Generalized gridding reconstruction from nonuniformly sampled data

Hossein Sedarat; Dwight G. Nishimura

doi:10.1117/12.365857

18 October 1999 Generalized gridding reconstruction from nonuniformly sampled data

Hossein Sedarat, Dwight G. Nishimura

Proceedings Volume 3808, Applications of Digital Image Processing XXII; (1999) https://doi.org/10.1117/12.365857
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Gridding reconstruction is a method to derive data on a Cartesian grid from a set of non-uniformly sampled measurements. This method is appreciated for being robust and computationally fast. However, it lacks solid analysis and design tools to quantify or minimize the reconstruction error. Least squares reconstruction, on the other hand, is another method which is optimal in the sense that it minimizes the reconstruction error. This method is computationally intensive and, in many cases, sensitive to measurement noise; hence it is rarely used in practice. Despite the seemingly different approaches of reconstruction, the gridding and least squares reconstruction methods are shown to be closely related. The similarity between these two methods is accentuated when they are properly expressed in a common matrix form. It is shown that the gridding algorithm can be considered an approximation to the least squares method. The optimal gridding parameters are defined as ones yielding the least approximation error. These parameters are calculated by minimizing the norm of an approximation error matrix. This method is used to find the optimal density compensation factors which minimize the weighted approximation error. An iterative method is also proposed for joint optimization of the interpolating kernel and the deapodization function. Some applications in magnetic resonance imaging are presented.

Citation Download Citation

Hossein Sedarat and Dwight G. Nishimura "Generalized gridding reconstruction from nonuniformly sampled data", Proc. SPIE 3808, Applications of Digital Image Processing XXII, (18 October 1999); https://doi.org/10.1117/12.365857

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