An imaging device that uses the wavelet transformation as the image reconstruction algorithm

Many imaging devices have been constructed that use fourier transform techniques for image reconstruction as well as for image analysis. The basis functions in the fourier transform space are sinusoids. These are not localized. Therefore it should not be expected that highly localized behavior of a signal be characterized well using functions distributed evenly throughout the interval of the integral transform. Also, the phase cancellations of a conventional impulse signal are not handled well by fourier techniques. On the other hand, the basis functions of the wavelet transformation are highly localized, i.e., these exhibit compact support, yet are orthonormal. The multispectral decomposition algorithm of the wavelet transformation is used to analyze the signal returning from the reflections of a single ultrasonic transducer with a focused beam and operated in the focal zone. The choice of frequency depends upon the mutually antagonistic factors of penetration (αf^–2) and resolution (αf). The signal sent into the sample should not be the impulse response signal used in conventional devices; rather, it should be a time-reversed replica of a single or a linear combination of the most highly localized basis function wavelets. The returning signal is a sequence of translates of the wavelets plus perhaps some lower-resolution wavelets. The translations are proportational to the time of flight of the signal. The wavelet transformation is superb at discriminating the population of each of these translates which is identically the A-scan signal. The transmitted signal, which is a time-reversed single wavelet or a linear combination of wavelets, is not easy to produce. Inexpensive ultrasound transducers have resonances which make it difficult to produce any desired wave form. Wavelet shape is far from arbitrary. Precise wave shaping is performed by measuring the impulse response function of the transducer; then, the desired wave shape is convolved with the inverse of the measured impulse response function of the transducer. This produces the signal to be presented to the pulse generation circuit. Care is taken to damp the impulse response so that there are no zeros. The received signal is sampled at an even rate which is carefully chosen to match the time delay of one wavelet translate to the next. B-scan, C-scan, and volume imaging are easily accomplished using a sequence of A-scan data, all by conventional techniques. A single A-scan requires less than 2 ms to perform and reconstruct with a high-speed arithmetic unit which was designed in conjunction with this work and is now commercially available.