Abstract
Minimum Entropy Deconvolution (MED) is a sparse blind deconvolution method that searches for a deconvolution filter that leads to the most sparse output, assuming that the desired signal is originally sparse. The present work establishes sufficient conditions for the blind deconvolution of sparse images. Then, based on a measure of sparsity given by the ratio of \(L_p\)-norms, we derive a gradient based algorithm for the blind deconvolution of bi-level images, more specifically, for the blind deconvolution of blurred QR Codes. Finally, simulation results are presented considering both synthetic and real data and shows the possibility of achieving really good results by the light of a very simple algorithm.
The authors would like to thanks to CAPES, CNPq and FAPESP (process number 2015/07048-4) for the financial support.
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Notes
- 1.
For simplicity, we derive the algorithm for \(p \in [1,2[\) only. The difference is that, for \(q \in ]2,\infty [\), we obtain a maximization problem.
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Nose-Filho, K., Takahata, A.K., Suyama, R., Lopes, R., Romano, J.M.T. (2017). On Minimum Entropy Deconvolution of Bi-level Images. In: Tichavský, P., Babaie-Zadeh, M., Michel, O., Thirion-Moreau, N. (eds) Latent Variable Analysis and Signal Separation. LVA/ICA 2017. Lecture Notes in Computer Science(), vol 10169. Springer, Cham. https://doi.org/10.1007/978-3-319-53547-0_46
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