users sustain harmfully elevated glycated haemoglobin (HbA1c) levels. The key element essential for effective and safe insulin therapy is frequent dosage titration to overcome constant variations in insulin requirements. In reality, dosage titration is done sporadically during clinic visits. A scalable solution to this problem is being reviewed. A diabetes nurses service improves glycaemic control without overburdening the health system. The service relies on a handheld device, which provides patients with an insulin dose recommendation for each injection while using the device to monitor glucose. Similar to the approach providers use during clinical encounters, the device analyses stored glucose trends and constantly titrates insulin dosage without care providers’ supervision. In this report, we describe the logic behind the technology by providing examples from users.