First-order statistics of speckle around a scatterer volume density edge and edge detection in ultrasound images

Ultrasonic imaging plays an important role in medical imaging. But the images exhibit a granular structure, commonly known as speckle. The speckle tends to mask the presence of low-contrast lesions and reduces the ability of a human observer to resolve fine details. Our interest in this research is to examine the problem of edge detection and come up with methods for improving the visualization of organ boundaries and tissue inhomogeneity edges. An edge in an image can be formed either by acoustic impedance change or by scatterer volume density change (or both). The echo produced from these two kinds of edges has different properties. In this work, it has been proved that the echo from a scatterer volume density edge is the Hilbert transform of the echo from a rough impedance boundary (except for a constant) under certain conditions. This result can be used for choosing the correct signal to transmit to optimize the performance of edge detectors and characterizing an edge. The signal to noise ratio of the echo produced by a scatterer volume density edge is also obtained. It is found that: (1) By transmitting a signal with high bandwidth ratio and low center frequency, one can obtain a higher signal to noise ratio. (2) For large area edges, the farther the transducer is from the edge, the larger is the signal to noise ratio. But for small area edges, the nearer the transducer is to the edge, the larger is the signal to noise ratio. These results enable us to maximize the signal to noise ratio by adjusting these parameters. (3) The signal to noise ratio is not only related to the ratio of scatterer volume densities at the edge, but also related to the absolute value of scatterer volume densities. Some of these results have been proved through simulation and experiment. Different edge detection methods have been used to detect simulated scatterer volume density edges to compare their performance. A so-called interlaced array method has been developed for speckle reduction in the images formed by synthetic aperture focussing technique, and experiments have been done to evaluate its performance.