Title: Mixed one-bit compressive sensing with applications to overexposure correction for CT reconstruction,
Abstract: When a measurement falls outside the quantization or measurable range, it
becomes saturated and cannot be used in classical reconstruction methods. For
example, in C-arm angiography systems, which provide projection radiography,
fluoroscopy, digital subtraction angiography, and are widely used for medical
diagnoses and interventions, the limited dynamic range of C-arm flat detectors
leads to overexposure in some projections during an acquisition, such as
imaging relatively thin body parts (e.g., the knee). Aiming at overexposure
correction for computed tomography (CT) reconstruction, we in this paper
propose a mixed one-bit compressive sensing (M1bit-CS) to acquire information
from both regular and saturated measurements. This method is inspired by the
recent progress on one-bit compressive sensing, which deals with only sign
observations. Its successful applications imply that information carried by
saturated measurements is useful to improve recovery quality. For the proposed
M1bit-CS model, alternating direction methods of multipliers is developed and
an iterative saturation detection scheme is established. Then we evaluate
M1bit-CS on one-dimensional signal recovery tasks. In some experiments, the
performance of the proposed algorithms on mixed measurements is almost the same
as recovery on unsaturated ones with the same amount of measurements. Finally,
we apply the proposed method to overexposure correction for CT reconstruction
on a phantom and a simulated clinical image. The results are promising, as the
typical streaking artifacts and capping artifacts introduced by saturated
projection data are effectively reduced, yielding significant error reduction
compared with existing algorithms based on extrapolation.