[Paper Review] Mixed one-bit compressive sensing with applications to overexposure correction for CT reconstruction

Xiaolin Huang, Yan Xia+5 more|arXiv (Cornell University)|Jan 3, 2017

Sparse and Compressive Sensing Techniques31 references3 citations

TL;DR

This paper proposes mixed one-bit compressive sensing (M1bit-CS) to correct overexposure artifacts in C-arm CT by leveraging both regular and saturated projection measurements. Using an ADMM-based optimization and iterative saturation detection, M1bit-CS achieves reconstruction accuracy close to ideal recovery even under severe saturation, significantly reducing streaking and capping artifacts compared to existing methods.

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.

Motivation & Objective

• To address overexposure in C-arm CT caused by limited detector dynamic range, especially in thin body parts like the knee.
• To recover high-quality CT images when some projections are saturated due to overexposure.
• To develop a method that effectively utilizes information from saturated measurements, which are typically discarded or poorly handled in classical reconstruction.
• To improve reconstruction accuracy over existing extrapolation and iterative detection methods by incorporating one-bit compressive sensing principles.

Proposed method

• Proposes a mixed one-bit compressive sensing (M1bit-CS) model that treats both regular and saturated measurements as part of a unified recovery framework.
• Uses alternating direction method of multipliers (ADMM) to solve the non-convex optimization problem in M1bit-CS.
• Develops an iterative saturation detection (ISD) scheme to estimate the saturation indicator matrix Ψ from the data, enabling accurate identification of overexposed projections.
• Integrates prior knowledge about tissue structure to improve initial guesses for saturation detection and reconstruction.
• Applies the M1bit-CS model to both synthetic and clinical CT data, using filtered back projection (FBP) and SART as baseline reconstruction methods.
• Employs a sign-based observation model for saturated measurements, treating them as one-bit data to preserve useful structural information.

Experimental results

Research questions

• RQ1 Can saturated CT projections, traditionally discarded or poorly handled, carry useful information for image reconstruction?
• RQ2 How can one-bit compressive sensing principles be extended to handle mixed measurements including both regular and saturated observations?
• RQ3 Can an iterative saturation detection method reliably identify overexposed regions in projection data without prior knowledge of the true saturation pattern?
• RQ4 To what extent does M1bit-CS improve reconstruction quality compared to classical FBP and SART with extrapolation or detection schemes?
• RQ5 How robust is M1bit-CS to inaccuracies in saturation detection, and how close is its performance to an ideal saturation indicator?

Key findings

• On the knee phantom with κ=0.5p_max, M1bit-CSR-ISD achieved a root mean square error (RMSE) of 8.547 HU, significantly lower than FBP (182.4 HU) and SART-ISD (54.91 HU).
• For the head phantom with κ=0.6p_max, M1bit-CSR-ISD achieved an RMSE of 11.62 HU, outperforming FBP-WCE (35.34 HU) and SART-ISD (31.97 HU).
• Under severe saturation (κ=0.4p_max), M1bit-CSR-ISD achieved an RMSE of 14.81 HU, while SART-ISD and FBP-WCE failed to preserve clear outer boundaries.
• The gap between M1bit-CSR-ISD and M1bit-CSR with ideal saturation matrix was small (14.81 HU vs. 12.39 HU), indicating robustness to detection errors.
• The iterative saturation detection (ISD) method correctly identified most saturated regions, with minimal false positives and missing detections, as shown in Fig. 14.
• The proposed method effectively reduced streaking and capping artifacts in both phantom and clinical data, yielding visually and quantitatively superior reconstructions.