Radon Inversion Reconstruction for Kooshball-Like Sampling Trajectory in Cine

Area of Science:

• Medical Imaging
• Image Reconstruction
• Magnetic Resonance Imaging (MRI)

Background:

• Cine MRI data is often sparse and noisy, impacting image quality.
• Current state-of-the-art reconstruction for non-Cartesian sampling, the non-uniform fast Fourier transform (NuFFT), requires data gridding.
• Gridding interpolates data to Cartesian points, which can be time-consuming and limit real-time processing.

Purpose of the Study:

• To develop a novel image reconstruction algorithm for cine MRI that avoids data gridding.
• To enhance the signal-to-noise ratio (SNR) and reduce mean squared error in reconstructed images.
• To enable faster, potentially real-time, image reconstruction by processing data as it is acquired.

Main Methods:

• A revised 3D Radon inversion formula is proposed for direct image reconstruction without gridding.
• The method involves a 1D inverse Fourier transform along radial trajectories (koosh-ball rays).
• A 1D Laplacian filter is applied, followed by rotation-based 3D Radon backprojection.

Main Results:

• The proposed 3D Radon inversion method achieves a higher signal-to-noise ratio (SNR) compared to the NuFFT method.
• The new method demonstrates a lower mean squared error (MSE) in reconstructed images.
• Reconstruction steps (1D inverse Fourier transform, Laplacian filtration, backprojection) can be performed immediately after each radial spoke acquisition.

Conclusions:

• The proposed 3D Radon inversion technique offers a significant improvement over the NuFFT method for cine MRI reconstruction.
• Its ability to reconstruct images without gridding and process data incrementally allows for enhanced SNR, reduced MSE, and faster reconstruction.
• This method holds potential for real-time cine MRI applications due to its efficiency and improved image quality.