Computational Methods for Inverse Problems
Computational Methods for Inverse Problems
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Magnetic Particle Imaging is an emerging reconstructive imaging method that can create images of the spatial distribution of magnetizable nanoparticles in an object. A magnetic particle image is reconstructed by solving a discrete approximation to a linear integral equation that models the data acquisition. So far, an explicit formula for the kernel of this integral equation has been missing, forcing one to determine the matrix of the linear equation to be solved by time consuming measurements. Also, this matrix is huge and dense so that the reconstruction times tend to be long. Here, we present an explicit formula for the kernel of the modeling integral operator, transform this operator into a spatial convolution operator, and point out fast reconstruction algorithms that make use of Nonuniform Fast Fourier Transforms.