An MRI imaging sequence based on reconstruction by orthogonal polynomials

This MRI sequence is based on a spin echo radial sequence. The radial gradient is an arcsine shape rather than a linear gradient. The resulting phase evolution leads to a nonlinear Fourier transform of the magnetic dipole density. Elementary signal processing operations on the FID signal result in input to the circular harmonic transform reconstruction algorithm based on Zernike polynomial/Chebyshev polynomial orthogonal function pairs. Simulations of the signal processing operations confirm the feasibility of the imaging sequence. Difficulties associated with interpolation and gridding are avoided in the reconstruction process. An existing CHT reconstruction algorithm allows for the direct reconstruction of radial sequence data. This algorithm has proven robustness and has lower computational complexity than filtered backprojection. Concerns about the unstable nature of the exterior CHT transform have proven to be groundless. There are other practical concerns about the implementation of the imaging sequence. The fast rise of the gradient at the edge of the field of view makes it difficult to implement, more so than linear gradients. So there is no practical application at present.