Radon Inversion Reconstruction for Kooshball-Like Sampling Trajectory in Cine

In cine MRI, data is often sparse and noisy. To enhance the signal-to-noise ratio (SNR), a reconstruction algorithm that avoids data gridding is beneficial. Currently the state-of-the-art image reconstruction for non-Cartesian grid sampling is the non-uniform fast Fourier transform (NuFFT) method that involves interpolating sampled values to Cartesian grid points. We propose a revised 3D Radon inversion formula to directly reconstruct images without gridding. Our method involves performing a 1D inverse Fourier transform along each radial trajectory of the koosh-ball ray, followed by a 1D Laplacian filter. The proposed 3D Radon backprojection is rotation based. The primary benefit of the proposed method compared to the NuFFT method is its higher signal-to-noise ratio and lower mean squared error. Additionally, the proposed method allows for the 1D inverse Fourier transform, Laplacian filtration, and backprojection to be performed immediately after each spoke is acquired. In contrast, gridding can only be performed once all spokes have been acquired.