Polyhedral Phantom Framework with Analytical Fourier Transform with Intensity Gradients

Analytical phantoms with closed form solutions for their Fourier Transforms (FT) enable accurate and arbitrary sampling of k-space. Though most phantoms are limited to simple shapes such as rectangles or ellipsoids, we have recently presented an expression for the 3D FT of a polyhedron of uniform intensity. This work provides the mathematical framework that extends the original polyhedral FT to account for linear gradients in intensity. A computationally efficient implementation is demonstrated.

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