Convolutional sparse representations and convolutional dictionary learning are mathematical models
that consist in representing a whole signal or image as a sum of convolutions between dictionary filters
and coefficient maps. Unlike the patch-based counterparts, these convolutional forms are receiving
an increase attention in multiple image processing tasks, since they do not present the usual patchwise
drawbacks such as redundancy, multi-evaluations and non-translational invariant. Particularly, the
convolutional dictionary learning (CDL) problem is addressed as an alternating minimization between
coefficient update and dictionary update stages. A wide number of different algorithms based on FISTA
(Fast Iterative Shrinkage-Thresholding Algorithm), ADMM (Alternating Direction Method of Multipliers)
and ADMM consensus frameworks have been proposed to efficiently solve the most expensive
steps of the CDL problem in the frequency domain. However, the use of the existing methods on large
sets of images is computationally restricted by the dictionary update stage.
The present thesis report is strategically organized in three parts. On the first part, we introduce
the general topic of the CDL problem and the state-of-the-art methods used to deal with each stage.
On the second part, we propose our first computationally efficient method to solve the entire CDL
problem using the Accelerated Proximal Gradient (APG) framework in both updates. Additionally, a
novel update model reminiscent of the Block Gauss-Seidel (BGS) method is incorporated to reduce the
number of estimated components during the coefficient update. On the final part, we propose another
alternative method to address the dictionary update stage based on APG consensus approach. This last
method considers particular strategies of theADMMconsensus and our first APG framework to develop
a less complex solution decoupled across the training images. In general, due to the lower number of
operations, our first approach is a better serial option while our last approach has as advantage its
independent and highly parallelizable structure.
Finally, in our first set of experimental results, which is composed of serial implementations, we
show that our first APG approach provides significant speedup with respect to the standard methods by a
factor of 1:6 5:3. A complementary improvement by a factor of 2 is achieved by using the reminiscent
BGS model. On the other hand, we also report that the second APG approach is the fastest method
compared to the state-of-the-art consensus algorithm implemented in serial and parallel. Both proposed
methods maintain comparable performance as the other ones in terms of reconstruction metrics, such
as PSNR, SSIM and sparsity, in denoising and inpainting tasks. / Tesis
| Identifer | oai:union.ndltd.org:PUCP/oai:tesis.pucp.edu.pe:20.500.12404/13903 |
| Date | 05 April 2019 |
| Creators | Silva Obregón, Gustavo Manuel |
| Contributors | Rodríguez Valderrama, Paul Antonio |
| Publisher | Pontificia Universidad Católica del Perú, PE |
| Source Sets | Pontificia Universidad Católica del Perú |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Format | application/pdf |
| Rights | Atribución 2.5 Perú, info:eu-repo/semantics/openAccess, http://creativecommons.org/licenses/by/2.5/pe/ |
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