Statistical properties of radio-frequency and envelope-detected signals with applications to medical ultrasound

Abstract

Both radio-frequency (rf) and envelope-detected signal analyses have lead to successful tissue discrimination in medical ultrasound. The extrapolation from tissue discrimination to a description of the tissue structure requires an analysis of the statistics of complex signals. To that end, firstand second-order statistics of complex random signals are reviewed, and an example is taken from rf signal analysis of the backscattered echoes from diffuse scatterers. In this case the scattering form factor of small scatterers can be easily separated from long-range structure and corrected for the transducer characteristics, thereby yielding an instrument-independent tissue signature. The statistics of the more economical envelope-and square-law-detected signals are derived next and found to be almost identical when normalized autocorrelation functions are used. Of the two nonlinear methods of detection, the square-law or intensity scheme gives rise to statistics that are more transparent to physical insight. Moreover, an analysis of the intensity-correlation structure indicates that the contributions to the total echo signal from the diffuse scatter and from the steady and variable components of coherent scatter can still be separated and used for tissue characterization. However, this analysis is not system independent. Finally, the statistical methods of this paper may be applied directly to envelope signals in nuclear-magnetic-resonance imaging because of the approximate equivalence of second-order statistics for magnitude and intensity.

Speckle classification for sensorless freehand 3-D ultrasound

“…For fully developed speckle, the received complex RF echo at any point is a circularly symmetric Gaussian random variable (RV) with the real and imaginary parts independent, zeromean Gaussian RV's with the same variance [1,3,30,31]. As mentioned earlier, under these conditions, the phasor magnitudes (i. e. the echo amplitudes as given by Eq.…”

“…Due to the coloured nature of the received RF echo, it is possible to estimate the local shape of the resolution cell via the spatial decorrelation of the RF echo intensity. For scans comprising fully developed speckle, there is a direct relationship between the resolution cell's dimensions and the decorrelation functions in the principal scanning directions [2,5,31,32]. We therefore measured decorrelation functions in the elevational and axial directions by scanning a speckle phantom with Rayleigh backscatter and uniform attenuation of 0.4 dB/cm/MHz 4 [17,19].…”

Subsample interpolation strategies for sensorless freehand 3D ultrasound

“…Referring to Figure 2, this involves fitting some function f (d l ) to the available samples of ρ, then determining d * l and ρ * from the peak of f (d l ). The most natural choice for f (d l ) is the true shape of a lateral decorrelation curve, which is approximately Gaussian when imaging fully developed speckle at the beam's focus and correlating the intensity or amplitude envelope of the RF echo signal [14,17,18]. Away from the focus, there are side-lobes in the point spread function and a Gaussian curve is no longer appropriate.…”

Evaluation of in vivo Liver Tissue Characterization with Spectral RF Analysis versus Elasticity

“…Estimation of the scattering power index (SPI) For independent scatterers of size smaller than the wavelength, theoretical approaches [7] lead to a BSC frequency dependence in 4 f : this is called the Rayleigh limit. In practice, it was observed that this simple model fails in soft tissues [8], leading to a generalization of the BSC frequency dependence model as:…”