A Hierarchical Bayesian Model for Frame Representation

In many signal processing problems, it may be fruitful to represent the signal under study in a frame. If a probabilistic approach is adopted, it becomes then necessary to estimate the hyper-parameters characterizing the probability distribution of the frame coefficients. This problem is difficult since in general the frame synthesis operator is not bijective. Consequently, the frame coefficients are not directly observable. This paper introduces a hierarchical Bayesian model for frame representation. The posterior distribution of the frame coefficients and model hyper-parameters is derived. Hybrid Markov Chain Monte Carlo algorithms are subsequently proposed to sample from this posterior distribution. The generated samples are then exploited to estimate the hyper-parameters and the frame coefficients of the target signal. Validation experiments show that the proposed algorithms provide an accurate estimation of the frame coefficients and hyper-parameters. Application to practical problems of image denoising show the impact of the resulting Bayesian estimation on the recovered signal quality

A Proximal Approach for a Class of Matrix Optimization Problems

In recent years, there has been a growing interest in mathematical models leading to the minimization, in a symmetric matrix space, of a Bregman divergence coupled with a regularization term. We address problems of this type within a general framework where the regularization term is split in two parts, one being a spectral function while the other is arbitrary. A Douglas-Rachford approach is proposed to address such problems and a list of proximity operators is provided allowing us to consider various choices for the fit-to-data functional and for the regularization term. Numerical experiments show the validity of this approach for solving convex optimization problems encountered in the context of sparse covariance matrix estimation. Based on our theoretical results, an algorithm is also proposed for noisy graphical lasso where a precision matrix has to be estimated in the presence of noise. The nonconvexity of the resulting objective function is dealt with a majorization-minimization approach, i.e. by building a sequence of convex surrogates and solving the inner optimization subproblems via the aforementioned Douglas-Rachford procedure. We establish conditions for the convergence of this iterative scheme and we illustrate its good numerical performance with respect to state-of-the-art approaches

MASCOT : metadata for advanced scalable video coding tools : final report

The goal of the MASCOT project was to develop new video coding schemes and tools that provide both an increased coding efficiency as well as extended scalability features compared to technology that was available at the beginning of the project. Towards that goal the following tools would be used: - metadata-based coding tools; - new spatiotemporal decompositions; - new prediction schemes. Although the initial goal was to develop one single codec architecture that was able to combine all new coding tools that were foreseen when the project was formulated, it became clear that this would limit the selection of the new tools. Therefore the consortium decided to develop two codec frameworks within the project, a standard hybrid DCT-based codec and a 3D wavelet-based codec, which together are able to accommodate all tools developed during the course of the project

Jasmonate promotes auxin-induced adventitious rooting in dark-grown Arabidopsis thaliana seedlings and stem thin cell layers by a cross-talk with ethylene signalling and a modulation of xylogenesis

Background: Adventitious roots (ARs) are often necessary for plant survival, and essential for successful micropropagation. In Arabidopsis thaliana dark-grown seedlings AR-formation occurs from the hypocotyl and is enhanced by application of indole-3-butyric acid (IBA) combined with kinetin (Kin). The same IBA + Kin-treatment induces AR-formation in thin cell layers (TCLs). Auxin is the main inducer of AR-formation and xylogenesis in numerous species and experimental systems. Xylogenesis is competitive to AR-formation in Arabidopsis hypocotyls and TCLs. Jasmonates (JAs) negatively affect AR-formation in de-etiolated Arabidopsis seedlings, but positively affect both AR-formation and xylogenesis in tobacco dark-grown IBA + Kin TCLs. In Arabidopsis the interplay between JAs and auxin in AR-formation vs xylogenesis needs investigation. In de-etiolated Arabidopsis seedlings, the Auxin Response Factors ARF6 and ARF8 positively regulate AR-formation and ARF17 negatively affects the process, but their role in xylogenesis is unknown. The cross-talk between auxin and ethylene (ET) is also important for AR-formation and xylogenesis, occurring through EIN3/EIL1 signalling pathway. EIN3/EIL1 is the direct link for JA and ET-signalling. The research investigated JA role on AR-formation and xylogenesis in Arabidopsis dark-grown seedlings and TCLs, and the relationship with ET and auxin. The JA-donor methyl-jasmonate (MeJA), and/or the ET precursor 1-aminocyclopropane-1-carboxylic acid were applied, and the response of mutants in JA-synthesis and -signalling, and ET-signalling investigated. Endogenous levels of auxin, JA and JA-related compounds, and ARF6, ARF8 and ARF17 expression were monitored. Results: MeJA, at 0.01 μM, enhances AR-formation, when combined with IBA + Kin, and the response of the early-JA-biosynthesis mutant dde2–2 and the JA-signalling mutant coi1–16 confirmed this result. JA levels early change during TCL-culture, and JA/JA-Ile is immunolocalized in AR-tips and xylogenic cells. The high AR-response of the late JA-biosynthesis mutant opr3 suggests a positive action also of 12-oxophytodienoic acid on AR-formation. The crosstalk between JA and ET-signalling by EIN3/EIL1 is critical for AR-formation, and involves a competitive modulation of xylogenesis. Xylogenesis is enhanced by a MeJA concentration repressing AR-formation, and is positively related to ARF17 expression. Conclusions: The JA concentration-dependent role on AR-formation and xylogenesis, and the interaction with ET opens the way to applications in the micropropagation of recalcitrant species

