APPLICATION OF THE KHOKHLOV-ZABOLOTSKAYA-KUZNETSOV EQUATION TO MODELING HIGH-INTENSITY FOCUSED ULTRASOUND BEAMS

High-intensity focused ultrasound is a form of therapeutic ultrasound which uses high amplitude acoustic waves to heat and ablate tissue. HIFU employs acoustic amplitudes that are high enough that nonlinear propagation effects are important in the evolution of the sound field. A common model for HIFU beams is the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation which accounts for nonlinearity, diffraction, and absorption. The KZK equation models diffraction using the parabolic or paraxial approximation. Many HIFU sources have an aperture diameter similar to the focal length and the paraxial approximation may not be appropriate. Here, results obtained using the “Texas code,” a time-domain numerical solution to the KZK equation, were used to assess when the KZK equation can be employed. In a linear water case comparison with the O’Neil solution, the KZK equation accurately predicts the pressure field in the focal region. The KZK equation was also compared to simulations of the exact fluid dynamics equations (no paraxial approximation). The exact equations were solved using the Fourier-Continuation (FC) method to approximate derivatives in the equations. Results have been obtained for a focused HIFU source in tissue. For a low focusing gain transducer (focal length 50λ and radius 10λ), the KZK and FC models showed excellent agreement, however, as the source radius was increased to 30λ, discrepancies started to appear. Modeling was extended to the case of tissue with the appropriate power law using a relaxation model. The relaxation model resulted in a higher peak pressure and a shift in the location of the peak pressure, highlighting the importance of employing the correct attenuation model. Simulations from the code that were compared to experimental data in water showed good agreement through the focal plane.

Learning a Family of Detectors

Object detection and recognition are important problems in computer vision. The challenges of these problems come from the presence of noise, background clutter, large within class variations of the object class and limited training data. In addition, the computational complexity in the recognition process is also a concern in practice. In this thesis, we propose one approach to handle the problem of detecting an object class that exhibits large within-class variations, and a second approach to speed up the classification processes. In the first approach, we show that foreground-background classification (detection) and within-class classification of the foreground class (pose estimation) can be jointly solved with using a multiplicative form of two kernel functions. One kernel measures similarity for foreground-background classification. The other kernel accounts for latent factors that control within-class variation and implicitly enables feature sharing among foreground training samples. For applications where explicit parameterization of the within-class states is unavailable, a nonparametric formulation of the kernel can be constructed with a proper foreground distance/similarity measure. Detector training is accomplished via standard Support Vector Machine learning. The resulting detectors are tuned to specific variations in the foreground class. They also serve to evaluate hypotheses of the foreground state. When the image masks for foreground objects are provided in training, the detectors can also produce object segmentation. Methods for generating a representative sample set of detectors are proposed that can enable efficient detection and tracking. In addition, because individual detectors verify hypotheses of foreground state, they can also be incorporated in a tracking-by-detection frame work to recover foreground state in image sequences. To run the detectors efficiently at the online stage, an input-sensitive speedup strategy is proposed to select the most relevant detectors quickly. The proposed approach is tested on data sets of human hands, vehicles and human faces. On all data sets, the proposed approach achieves improved detection accuracy over the best competing approaches. In the second part of the thesis, we formulate a filter-and-refine scheme to speed up recognition processes. The binary outputs of the weak classifiers in a boosted detector are used to identify a small number of candidate foreground state hypotheses quickly via Hamming distance or weighted Hamming distance. The approach is evaluated in three applications: face recognition on the face recognition grand challenge version 2 data set, hand shape detection and parameter estimation on a hand data set, and vehicle detection and estimation of the view angle on a multi-pose vehicle data set. On all data sets, our approach is at least five times faster than simply evaluating all foreground state hypotheses with virtually no loss in classification accuracy.