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H2020

DEDALE Report Summary

Project ID: 665044
Funded under: H2020-EU.1.2.1.

Periodic Reporting for period 1 - DEDALE (Data Learning on Manifolds and Future Challenges)

Reporting period: 2015-10-01 to 2016-09-30

Summary of the context and overall objectives of the project

The goals of the DEDALE project is to introduce new models and methods to analyze and restore complex, multivariate, manifold-based signals; ii) exploit the current knowledge in optimization and operations research to build efficient numerical data processing algorithms in the large-scale settings; and iii) show the reliability of the proposed data modeling and analysis technologies to tackle Scientific Big Data challenges in two different applications: one in cosmology, to map the dark matter mass map of the universe, and one in remote sensing to increase the capabilities of automatic airborne imaging analysis systems.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

WP 1: Project Management
The Consortium Agreement has been signed by all partners.
We realized during the KoM that some of the requests asked by the first P.O. of DEDALE, related to the deadline of some deliveries, introduce some inconsistencies in the starting date of few tasks. Having earlier deadlines implies that some WP should also start earlier. This should however not be problem.
A typo has been signaled in the deliveries D3.1 related to the task 3.1 of WP 3. Indeed, it should be “LineThe Consortium Agreement has been signed by all partners.
ar inverse problems with sparsity contraints” and not “Non linear inverse ….”

Three documents have been delivered, the DEDALE Management plan document, the DEDALE Risk assessment document, and the dissemination plan document.
A web site has been created, http://dedale.cosmostat.org, which contains a private area (user: dedale pwd: minautor.2015) where the internal documents are stored. The three documents are available on the website.
Four technical documents have also been delivered.
Regarding the Open Access issue: we plan to put all our manuscripts on ArXiv, in parallel to the submission to journals.

The Kick-off-Meeting took place in Paris, on October 22-23. The second meeting took place on April 18-19 2016 at TUB in Berlin.
The agenda, all presentations and the minutes are available on the web site.

Joanna Maria Frontera, has been hired on Oct 1st by CEA, as a postdoc, to work on WP2.
Samuel Farrens has been hired on Oct 1st by CEA, as a postdoc, to work on WP5.
Michael Röse has been hired on Jan 1st by TUB, as a PhD student, to work on WP2.

WP 2: Low-Dimensional Models for Complex Structured Data
Task 2.1: Adaptive multiscale transforms for manifold-valued data:
In this task we aim to analyze sparse approximation properties of adapted shearlet systems gained via (structured) dictionary learning for vector-valued and spherical data.
More precisely, we strive to extend the present shearlet transform by introducing flexible parameters (providing for instance a flexible choice regarding scaling, translation and generators) which are then determined through learning strategies for specific model situations maintaining the structure of the shearlet system.
Building on the shearlet transform for vector-valued data we implemented alpha-shearlets (both for compactly supported and for bandlimited elements) which exhibit different scaling matrices in the construction depending on the chosen parameter alpha. In the next steps we want to apply the concept of dictionary learning to those alpha-shearlets followed by an in-depth investigation of the reconstruction error for typical applications such as compression, denoising and inpainting.
Task 2.2 Dictionary Learning for Multivariate / Multispectral Data:
This tasks consists in extending dictionary learning techniques to the case of multivariate manifold-valued data, based on structured sparsity, low rank constraints and source separation. Application to polarized data on the sphere will be considered as a test application.
So far, an inpainting algorithm for large-scale polarized data on the sphere has been developed, resulting in an improved polarized E map due to a smaller T mask and cross-correlations in the TE power spectrum. A source separation technique on the sphere based on sparsity (coined L-GMCA) has also been employed for Planck 2015 data and WMAP9 data to provide a full-sky map with very low foreground contamination even in the galactic center, and no thermal SZ contamination. The paper has been submitted for publication.
In parallel, a study on the possible extensions of dictionary learning techniques to color images has started, comparing learning a dictionary for RGB color images using either vectorized patches or separating the color components.
Task 2.3: Non-linear learning on complex imaging data
In this task, effort was put in the investigation of deep learning for image enhancement problems. We consider two exemplary architectures, convolutional sparse coding and sparse autoencoders. The problem was modeled through an innovative low-dimensional learning framework where instead of feature engineering, we considered feature learning via deep sparse autoencoders. The learned features were subsequently used in a coupled sparse dictionary learning method for estimating an extended dynamic range sequence of a scene.
We considered the problem of dynamic range extension, a problem also known as High Dynamic Range (HDR) imaging, where the objective is to increase the range between the maximum and minimum values in an image. As an end goal, we aim at developing a method that will consider as an input a single or a small number of images of low dynamic range and extract a sequence of images that cover a much larger dynamic range. These images can then be combined to an optimal exposure revealing the full content of information encoded in the image.

WP 3: Signal Processing on Complex Data
This work-package consists in proposing algorithms to solve inverse problems using sparse priors based either on linear representation such as described in WP 2 (task 3.1) or non-linear (task 3.2) signal representations, and evaluating them by building a numerical toolbox with benchmark tests (task 3.3).

Task 3.1: Linear inverse problems with sparsity constraints this task starts at M6.

