SHAPE BASED IMAGE RECONSTRUCTION USING LINEARIZED DEFORMATIONS.

Area of Science:

• Medical Imaging
• Computational Imaging
• Applied Mathematics

Background:

• Ill-posed linear inverse problems are common in medical imaging.
• Reconstructing images from limited or sparse measurements remains a significant challenge.
• Incorporating prior information can improve the accuracy of image reconstruction.

Purpose of the Study:

• To develop a novel reconstruction framework for ill-posed linear inverse problems in imaging.
• To integrate shape-related a priori information into the reconstruction process.
• To demonstrate the framework's efficacy using 2D tomography with sparse measurements.

Main Methods:

• A variational scheme is employed for image reconstruction.
• A shape functional is defined using deformable templates from shape theory.
• The framework is applied to 2D tomography with very sparse measurement data.

Main Results:

• The proposed shape-based reconstruction framework demonstrates strong empirical results.
• Effective incorporation of shape prior information leads to improved reconstructions.
• The method shows promise for handling severely underdetermined inverse problems.

Conclusions:

• The developed framework offers a powerful approach for image reconstruction in scenarios with limited data.
• Shape-based priors can significantly enhance the quality of reconstructed images.
• This method has potential applications in various medical imaging modalities requiring robust reconstruction.