Rapid, Embeddable Design Method for Spiral Magnetic Resonance Image Reconstruction Resampling Kernels

After formulating the design problem for Resampling Kernels used in Magnetic Resonance Spiral Image Reconstruction, we show that an iterative Gauss-Seidel-type interior-point optimization method is suitable (fast and light-weight) for embedded uses. In contrast to previous practice, we directly optimize a computationally efficient, piecewise-linear kernel rather than an analytic function (Kaiser-Bessel). We also optimize our kernels for worst-case (infinity-norm) signal aliasing, rather than the usual proxy energy function (2-norm) minimization. In numerical simulations of undesirable near-frequency systematic noise the new kernel significantly outperforms a conventional Kaiser-Bessel-based solution.