All Roads Lead To Rome
نویسنده
چکیده
Legendary mathematician Paul Erdos liked to talk about the perfect proofs of mathematical theorems maintained by God. In [1], six different proofs are given to the infinity of prime numbers. Unlike mathematical proofs which are mentally reproducible objects, signal processing researchers can have an intimate discussion with God by creating computational algorithms which are experimentally reproducible objects. This article presents a class of projectionbased solution algorithms to the problem considered in the pioneering work on compressed sensing [2] perfect reconstruction of a phantom image from 22 radial lines in the frequency domain. Under the framework of projectionbased image reconstruction, we will show experimentally that several old and new tools of nonlinear filtering all lead to perfect reconstruction of the phantom image, which suggests that the result achieved by l1-optimization is less like magic.
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عنوان ژورنال:
- CoRR
دوره abs/1103.1587 شماره
صفحات -
تاریخ انتشار 2011