Estimating the minimum SNR necessary for object detection in the projection domain.

The Rose criterion, stating that an object is detectable if it is five standard deviations above background, has been used as a rule of thumb for decades but its applicability is limited in computed tomography. Recent denoising algorithms, powered by convolutional neural networks, promise to reveal objects that were previously obscured by noise, but any denoising algorithm is fundamentally limited by the statistics of the sinogram. In this work, we estimate the minimum SNR necessary for detecting one of a set of objects in the projection domain. We assume there is a set of objects O for which detection is desired, and we study an ideal observer that sequentially compares each member of O to the null hypothesis. This comparison can be reduced to the classic one-dimensional signal detection problem between two Gaussians with different mean values, and from this we define a quantity, the projection SNR. We use simulations to estimate the minimum projection SNR necessary to achieve a sensitivity of 80% and specificity of 80%. We find that when we model a search task of a circular 6 mm lesion in a region of interest that is 60 mm by 60 mm by 10 slices, the minimum projection SNR is 5.1. This required SNR is reminiscent of the Rose criterion but is derived with entirely different assumptions, including the application of the ideal observer in the projection domain.