WOLD decomposition of the backscatter echo in ultrasound images of soft tissue organs

This paper deals with a method of detecting and estimating the scatterer spacing between the regularly spaced resolvable coherent scatterers in tissue. Scatterer spacing has been successfully used in classifying tissue structure, in differentiating between normal and cirrhotic liver, and in detecting diffuse liver disease. This paper presents a WOLD decomposition of the radio frequency (RF) field into its diffused and coherent components from which maximum likelihood estimates (MLE) or minimum mean square error (MMSE) estimates of the scattering spacing are easily computed. The MLE are efficient and for relatively long record are unbiased. They result in accurate estimates in low signal-to-noise (SNR) ratios. Unfortunately, they require nonlinear minimization and knowledge of the probability density associated with the RF backscatter echo. The MMSE estimates, on the other hand, are computationally simple, yield unique closed form solutions, do not require a-priori knowledge of the probability distribution function of the backscatter echo, and result in accurate estimates in low SNR ratios. This paper also presents an unbiased decision rule to detect whether or not an RF echo exhibits any specular scattering relative to the wavelength of the interrogating ultrasonic pulse. The approach has been tried on simulations as well as on in-vivo scans of liver data, and appears to perform well.