Page 12 - Summer 2008

Fig. 5. Model-based matched-field processor for acoustical imaging applications. Raw array field measurements and back- propagated model measurements are compared (decision function) creating a power image that is thresholded for detec- tion and localization.
valve radiates a sound with each beat that is measured by the microphone(s) positioned on the patient’s chest. The noisy measurement data is enhanced and initially analyzed (Fig. 4c) and then processed further. Here a spectrum and instanta- neous spectrogram are estimat- ed from the model parameters and displayed in Fig. 4d. The frequency peaks in the spectro- gram are estimated, and a peak resonant frequency probability distribution histogram is con- structed to provide a feature vector that can be used to per- form the classification deter- mining the valve’s condition.12
Step 4: Model-based processing (lumped physical approach)
Model-based signal pro-
cessing7 is the next step in the
signal processing approach. It
has distinct advantage over
other approaches because the processor is developed directly in the acoustician’s frame-of-reference, that is, in his phenom- enological space. Not only does it require physics-based mod- els of the underlying phenomenology, but it also requires knowledge of the measurement instrumentation and noise processes to construct a good processor. Here the acoustician is “thinking” directly in terms of the acoustics and not infer- ring results from a variety of analysis tools (e.g., Fourier and wavelet transforms) that are not directly related to the under- lying propagation physics. The model-based approach is sim- ply incorporating mathematical models of the underlying phe- nomenology including measurements and noise into the pro- cessing scheme—this is exactly how the acoustician becomes an integral part of the processing by providing the acoustic models that are embedded into the model-based processor (MBP). Not only is there direct benefits of thinking in the same physical coordinates of the acoustic problem, but also gaining a deeper understanding of the instrumentation per- formance and noise/uncertainty processes that contaminate the problem. This is the good news. Of course, if the model is inaccurate and does not represent the phenomenology ade- quately, then the results can be erroneous and sometimes very misleading (science or science fiction?). Fortunately, many of these processors provide “self-checking” validation tools such as residuals (difference between the measurements and model predictions) that can be statistically tested for validity and used
7
by the processor to assure accurate performance. With this in
mind, we introduce two of the most popular model-based approaches in the literature: model-based matched-field pro- cessing8,9 (imaging) and model-based recursive (in-time or in-
space or both) processors (e.g., MBP or Kalman filters).
7
Model-based matched-field imaging for nondestructive evaluation
Typical image processing techniques in acoustics consist of pre-processing the raw data to provide enhanced signals as input to the image formation algorithm as well as post-pro- cessing of the two-dimensional image to enhance, extract, and classify certain features of high interest. In this article, we concentrate primarily on the same theme that we have used throughout, the development of processors that incorporate more and more a priori information about the acoustics gen- erating the data and its incorporation into a model-based imaging algorithm.
We saw in the previous example of a plane wave imping- ing on an array, how modern spatial spectral estimators (beamformers) can be used to estimate the wave’s spatial and temporal spectral features. The model-based approach uses all of the a priori information about the plane wave propaga- tion and noise measurements to extract the parameters directly solving the problem. The same idea can be extrapo- lated to the imaging problem. We assume that we have an array of sensors either physical or synthetically created, and we have developed a sequence of measurements resulting by exciting the medium under investigation. For instance, it can be an active sonar system in the ocean or an ultrasonic scan- ner in biomedical or nondestructive evaluation (NDE), or a passive array listening to a surveillance volume for passing airborne targets.
Here we consider the acoustic application of a laser ultra- sound experiment for the NDE of an aluminum part. Our first approach is to apply the synthetic aperture focus tech-
nique (SAFT) to image the part under investigation.
13,14
We
Signal Processing in Acoustics 11