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The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator(More)
Abstract. Dual Gramian analysis is one of the fundamental tools developed in a series of papers [37, 40, 38, 39, 42] for studying frames. Using dual Gramian analysis, the frame operator can be represented as a family of matrices composed of the Fourier transforms of the generators of (generalized) shiftinvariant systems, which allows us to characterize most(More)
In electron microscopy, 3D reconstruction is one key component in many computer-<lb>ized techniques for solving 3D structures of large protein assemblies using electron microscopy images<lb>of particles. Main challenges in 3D reconstruction include very low signal-to-noise ratio and very large<lb>scale of data sets involved in the computation. Motivated by(More)
Transmission imaging, as an important imaging technique widely used in astronomy, medical diagnosis, and biology science, has been shown in [49] quite different from reflection imaging used in our everyday life. Understanding the structures of images (the prior information) is important for designing, testing, and choosing image processing methods, and good(More)
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