A low-complexity 2-point step size gradient projection method with selective function evaluations for smoothed total...

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Total Variation (TV) based Cone Beam CT (CBCT) reconstruction methods are gaining attention.
• The Barzilai-Borwein (BB) 2-point step size gradient method accelerates these reconstructions.
• Ensuring convergence properties is crucial for clinical viability.

Purpose of the Study:

• To propose a novel, fast-converging gradient projection BB method for CBCT reconstruction.
• To address the convergence property limitations of existing BB methods.
• To develop a computationally efficient algorithm for high-quality 3D CBCT image reconstruction.

Main Methods:

• Introduced a Selective Function Evaluation (GPBB-SFE) method for gradient projection BB.
• Combined GPBB-SFE with smoothed TV or other differentiable priors for guaranteed convergence.
• Implemented the algorithm on an NVIDIA GTX 480 GPU for accelerated reconstruction.
• Compared GPBB-SFE with existing BB-based methods using numerical and physical phantoms, and a clinical patient dataset.

Main Results:

• GPBB-SFE demonstrated faster convergence speed/time and superior convergence properties compared to existing BB-based algorithms.
• Reconstructed a CatPhan 600 physical phantom image with FDK quality using only 60 projections (3 function evaluations in 30 iterations).
• Achieved visibly equivalent CBCT image quality for a head-and-neck patient using 180 projections (18 function evaluations in 30 iterations) compared to FDK with 364 projections.

Conclusions:

• The proposed GPBB-SFE algorithm offers fast and guaranteed convergence for 3D CBCT image reconstruction with minimal computational complexity.
• GPBB-SFE significantly reduces the number of projections required while maintaining image quality.
• The method shows strong potential for clinical applicability in CBCT imaging.