### ASA 124th Meeting New Orleans 1992 October

## 3pBV7. Application of wavelet transforms to ultrasonic medical imaging.

**Woon S. Gan
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*Acoust. Services Pte Ltd., 29 Telok Ayer St., Singapore 0104, Republic of
Singapore
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In this paper, wavelet transform is applied to study ultrasonic medical
imaging. Nondiffracting source ultrasonic computed tomography and diffraction
ultrasonic tomography are considered. The multiresolution property of wavelet
transform is used. Wavelet transform is also applied to study nonstationary
ultrasonic medical images such as blood flow in heart which windowed Fourier
transform (short-time Fourier transform or Gabor transforms) is not convenient
to use. For the nondiffracting (straight ray) sources, the Fourier slice
theorem and parallel and fanbeam reconstruction algorithm are modified for
wavelet transforms. For diffracting sources, and Fourier diffraction theorem is
modified for wavelet transforms. The wavelet approach to multiresolution
decomposition is studied. The multiresolution wavelet model is reviewed which
shows that the difference of information between two successive resolutions can
be computed by decomposing the signal in a wavelet orthonormal basis. This is
an improved multiresolution pyramid algorithm. The equivalence between
multiresolution approximations and wavelet basis is used to derive wavelet
bases. The concept of multiresolution which gives different information of an
image at two different resolutions is particularly useful to texture
discrimination in medical imaging. A preliminary simulation result is given.