Abstract
Image restoration is a research field that attempts to recover a blurred and noisy image. Although we have one-step algorithms that are often fast for image restoration, iterative formulations allow a better control of the trade-off between the enhancement of high frequencies (image details) and noise amplification. Projections onto convex sets (POCS) is an iterative—and parametric-based approach that employs a priori knowledge about the blurred image to guide the restoration process, with promising results in different application domains. However, a proper choice of its parameters is a high computational burden task, since they are continuous-valued and there are an infinity of possible values to be checked. In this paper, we propose to optimize POCS parameters by means of harmony search-based techniques, since they provide elegant and simple formulations for optimization problems. The proposed approach has been validated in synthetic and real images, being able to select suitable parameters in a reasonable amount of time.
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Notes
Image restoration and reconstruction attempt at the same purpose, they are just used under different names depending on the field of knowledge.
Under-projections refer to RAP constrained to \(\lambda < 1\), and over-projections refer to RAP constrained to \(\lambda > 1\).
The better is the quality of the restored image \({\hat{f}}\), we have that \(({\hat{f}}-f)^2\rightarrow 0\). Thus, \(\frac{(g-f)^2}{({\hat{f}}-f)^2}\rightarrow \infty \), which means that high ISNR values stand for better restored images.
The original (uncorrupted) image that has been degraded is the so-called “phantom image”.
We have used 60 agents and 30 iterations for both BHA and HS techniques.
The search range for \(\lambda \) was executed within [0, 2] with steps of 0.05, and the search range of K was executed within the range [1, 20] with steps of 1. This means we have 800 evaluations of the fitness function considering the near-exhaustive search. Although one could meta-optimize the step of grid-search, we do not recommend that, since it might be too costly.
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Acknowledgments
The authors would like to thank Capes and FAPESP Grants #2009/16206-1, #2011/14094-1, #2013/20387-7 and #2014/16250-9, as well as CNPq Grants #303182/2011-3, #470571/2013-6 and #306166/2014-3.
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Pires, R.G., Pereira, D.R., Pereira, L.A.M. et al. Projections onto convex sets parameter estimation through harmony search and its application for image restoration. Nat Comput 15, 493–502 (2016). https://doi.org/10.1007/s11047-015-9507-4
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DOI: https://doi.org/10.1007/s11047-015-9507-4