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Mathematical Problems in Engineering
Volume 2015, Article ID 414561, 9 pages
Research Article

An Image Filter Based on Shearlet Transformation and Particle Swarm Optimization Algorithm

1Nanjing University of Information Science and Technology, Nanjing 210044, China
2Southeast University, Nanjing 210000, China
3PLA University of Science and Technology, Nanjing 210000, China

Received 26 August 2014; Revised 18 October 2014; Accepted 19 October 2014

Academic Editor: Erik Cuevas

Copyright © 2015 Kai Hu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Digital image is always polluted by noise and made data postprocessing difficult. To remove noise and preserve detail of image as much as possible, this paper proposed image filter algorithm which combined the merits of Shearlet transformation and particle swarm optimization (PSO) algorithm. Firstly, we use classical Shearlet transform to decompose noised image into many subwavelets under multiscale and multiorientation. Secondly, we gave weighted factor to those subwavelets obtained. Then, using classical Shearlet inverse transform, we obtained a composite image which is composed of those weighted subwavelets. After that, we designed fast and rough evaluation method to evaluate noise level of the new image; by using this method as fitness, we adopted PSO to find the optimal weighted factor we added; after lots of iterations, by the optimal factors and Shearlet inverse transform, we got the best denoised image. Experimental results have shown that proposed algorithm eliminates noise effectively and yields good peak signal noise ratio (PSNR).