Woon S. Gan
Acoust. Services Pte Ltd., 29 Telok Ayer St., Singapore 0104, Republic of Singapore
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.