Low Complexity Regularization of Linear Inverse Problems

Inverse problems and regularization theory is a central theme in contemporary signal processing, where the goal is to reconstruct an unknown signal from partial indirect, and possibly noisy, measurements of it. A now standard method for recovering the unknown signal is to solve a convex optimization problem that enforces some prior knowledge about its structure. This has proved efficient in many problems routinely encountered in imaging sciences, statistics and machine learning. This chapter delivers a review of recent advances in the field where the regularization prior promotes solutions conforming to some notion of simplicity/low-complexity. These priors encompass as popular examples sparsity and group sparsity (to capture the compressibility of natural signals and images), total variation and analysis sparsity (to promote piecewise regularity), and low-rank (as natural extension of sparsity to matrix-valued data). Our aim is to provide a unified treatment of all these regularizations under a single umbrella, namely the theory of partial smoothness. This framework is very general and accommodates all low-complexity regularizers just mentioned, as well as many others. Partial smoothness turns out to be the canonical way to encode low-dimensional models that can be linear spaces or more general smooth manifolds. This review is intended to serve as a one stop shop toward the understanding of the theoretical properties of the so-regularized solutions. It covers a large spectrum including: (i) recovery guarantees and stability to noise, both in terms of $\ell^2$-stability and model (manifold) identification; (ii) sensitivity analysis to perturbations of the parameters involved (in particular the observations), with applications to unbiased risk estimation ; (iii) convergence properties of the forward-backward proximal splitting scheme, that is particularly well suited to solve the corresponding large-scale regularized optimization problem

