Recently, there is some interest in the application of set-theoretic methods to the solution of the image recovery problem in electron microscopy. Several current studies have reported promising results.The purpose of this paper is to introduce set-theoretic methods to the electron microscopy community.In electron microscopy, the image recovery problem refers to obtaining an estimate of the ideal three-dimensional (3-D) image distribution from its incomplete and possibly noisy Fourier transform data.In the spatial domain, the recovery problem is stated on the basis of the observation equation:where vectors g, f and n ∈ RN denote the lexicographical ordering of the (N-voxel) measured (degraded) image distribution, the ideal image distribution and the noise processes, respectively. The operator D : RN → RN denotes the degradation operator that effectively limits the data to the “data cone” in the frequency domain. The degradation operator can be adequately modeled by a space-invariant (convolutional) operator, and therefore D has a block-Toeplitz structure.
Tensor Decompositions for Signal Processing Applications: From two-way to multiway component analysis
