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Conventional optimal bounding ellipsoid (OBE) algorithms require a priori knowledge of error bounds which is unknown in most applications. Conservative (overestimated) error bounds used in practice may lead to inconsistent parameter estimation. This paper presents an enhanced OBE algorithm that is proven to be consistently convergent without a priori knowledge of error bounds. Only a lower bound of the 'tail probability' of the disturbance process is required. Simulations comparing conventional and the enhanced OBE algorithm is provided.1998 John Wiley & Sons, Ltd. -The name ''OBE'' is widely used in the literature to indicate the class of algorithms in which the bounding ellipsoid is optimized pointwise as described below. This paper is restricted to such algorithms. Other optimization strategies and heuristic measures that generally increase computational complexity can result in 'better' ellipsoidal bounding sets (e.g., References 16 and 17). include superior tracking properties in the presence of non-stationary dynamics, and more accurate and more-quickly converging solutions in the stationary, finite-data case (e.g., Reference 1). Further, the OBE algorithms can be structured to be more computationally efficient than RLS and similar methods. Additionally (as with any bounded-error identification method), OBE algorithms yield a feasible set of solutions that can be exploited in certain applications, whereas the centroid of the set (computed recursively) provides a convenient point estimate which is interpretable as a weighted-least-square-error estimate. Finally, the asymptotic convergence properties of OBE methods are beginning to be well-understood and suggest that the OBE methods may offer significant advantages in certain (especially coloured) noise environments.

Focused ultrasound (FUS) is a recently discovered noninvasive technique for local and temporal enhancement of vascular permeability, which facilitates drug delivery from the vessels into the surrounding tissue. However, exposure to FUS at a high intensity may cause permanent damage. To investigate the effects of the FUS treatment on blood vessels, we propose to use fluorescein angiography (FA) and optical coherence tomography (OCT) for real-time observation of the diffusion of fluorescence dye from blood vessels and to evaluate the morphological changes of the vessels in vivo. With time-resolved FA imaging, the relationship between the exposed power and the improved permeability of the vessels can be assessed according to the enhancement of the fluorescent intensity due to the dye leakage. Furthermore, the variation of the time-resolved fluorescent intensities can be used to identify the occurrence of dye leakage. In contrast, OCT can be implemented for the reconstruction of tissue microstructures. To quantitatively evaluate the morphological changes of the vessels after the FUS exposure with OCT, a new algorithm was proposed to estimate the vessel area based on the comparison of backscattering properties resulting from the tissue and vascular structures. Results showed that the vessel area increased as the exposed power increased, and the area became significantly larger at a higher FUS exposure power of 10 W. In conclusion, integrated FA and OCT observation can be potentially effective for monitoring the outcome and investigating the effects of FUS treatment.

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