Phase-Derivative Imaging II: Effects of Beam Diffraction and Scatterer Density

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Abstract
The potential of using the phase derivative (PD) of the radio-frequency echograms for producing 2-dimensional grey scale images was further investigated. The PD images were produced by five different algorithms, which according to the results described in the companion paper yield PD images dominated by the amplitude (envelope, ENV), mixed PD-AM images and pure PD images. These images are termed according to their algorithms: ZCS, zero crossing counter with squelch; ASS, analytic signal with squelch; ASW, analytic signal with Wiener kernel; UNP, unwrapped phase; and SAS, smoothed analytic signal. The rf data were obtained from simulations and from experiments with a tissue mimicking phantom. PD images were analysed by calculation of the first and second order grey level statistics: mean level, signal-to-noise ratio (SNR) and the full width at half maximum (FWHM) of the autocovariance functions (ACVF). These parameters were systematically investigated for a range of depths with respect to the transducer and a range of scatterer densities of the insonated medium. The UNP and SAS images do not suffer much from the diffraction effect but do not display much information about the scatterer density either. The ASW and ASS images qualitatively display beam diffraction effects similar to those of the AM images, with the exception of the mean value which is at the minimum in the focus, where the AM yields a sharp maximum at that depth. The mean and the SNR of the ASW and ASS images increase with increasing scatterer density and saturate at a density of 5000 cm-3. The mean value of the envelope, however, displays a square root dependency over the whole range. The axial and lateral FWHM of the ACVF of the UNP and SAS methods are not significantly dependent on the scatterer density and decrease with increasing density for the ASW and ASS images, as was observed in the envelope images. It may be concluded that ASW and ASS methods produce PD grey scale images which are equally well suited for the diagnosis of diffuse diseases of parenchymal tissues as conventional AM images. The smaller “speckle” size of the ASW images might be advantageous, for the detection of focal lesions, but the lesion contrast is found to be much lower than for the ENV.