Activity has already started with a simple example of denoising a sparse signal sparse in a multiscale representation of S1^N (build on previous works [Ur-Rahman (2005)], [Starck 2009]), contaminated by Gaussian noise in R^2N. For the cost function, we used a sparse prior, a constraint on S1^N and a quadratic constraint set according to the statistics of the noise.
We investigated the use of a proximal algorithm in this non-convex setting: we employed a nested Douglas-Rachford algorithm to solve this inverse problem composed of two non-smooth terms (here sparse prior on one side, and sum of quadratic constraint and sought-after signal in S1^N on the other side). This algorithm was shown recently to give interesting local convergence results even in non-convex scenarii [Borwein 2011, Hesse2014]. We have experimented that provided some hyper-parameters are set in a range of values, the algorithm converges to a sparse signal respecting the constraints and give good denoising results. The next steps involve investigating parameters affecting the speed of convergence, additional checks on the local convergence of the algorithm, and adding an extra degradation operator to solve an inverse problem (starting with inpainting).

In addition, we considered the problem of high-spectral resolution imaging, aiming to provide critical information enabling a better identification and characterization of the objects in a scene of interest. Multiple factors may impair spectral resolution, as in the case of modern snapshot spectral imagers that associate each “hyperpixel” with a specific spectral band. We propose a novel post-acquisition computational technique aiming to enhance the spectral dimensionality of imaging systems by exploiting the mathematical frameworks of Sparse Representations and Dictionary Learning.
The key contribution of this effort is a novel Coupled Sparse Dictionary Learning model which considers coupled feature spaces, composed of low and high spectral resolution hypercubes. In order to address the spectral super-resolution problem, we formulated our spectral coupled dictionary learning technique within the context of the Alternating Direction Method of Multipliers, optimizing each variable via closed-form expressions. Experimental results demonstrate the ability of the proposed approach to synthesize high-spectral resolution three-dimensional hypercubes, achieving better performance compared to state-of-the-art resolution enhancement methods.

WP 4: Signal Processing on Complex Data
Activities in WP4 started with examining state of the art tools for distributed learning over large-scale datasets (Task 4.2, M1-M12).
We performed a bibliography search on current state of the art for distributed computing methods, examining aspects related to their suitability to handle iterative computations, which are essential for solving optimization and learning problems. Our study concluded that the Apache Spark framework is the optimal solution, and based on our findings we designed and developed the DEDALE Distributed Learning Platform, which capable of considering both physical as well as virtual (i.e., in the form of cloud computing) resources.
We explored how the characteristics of different scenarios can be utilized for the efficient parallelization of the learning problem at hand. Two use cases are examined, namely: (a) the super-resolution of a stream of sub-sampled hyper-spectral data, using the Sparse Coupled Dictionary Learning Technique, (b) the removal of PSF distortion from noisy galaxy images using a sparsity prior regularization process. The benchmark studies indicated improvement of ~60% in time response terms against the conventional computing solutions.
To the best of our knowledge, this work is the first attempt to address complex application scenarios from the Remote Sensing and Astrophysics application domains with the Apache Spark framework and we plan to submit the results of this work to a system’s perspective journal highlighting the cross-disciplinary interaction and the insights into the computational trade-offs and the limitations of Spark are extracted.

WP5: Applications on the Euclid Mission
A study is ongoing to evaluate how dictionary learning could be useful for spectroscopic redshift estimation.
A method has been developed to build superresolved Euclid PSF from a set of subsampled PSF.
A mass mapping reconstruction method has been developed which use sparse regularization. A paper has been published.
A new deconvolution algorithm has been developed for big survey images in astrophysics, which used low rank minimization techniques. A paper is submitted.
Optimal transport has been investigated for PSF interpolation. A paper has been submitted.

Dr Bruno Moreas (male), PostDoc was appointed by UCL in June 2016 to work on WP5.
Mr Niall Jeffrey (male), a PhD Research Student at UCL, had worked on WP5 full-time since the start of the project, i.e. October 2015.

WP6: Applications in Remote Sensing
This WP starts at M18.

WP 7: Dissemination and Exploitation
A professional looking website has been developed and is now active. It contains various resources that should help all of the DEDALE members keep track of the project progress and events.
A social media account has been activited.
A dissemination and data management plan documents have been submitted and approved.
A workshop has been organized (web site, management, etc).
A video has been made and is available on the DEDALE web site.
A tutorial day has been organized.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

"- A new video sequence enhancement method( see FIg 1)
K. Fotiadou, G. Tsagkatakis, and P. Tsakalides, "Spectral Resolution Enhancement of Hyperspectral Images via Sparse Representations", in Proc. 2016 IS&T International Symposium on Electronic Imaging, Computational Imaging, San Francisco, CA, February 15-19, 2016.

K. Fotiadou, G. Tsagkatakis, and P. Tsakalides. “Spectral super-resolution via coupled sparse dictionary learning.” submitted to IEEE Transactions on Computational Imaging, Special issue on Computational Imaging for Earth Sciences, 2016.

- The most accurate estimate of the cosmic microwave background from most recent available data set (WMAP-9yr and Planck-PR2), see Fig. 2
J. Bobin, F. Sureau, J-L Starck, CMB reconstruction from the WMAP and Planck PR2 data, submitted to Astronomy and Astrophysics."

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