Cascaded analysis of signal and noise propagation through a heterogeneous breast model

The detectability of lesions in radiographic images can be impaired by patterns caused by the surrounding anatomic structures. The presence of such patterns is often referred to as anatomic noise. Others have previously extended signal and noise propagation theory to include variable background structure as an additional noise term and used in simulations for analysis by human and ideal observers. Here, the analytic forms of the signal and noise transfer are derived to obtain an exact expression for any input random distribution and the "power law" filter used to generate the texture of the tissue distribution.

A cascaded analysis of propagation through a heterogeneous model is derived for x-ray projection through simulated heterogeneous backgrounds. This is achieved by considering transmission through the breast as a correlated amplification point process. The analytic forms of the cascaded analysis were compared to monoenergetic Monte Carlo simulations of x-ray propagation through power law structured backgrounds.

As expected, it was found that although the quantum noise power component scales linearly with the x-ray signal, the anatomic noise will scale with the square of the x-ray signal. There was a good agreement between results obtained using analytic expressions for the noise power and those from Monte Carlo simulations for different background textures, random input functions, and x-ray fluence.

Analytic equations for the signal and noise properties of heterogeneous backgrounds were derived. These may be used in direct analysis or as a tool to validate simulations in evaluating detectability.