We consider a system of transmission of the wave equation with Neumann feedback control that contains a delay term and acts on the exterior boundary. First, we prove under some assumptions that the closed-loop system generates a C 0 -semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multiplier method together with an estimate taken from Lasiecka & Triggiani (1992, Appl. Math. Optim., 25, 189–244.) (Lemma 7.2) and compactness-uniqueness argument.

We consider a system of transmission of the wave equation with Neumann feedback control that contains a delay term and acts on the exterior boundary. First, we prove under some assumptions that the closed-loop system generates a C 0 -semigroup of contractions on an appropriate Hilbert space. Then, under further assumptions, we show that the closed-loop system is exponentially stable. To establish this result, we introduce a suitable energy function and use multiplier method together with an estimate taken from Lasiecka & Triggiani (1992, Appl. Math. Optim., 25, 189–244.) (Lemma 7.2) and compactness-uniqueness argument.

In radiotherapy using 18-fluorodeoxyglucose positron emission tomography (18F-FDG-PET), the accurate delineation of the biological tumour volume (BTV) is a crucial step. In this study, the authors suggest a new approach to segment the BTV in 18F-FDG-PET images. The technique is based on the k-means clustering algorithm incorporating automatic optimal cluster number estimation, using intrinsic positron emission tomography image information. Clinical dataset of seven patients have a laryngeal tumour with the actual BTV defined by histology serves as a reference, were included in this study for the evaluation of results. Promising results obtained by the proposed approach with a mean error equal to (0.7%) compared with other existing methods in clinical routine, including fuzzy c-means with (35.58%), gradient-based method with (19.14%) and threshold-based methods.

In radiotherapy using 18-fluorodeoxyglucose positron emission tomography (18F-FDG-PET), the accurate delineation of the biological tumour volume (BTV) is a crucial step. In this study, the authors suggest a new approach to segment the BTV in 18F-FDG-PET images. The technique is based on the k-means clustering algorithm incorporating automatic optimal cluster number estimation, using intrinsic positron emission tomography image information. Clinical dataset of seven patients have a laryngeal tumour with the actual BTV defined by histology serves as a reference, were included in this study for the evaluation of results. Promising results obtained by the proposed approach with a mean error equal to (0.7%) compared with other existing methods in clinical routine, including fuzzy c-means with (35.58%), gradient-based method with (19.14%) and threshold-based methods.

In radiotherapy using 18-fluorodeoxyglucose positron emission tomography (18F-FDG-PET), the accurate delineation of the biological tumour volume (BTV) is a crucial step. In this study, the authors suggest a new approach to segment the BTV in 18F-FDG-PET images. The technique is based on the k-means clustering algorithm incorporating automatic optimal cluster number estimation, using intrinsic positron emission tomography image information. Clinical dataset of seven patients have a laryngeal tumour with the actual BTV defined by histology serves as a reference, were included in this study for the evaluation of results. Promising results obtained by the proposed approach with a mean error equal to (0.7%) compared with other existing methods in clinical routine, including fuzzy c-means with (35.58%), gradient-based method with (19.14%) and threshold-based methods.

In radiotherapy using 18-fluorodeoxyglucose positron emission tomography (18F-FDG-PET), the accurate delineation of the biological tumour volume (BTV) is a crucial step. In this study, the authors suggest a new approach to segment the BTV in 18F-FDG-PET images. The technique is based on the k-means clustering algorithm incorporating automatic optimal cluster number estimation, using intrinsic positron emission tomography image information. Clinical dataset of seven patients have a laryngeal tumour with the actual BTV defined by histology serves as a reference, were included in this study for the evaluation of results. Promising results obtained by the proposed approach with a mean error equal to (0.7%) compared with other existing methods in clinical routine, including fuzzy c-means with (35.58%), gradient-based method with (19.14%) and threshold-based methods.

Wavelets are known particularly to be an effective tool for extracting discriminative features in the scattered RF signals of both solid and gaseous emboli. However, the selection of an appropriate mother wavelet for the signal being analyzed is an important criterion. This offers the possibility to perform an optimization procedure to obtain the best wavelet. The purpose of the study is to propose a new approach to classify microembolic echoes using a discrete wavelet transform (DWT) based on genetic algorithm optimization and support vector machine (SVM) classifier. The experimental setup consists of a flow phantom (ATSLaB) containing a tube of 6 mm in diameter. In order to mimic the ultrasonic behavior of gaseous emboli, contrast agents consisting of microbubbles are used in our experimental setup. However, to mimic the behavior of the solid emboli we have used the Doppler fluid which contains particles with scatter characteristics comparable to red blood cells. The acquisitions are carried out at 2 MHz and 3.5 MHz transmit frequency. Ultrasound waves are transmitted at different intensities corresponding to mechanical indices (MI) of 0.21 and 0.42 for the transmit frequency of 2 MHz, and 0.31 and 0.62 for the transmit frequency of 3.5 MHz. Two concentrations of the contrast agent (100 μl and 200 μl) are diluted into a 100 ml volume of water. The polyphase representation of the discrete wavelet transform (DWT) is exploited in this study. Such representation allows generating a wavelet filter bank from a set of angular parameters, in order to minimize the fitness function based on genetic algorithm optimization and the SVM classifier. The best accuracy classifications of microemboli obtained in this study are equal to 99.90% for 2MHz and to 99.60% for 3.5MHz. These results illustrate that wavelet optimization approach works well for microemboli classification using RF signals.