Reconstruction of MR images from data acquired on an arbitrary k‐space trajectory using the same‐image weight

Abstract

A sampling density compensation function denoted "same-image (SI) weight" is proposed to reconstruct MR images from the data acquired on an arbitrary k-space trajectory. An equation for the SI weight is established on the SI criterion and an iterative scheme is developed to find the weight. The SI weight is then used to reconstruct images from the data calculated on a random trajectory in a numerical phantom case and from the data acquired on interleaved spirals in an in vivo experiment, respectively. In addition

Basis function cross‐correlations for Robust k‐space sample density compensation, with application to the design of radiofrequency excitations

“…Consider, for example, an unsuccessful attempt that has been previously described to reduce the computational burden by limiting the number of neighboring samples considered when computing the weight of each sample (8). In that particular case, 21 samples surrounding that whose weight was being computed were used, while the failure of this approach was attributed to an unknown reason.…”

“…For comparison, all experiments and simulations were also performed for excitations compensated using weights computed from the Voronoi tessellation density method (6) and the Same-Image method (8). As described in (8), application of this method to spirals benefits from a good initial solution and regularization parameter that reduces toward the center of the trajectory.…”

“…Voronoi weights were thus used to achieve similar results. Furthermore, an error tolerance of 0.05 and a step size of 0.5 were used (8). Finally, a derivative limitation was implemented within the Same-Image iteration in order to avoid discontinuities and reduce the maximum B 1 amplitude required by the resulting waveforms.…”

“…Numerical density compensation approaches have concentrated primarily on molding the point spread function (PSF) achieved by the trajectory, in order to satisfy some desired identity constraint (7,8). This is closely related to regridding fast Fourier transform (FFT) image reconstruction (3,9), essentially requiring that the image reconstructed from the weighted and regridded nonuniform samples be the same as one reconstructed from data acquired on a Cartesian grid.…”

“…Advances in hardware and trajectory optimization (22)(23)(24) will continue to increase the complexity of the density compensation problem, where heuristic and analytic solutions may not apply. In this case few numerical methods can be applied (7,8), and even fewer apply specifically to the problem of RF excitation (25). Furthermore, iteration is typically required to converge to a solution.…”