A minimum SNR criterion for computed tomography object detection in the projection domain

Background: A common rule of thumb for object detection is the Rose criterion, which states that a signal must be five standard deviations above background to be detectable to a human observer. The validity of the Rose criterion in CT imaging is limited due to the presence of correlated noise. Recent reconstruction and denoising methodologies are also able to restore apparent image quality in very noisy conditions, and the ultimate limits of these methodologies are not yet known. Purpose: To establish a lower bound on the minimum achievable signal-to-noise ratio (SNR) for object detection, below which detection performance is poor regardless of reconstruction or denoising methodology. Methods: We consider a numerical observer that operates on projection data and has perfect knowledge of the background and the objects to be detected, and determine the minimum projection SNR that is necessary to achieve predetermined lesion-level sensitivity and case-level specificity targets. We define a set of discrete signal objects (Formula presented.) that encompasses any lesion of interest and could include lesions of different sizes, shapes, and locations. The task is to determine which object of (Formula presented.) is present, or to state the null hypothesis that no object is present. We constrain each object in (Formula presented.) to have equivalent projection SNR and use Monte Carlo methods to calculate the required projection SNR necessary. Because our calculations are performed in projection space, they impose an upper limit on the performance possible from reconstructed images. We chose (Formula presented.) to be a collection of elliptical or circular low contrast metastases and simulated detection of these objects in a parallel beam system with Gaussian statistics. Unless otherwise stated, we assume a target of 80% lesion-level sensitivity and 80% case-level specificity and a search field of view that is 6 cm by 6 cm by 10 slices. Results: When (Formula presented.) contains only a single object, our problem is equivalent to two-alternative forced choice (2AFC) and the required projection SNR is 1.7. When (Formula presented.) consists of circular 6-mm lesions at different locations in space, the required projection SNR is 5.1. When (Formula presented.) is extended to include ellipses and circles of different sizes, the required projection SNR increases to 5.3. The required SNR increases if the sensitivity target, specificity target, or search field of view increases. Conclusions: Even with perfect knowledge of the background and target objects, the ideal observer still requires an SNR of approximately 5. This is a lower bound on the SNR that would be required in real conditions, where the background and target objects are not known perfectly. Algorithms that denoise lesions with less than 5 projection SNR, regardless of the denoising methodology, are expected to show vanishing effects or false positive lesions.