Wavelet domain least squares deconvolution for ultrasonic backscattered signals

In biomedical ultrasound, it is often required to eliminate the spectral shaping caused by the transducer from the backscattered signal to obtain the pure tissue response for diagnostic purposes. Here, the authors deconvolve ultrasonic backscattered signals using a least squares deconvolution method in the wavelet domain. The ultrasonic echo is often modeled as the convolution of the transducer impulse response and the response of the medium. The authors solve this deconvolution problem by estimating a filter which approximates the inverse of the transducer impulse response. Therefore, applying this filter to the echo yields the tissue response and applying it to the transducer impulse response results in an impulse function. In this work, the authors assume that the tissue response exhibits 1/f type spectral behavior. Hence, they use the wavelet transform in the deconvolution algorithm for the 1/f signals, which has the useful property that the logarithm of the variance of the wavelet coefficients in each stage progresses linearly. Initially the authors estimate a rough inverse filter using the transducer impulse response. Then, they optimize this filter by minimizing an error criterion defined by using the linear progression property of the logarithmic variance of the wavelet coefficients for the 1/f signals. The authors present the error minimization algorithm and the deconvolution results for tissue mimicking phantom data