A weighted difference of L1 and L2 on the gradient minimization based on alternating direction method for circular...

Area of Science:

• Medical Imaging
• Computational Imaging
• Image Reconstruction

Background:

• Iterative reconstruction algorithms in computed tomography (CT) utilize total variation (TV) regularization for accurate and stable results.
• TV minimization, an L1-norm approach, serves as a convex relaxation for L0 norm, enhancing image sparsity.
• Existing methods face challenges in balancing reconstruction accuracy, computational speed, and sparsity representation.

Purpose of the Study:

• To propose and investigate a novel, fast, and efficient algorithm for CT image reconstruction.
• To introduce a weighted difference of L1 and L2 (L1 - αL2) gradient minimization approach.
• To enhance the description of sparsity in optimization-based reconstruction algorithms compared to traditional TV minimization.

Main Methods:

• Developed a weighted difference of L1 and L2 (L1 - αL2) gradient minimization algorithm.
• Employed the alternating direction method for efficient solution of the proposed optimization model.
• Validated the algorithm using both simulated and real CT projection data.

Main Results:

• The proposed L1 - αL2 algorithm demonstrated superior image quality compared to TV minimization algorithms in simulations.
• Reconstructions achieved with significantly fewer views (7 views in 180 degrees) and reduced iteration numbers.
• The new algorithm exhibited faster computational performance than TV minimization methods.

Conclusions:

• The proposed L1 - αL2 gradient minimization algorithm provides an effective and efficient alternative for CT image reconstruction.
• This method offers improved sparsity description, leading to enhanced image quality and reduced computational cost.
• The algorithm shows promise for low-dose and fast CT imaging applications.