Best least-squares representation of signals by exponentials

McDonough, R. N.; Huggins, W. H.

doi:10.1109/tac.1968.1098950

Cited by 78 publications

(12 citation statements)

References 9 publications

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“…Prony ' s algorithm has been used in the fields of automatic control [16] and biological signal processing [17], but only to represent or synthesize a signal in terms of a set of exponentials which do not necessarily have any physical relationship to the system which produced the signal. The desire here, however, is to extract from a system 's transient response a set of complex exponentials which are in fact the characteristic resonances of the system being studied .…”

Section: The Numerical Methods For Extracting Polesmentioning

confidence: 99%

Techniques for Extracting the Complex Resonances of a System Directly from Its Transient Response.

Blaricum¹,

Mittra²

1977

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Section: The Numerical Methods For Extracting Polesmentioning

confidence: 99%

Techniques for Extracting the Complex Resonances of a System Directly from Its Transient Response.

Blaricum¹,

Mittra²

1977

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“…The goal is to find E i and α that minimize this cost function. Algorithms for solving similar least-squares problems exist in the literature, for example [14,15]. However, since this is a nonlinear problem, those algorithms tend to be iterative.…”

Section: Acoustic Attenuation Map Estimationmentioning

confidence: 99%

Identification of Malignant Breast Tumors Based on Acoustic Attenuation Mapping of Conventional Ultrasound Images

Harary

Walach

2013

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

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Abstract. Although breast cancer imaging techniques continue to improve rapidly, about 75% of all breast biopsies turn out to be benign. These unnecessary biopsies are expensive and very stressful for the patients. In this paper we propose a new method for reducing the number of unnecessary biopsies. Our approach consists of transforming conventional ultrasonic images into corresponding attenuation maps. These maps are then analyzed, yielding automatic classification of malignant tumors. We provide a proof of concept for this approach by testing it on a benchmark of clinical images from three different image acquisition systems. Our tests show excellent sensitivity and specificity, indicating that up to four-fold reduction in the number of unnecessary biopsies may be possible. Moreover, we demonstrate the system robustness by working on all the images without any system-specific tuning.

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“…where the amplitudes A n , phases / n , frequencies x n , and decay times s n are taken as fit parameters; unfortunately the Prony method requires a nonlinear fit procedure, and it is known to be computationally expensive and very sensitive to background noise [7,8].…”

Section: Spectral Power Density and Phase Estimatesmentioning

confidence: 99%

Sine-fit procedure for unevenly sampled, multiply clocked signals

Milotti

2005

Journal of Computational Physics

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Best least-squares representation of signals by exponentials

Cited by 78 publications

References 9 publications

Techniques for Extracting the Complex Resonances of a System Directly from Its Transient Response.

Techniques for Extracting the Complex Resonances of a System Directly from Its Transient Response.

Identification of Malignant Breast Tumors Based on Acoustic Attenuation Mapping of Conventional Ultrasound Images

Sine-fit procedure for unevenly sampled, multiply clocked signals

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