Abstract
An approach is presented that provides a justification for the use of the discrete Fourier transform in magnetic resonance (MR) image reconstruction. Without a priori knowledge of the Fourier transform, an imaging experiment is described that corresponds to the common spatial encoding process by means of magnetic field gradients. A regular matrix, the so‐called encoding matrix, describing a linear system of equations is obtained. The presented approach consists of numerical optimization of the encoding matrix by minimizing its condition number. To accomplish this, the necessary concepts of numerical analysis are thoroughly introduced, which reflects the educational character of the manuscript. As a result, we will see that a numerically optimized encoding matrix is equal to the discrete Fourier transform matrix; thus, an explanation for the use of the discrete Fourier transform in MR image reconstruction is obtained.