Nonlinear Programming: A Unified Approach

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Introduction To Electrodynamics

Over the coming decades, high-definition situationally-aware networks have the potential to create revolutionary applications in the social, scientific, commercial, and military sectors Ultrawide bandwidth (UWB) technology is a viable candidate for enabling accurate localization capabilities through time-of-arrival (TOA)-based ranging techniques These techniques exploit the fine delay resolution property of UWB signals by estimating the TOA of the first signal path Exploiting the full capabilities of UWB TOA estimation can be challenging, especially when operating in harsh propagation environments, since the direct path may not exist or it may not be the strongest In this paper, we first give an overview of ranging techniques together with the primary sources of TOA error (including propagation effects, clock drift, and interference) We then describe fundamental TOA bounds (such as the Cramer-Rao bound and the tighter Ziv-Zakai bound) in both ideal and multipath environments These bounds serve as useful benchmarks in assessing the performance of TOA estimation techniques We also explore practical low-complexity TOA estimation techniques and analyze their performance in the presence of multipath and interference using IEEE 802154a channel models as well as experimental data measured in indoor residential environments

/pdf/ranging-with-ultrawide-bandwidth-signals-in-multipath-illizjdvoz.pdf

Ranging With Ultrawide Bandwidth Signals in Multipath Environments

Pattern recognition

We have applied the minimum variance (MV) adaptive beamformer to medical ultrasound imaging and shown significant improvement in image quality compared to delay-and-sum (DAS). We demonstrate reduced main-lobe width and suppression of sidelobes on both simulated and experimental RF data of closely spaced wire targets, which gives potential contrast and resolution enhancement in medical images. The method is applied to experimental RF data from a heart phantom, in which we show increased resolution and improved definition of the ventricular walls. A potential weakness of adaptive beamformers is sensitivity to errors in the assumed wavefield parameters. We look at two ways to increase robustness of the proposed method; spatial smoothing and diagonal loading. We show that both are controlled by a single parameter that can move the performance from that of a MV beamformer to that of a DAS beamformer. We evaluate the sensitivity to velocity errors and show that reliable amplitude estimates are achieved while the mainlobe width and sidelobe levels are still significantly lower than for the conventional beam-former.

/pdf/adaptive-beamforming-applied-to-medical-ultrasound-imaging-1eqmhi5v2n.pdf

Adaptive Beamforming Applied to Medical Ultrasound Imaging

Currently, the nonadaptive delay-and-sum (DAS) beamformer is extensively used for ultrasound imaging, despite the fact that it has lower resolution and worse interference suppression capability than the adaptive standard Capon beamformer (SCB) if the steering vector corresponding to the signal of interest (SOI) is accurately known. The main problem which restricts the use of SCB, however, is that SCB lacks robustness against steering vector errors that are inevitable in practice. Whenever this happens, the performance of SCB may become worse than that of DAS. Therefore, a robust adaptive beamformer is desirable to maintain the robustness of DAS and adaptivity of SCB. In this paper we consider a recent promising robust Capon beamformer (RCB) for ultrasound imaging. We propose two ways of implementing RCB, one based on time delay and the other based on time reversal. RCB extends SCB by allowing the array steering vector to be within an uncertainty set. Hence, it restores the appeal of SCB including its high resolution and superb interference suppression capabilities, and also retains the attractiveness of DAS including its robustness against steering vector errors. The time-delay-based RCB can tolerate the misalignment of data samples and the time-reversal-based RCB can withstand the uncertainty of the Green's function. Both time-delay-based RCB and time-reversal-based RCB can be efficiently computed at a comparable cost to SCB. The excellent performances of the proposed robust adaptive beamforming approaches are demonstrated via a number of simulated and experimental examples.

Time-delay- and time-reversal-based robust capon beamformers for ultrasound imaging

We present a conceptually simple and computationally efficient algorithm, which is referred to as WRELAX for the well-known time delay estimation problem. The method is a relaxation-based minimizer of a complicated nonlinear least squares criterion, WRELAX can be applied to detecting and classifying roadway subsurface anomalies by using an ultra-wideband ground-penetrating radar. Numerical and experimental examples are provided to demonstrate the performance of the new algorithm.

An efficient algorithm for time delay estimation

Ultra-wideband (UWB) Microwave imaging (MWI) is a promising breast cancer detection technology which exploits the significant contrast in dielectric properties between normal breast tissue and tumor. Previously, data-independent methods, such as delay-and-sum (DAS) and space-time (ST) beamforming, have been used for microwave imaging. However, the low resolution and the poor interference suppression capability associated with the data-independent methods restrict their use in practice, especially when the noise is high and the backscattered signals are weak. In this paper, we develop two data-adaptive methods for microwave imaging, which are referred to as the robust weighted Capon beamforming (RWCB) method and the amplitude and phase estimation (APES) method. Due to their data-adaptive nature, these methods outperform their data-independent counterparts in terms of improved resolution and reduced sidelobe levels.

https://www.piers.org/piersonline/pdf/Vol1No3Page350to353.pdf

Microwave imaging via adaptive beamforming methods for breast cancer detection

A robust autofocus approach, referred to as AUTOCLEAN (AUTOfocus via CLEAN), is proposed for the motion compensation in ISAR (inverse synthetic aperture radar) imaging of moving targets. It is a parametric algorithm based on a very flexible data model which takes into account arbitrary range migration and arbitrary phase errors across the synthetic aperture that may be induced by unwanted radial motion of the target as well as propagation or system instability. AUTOCLEAN can be classified as a multiple scatterer algorithm (MSA), but it differs considerably from other existing MSAs in several aspects: (1) Dominant scatterers are selected automatically in the 2D image domain; (2) scatterers may not be well isolated or very dominant; (3) phase and RCS information from each selected scatterer are combined in an optimal way; (4) the troublesome phase unwrapping step is avoided. AUTOCLEAN is computationally efficient and involves only a sequence of FFTs. Another good feature associated with AUTOCLEAN is that its performance can be progressively improved by assuming a larger number of dominant scatterers for the target. Numerical and experimental results have shown that AUTOCLEAN is a very robust autofocus tool for ISAR imaging.

Robust autofocus algorithm for ISAR imaging of moving targets

We consider estimating time delays and amplitudes (real- or complex-valued) from the superposition of very closely spaced signals with known shapes. The well-known high resolution MODE (Method Of Direction Estimation) algorithm, which was originally proposed for angle estimation in array processing, is modified and used with our efficient time delay estimation method WRELAX (Weighted Fourier transform and RELAXation based) algorithm to deal with this problem. The proposed method is referred to as MODE-WRELAX. MODE-WRELAX provides better accuracy than MODE and higher resolution than WRELAX. Moreover, it can be used for both complex- and real-valued signals (including those with highly oscillatory correlation functions). Numerical results show that the MODE-WRELAX estimates can approach the corresponding Cramer-Rao bound. Efficient implementation of the algorithm is also discussed.

Renbiao Wu

Papers

Time-delay- and time-reversal-based robust capon beamformers for ultrasound imaging

An efficient algorithm for time delay estimation

Microwave imaging via adaptive beamforming methods for breast cancer detection

Robust autofocus algorithm for ISAR imaging of moving targets

Super resolution time delay estimation via MODE-WRELAX