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Title: On the continuity of images by transmission imaging
Authors: Wu, C. 
Keywords: Continuity
Measure zero
Parallel line geometry
Poisson noise
Radial function
Radon transform
Reflection imaging
Transmission imaging
Variational method
Issue Date: 2013
Abstract: Transmission imaging is an important imaging technique which is widely used in astronomy, medical diagnosis, and biology science, whose imaging principle is quite different from that of reflection imaging used in our everyday life. Images by reflection imaging are usually modeled as discontinuous functions and even piecewise constant functions in most cases. This discontinuity property is the basis for many successful image processing techniques such as the popular total variation (TV) regularization. In this paper we prove that almost all images by transmission imaging are continuous functions. For the convenience of description, we will consider transmission imaging with parallel line geometry of wave beam, which is a fundamental geometry in transmission imaging and has been extensively applied in microscopes. In this kind of imaging, people take images of the physical scene from many different projection directions. We will prove that for almost every projection direction, the generated image is a continuous function, even if the density function of the physical scene is discontinuous. If the density functions of the objects to be imaged are radial regardless of some coordinate shifts, then all the projection directions generate continuous images. This continuity property has not been published yet in the literature. As a straightforward application, we finally present a simple yet effective improvement of TV regularization for Poisson noise (which is the most significant noise in transmission imaging) removal. Numerical examples and comparisons verify our analysis and demonstrate the effectiveness of the improved model. © 2013 International Press.
Source Title: Communications in Mathematical Sciences
ISSN: 15396746
Appears in Collections:Staff Publications

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