Observer efficiency in discrimination tasks simulating malignant and benign breast lesions imaged with ultrasound

Abstract

We investigate and extend the ideal observer methodology developed by Smith and Wagner to detection and discrimination tasks related to breast sonography. We provide a numerical approach for evaluating the ideal observer acting on radio frequency (RF) frame data, which involves inversion of large nonstationary covariance matrices, and we describe a power-series approach to computing this inverse. Considering a truncated power series suggests that the RF data be Wiener-filtered before forming the final envelope image. We have compared human performance for Wiener-filtered and conventional B-mode envelope images using psychophysical studies for 5 tasks related to breast cancer classification. We find significant improvements in visual detection and discrimination efficiency in four of these five tasks. We also use the Smith-Wagner approach to distinguish between human and processing inefficiencies, and find that generally the principle limitation comes from the information lost in computing the final envelope image.

Fig. 1

A graphical model of ultrasonic signal processing used in this work. The top row shows the formation of a standard B-Mode image including the object scattering function, the acquired radio-frequency (RF) frame, demodulated In-Phase (I) and Quadrature (Q) signals, and the final envelope image. Images of the demodulated signals and the final envelope images are reduced in size to indicate downsampling during demodulation. In this work we investigate the effect of implementing a Weiner-filter on the radio-frequency frame data. After Wiener filtering, the signal is demodulated and an envelope image is computed.

Fig. 2

Variance profiles of “Malignant” and “Benign” scattering objects the 5 tasks. The third row is the difference in the variance profiles. In Task 1, the lesion is 3mm in diameter. In tasks 2–5 the lesion is approximately 5mm in diameter.

Fig. 3

Pulse profile used to generate RF data.

Fig. 4

Examples of noisy B-mode and Wiener filtered images for Task 3 (at exaggerated contrast for display clarity).

Fig. 5

Human observer performance for B-mode and Weiner-filtered envelope images. Proportion correct in 2AFC psychophysical experiments are given for each of the five tasks. Error bars represent 95% confidence intervals about the mean across the six observers.

Fig. 6

The detectability index d_A is plotted as a function of object contrast for the ideal observer derived from Monte-Carlo studies in parts A–E. The legend in Task 2 applies to all plots. Also plotted are the Smith-Wagner approximations for B-Mode and Weiner filtered (WF) envelope images, as well as average human observer performance (error bars represent +/−1 standard deviation across observers). Part F shows how visual detection efficiency is computed. We find the threshold contrast, C_I, that gives the same detectability index for the Ideal observer as the human observers at contrast C_H. Contrast values are combined to com-pute efficiency in Equation 17.

Fig. 7

Efficiency Data. Human observer efficiency in both Wiener-Filtered and B-Mode images is plotted in A. To better understand the sources of inefficiency in A, the efficiency of the B-Mode and Wiener-Filtered Envelope Smith-Wagner (SW) observers are given in B. The relative efficiency of human observers to the SW are given in C.