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 Carm 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.

Fast Signal Recovery From Saturated Measurements by Linear Loss and Nonconvex Penalties

“…The key difference between this model and the model in [12] is the use of linear loss. Thus we call (1) as mixed one-bit CS with linear loss (M1bit-CS-L).…”

“…α := α + ρ(x − z) 6: until the stopping criteria is satisfied ADMM is also applied in [11] and [12] for RDCS and M1bit-CS, respectively, but since the corresponding subproblems with both hard constraints and hinge losses do not have analytical updates, the algorithm for M1bit-CS-L, even with non-convex penalties, is much faster than both RDCS and M1bit-CS.…”

“…However, the traditional CS is not applicable to deal with saturation. Two methods for saturation in CS are saturation rejection [8,9] and saturation consistency [10][11][12][13][14]. Saturation rejection drops the saturated part and thus may lead to insufficient measurements and poor results.…”

“…Therefore, RDCS is not robust to sign flips. Instead of constraints, the hinge loss function is used in mixed one-bit compressive sensing (M1bit-CS) [12] to encourage the saturation consistency, and the method is robust to noise. However, the algorithms for both RDCS and M1bit-CS are slow and not applicable to large-scale problems, due to the use of hard constraints or the hinge loss.…”