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Published June 15, 2016 | metadata_only
Journal Article

Discrete Laguerre Gaussian Transforms and Their Applications


Laguerre Gaussian functions serve as a complete and orthonormal basis for a variety of physical problems, such as 2D isotropic quantum harmonic oscillators and circularly symmetric laser modes. In this paper, we propose "discrete Laguerre Gaussian functions," which are defined such that some elegant physical properties are preserved and a fast computation algorithm of complexity O(N logN) is available. Discrete Laguerre Gaussian transforms, as introduced in this paper, inherit nice properties from discrete Laguerre Gaussian functions and admit signal analysis over circularly symmetric patterns. It is demonstrated through examples that discrete Laguerre Gaussian transforms find applications in circular pattern keypoints selection, object detection, image compression, rotational invariance feature for pattern recognition, and rotational angle estimation.

Additional Information

© 2016 IEEE. Manuscript received December 29, 2013; revised May 09, 2015; accepted February 13, 2016. Date of publication March 02, 2016; date of current version April 21, 2016. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Pina Marziliano. This work was supported by the Ministry of Science and Technology, Taiwan, under Contract 103-2221-E-002-102.

Additional details

September 15, 2023
September 15, 2023