A new look at signal sparsity paradigm for low-dose computed tomography image reconstruction

Signal sparsity in computed tomography (CT) image reconstruction field is routinely interpreted as sparse angular sampling around the patient body whose image is to be reconstructed. For CT clinical applications, while the normal tissues may be known and treated as sparse signals but the abnormalities inside the body are usually unknown signals and may not be treated as sparse signals. Furthermore, the locations and structures of abnormalities are also usually unknown, and this uncertainty adds in more challenges in interpreting signal sparsity for clinical applications. In this exploratory experimental study, we assume that once the projection data around the continuous body are discretized regardless at what sampling rate, the image reconstruction of the continuous body from the discretized data becomes a signal sparse problem. We hypothesize that a dense prior model describing the continuous body is a desirable choice for achieving an optimal solution for a given clinical task. We tested this hypothesis by adapting total variation stroke (TVS) model to describe the continuous body signals and showing the gain over the classic filtered backprojection (FBP) at a wide range of angular sampling rate. For the given clinical task of detecting lung nodules of size 5mm and larger, a consistent improvement of TVS over FBP on nodule detection was observed by an experienced radiologists from low sample rate to high sampling rate. This experimental outcome concurs with the expectation of the TVS model. Further investigation for theoretical insights and task-dependent evaluations is needed.