Computational optical imaging with a photonic lantern

[EN] The thin and flexible nature of optical fibres often makes them the ideal technology to view biological processes in-vivo, but current microendoscopic approaches are limited in spatial resolution. Here, we demonstrate a route to high resolution microendoscopy using a multicore fibre (MCF) with an adiabatic multimode-to-single-mode "photonic lantern" transition formed at the distal end by tapering. We show that distinct multimode patterns of light can be projected from the output of the lantern by individually exciting the single-mode MCF cores, and that these patterns are highly stable to fibre movement. This capability is then exploited to demonstrate a form of single-pixel imaging, where a single pixel detector is used to detect the fraction of light transmitted through the object for each multimode pattern. A custom computational imaging algorithm we call SARA-COIL is used to reconstruct the object using only the pre-measured multimode patterns themselves and the detector signals.This work was funded through the "Proteus" Engineering and Physical Sciences Research Council (EPSRC) Interdisciplinary Research Collaboration (IRC) (EP/K03197X/1), by the Science and Technology Facilities Council (STFC) through STFC-CLASP grants ST/K006509/1 and ST/K006460/1, STFC Consortium grants ST/N000625/1 and ST/N000544/1. S.L. acknowledges support from the National Natural Science Foundation of China under Grant no. 61705073. DBP acknowledges support from the Royal Academy of Engineering, and the European Research Council (PhotUntangle, 804626). The authors thank Philip Emanuel for the use of his confocal image of A549 cells and Eckhardt Optics for their image of the USAF 1951 target. The authors sincerely thank the anonymous reviewers of this paper for their detailed and considered feedback which helped us to improve the quality of this paper significantly.Choudhury, D.; Mcnicholl, DK.; Repetti, A.; Gris-Sánchez, I.; Li, S.; Phillips, DB.; Whyte, G.... (2020). Computational optical imaging with a photonic lantern. Nature Communications. 11(1):1-9. https://doi.org/10.1038/s41467-020-18818-6S19111Wood, H. A. C., Harrington, K., Birks, T. A., Knight, J. C. & Stone, J. M. High-resolution air-clad imaging fibers. Opt. Lett. 43, 5311–5314 (2018).Akram, A. R. et al. In situ identification of Gram-negative bacteria in human lungs using a topical fluorescent peptide targeting lipid A. Sci. Transl. Med. 10, eaal0033 (2018).Shin, J., Bosworth, B. T. & Foster, M. A. Compressive fluorescence imaging using a multi-core fiber and spatially dependent scattering. Opt. Lett. 42, 109–112 (2017).Papadopoulos, I. N., Farahi, S., Moser, C. & Psaltis, D. Focusing and scanning light through a multimode optical fiber using digital phase conjugation. Opt. Express 20, 10583–10590 (2012).Čižmár, T. & Dholakia, K. Exploiting multimode waveguides for pure fibre-based imaging. Nat. Commun. 3, 1027 (2012).Plöschner, M., Tyc, T. & Čižmár, T. Seeing through chaos in multimode fibres. Nat. Photon. 9, 529–535 (2015).Birks, T. A., Gris-Sánchez, I., Yerolatsitis, S., Leon-Saval, S. G. & Thomson, R. R. The photonic lantern. Adv. Opt. Photon. 7, 107–167 (2015).Birks, T. A., Mangan, B. J., Díez, A., Cruz, J. L. & Murphy, D. F. Photonic lantern’ spectral filters in multi-core fiber. Opt. Express 20, 13996–14008 (2012).Edgar, M. P., Gibson, G. M. & Padgett, M. J. Principles and prospects for single-pixel imaging. Nat. Photon. 13, 13–20 (2019).Mahalati, R. N., Yu, Gu. R. & Kahn, J. M. Resolution limits for imaging through multi-mode fiber. Opt. Express 21, 1656–1668 (2013).Amitonova, L. V. & de Boer, J. F. Compressive imaging through a multimode fiber. Opt. Lett. 43, 5427–5430 (2018).Mallat, S. A Wavelet Tour of Signal Processing 2nd edn (Academic Press, Burlington, MA, 2009).Lustig, M., Donoho, D. & Pauly, J. M. Sparse MRI: the application of compressed sensing for rapid MR imaging. Magn. Reson. Med. 58, 1182–1195 (2007).Davies, M., Puy, G., Vandergheynst, P. & Wiaux, Y. A compressed sensing framework for magnetic resonance fingerprinting. SIAM J. Imaging Sci. 7, 2623–2656 (2014).Wiaux, Y., Puy, G., Scaife, A. M. M. & Vandergheynst, P. Compressed sensing imaging techniques in radio interferometry. Mon. Not. R. Astron. Soc. 395, 1733–1742 (2009).Carrillo, R. E., McEwen, J. D. & Wiaux, Y. Sparsity averaging reweighted analysis (SARA): a novel algorithm for radio-interferometric imaging. Mon. Not. R. Astron. Soc. 426, 1223–1234 (2012).Katz, O., Bromberg, Y. & Silberberg, Y. Compressive ghost imaging. Appl. Phys. Lett. 95, 131110 (2009).Sun, B., Welsh, S. S., Edgar, M. P., Shapiro, J. H. & Padgett, M. J. Normalized ghost imaging. Opt. Express 20, 16892–16901 (2012).Kim, M., Park, C., Rodriguez, C., Park, Y. & Cho, Y.-H. Superresolution imaging with optical fluctuation using speckle patterns illumination. Sci. Rep. 5, 16525 (2015).Combettes, P. L. & Pesquet, J. -C. in Fixed-Point Algorithms for Inverse Problems in Science and Engineering (Springer, New York, 2011).Komodakis, N. & Pesquet, J.-C. Playing with duality: an overview of recent primal dual approaches for solving large-scale optimization problems. IEEE Signal Proc. Mag. 32, 31–54 (2015).Chandrasekharan, H. K. et al. Multiplexed single-mode wavelength-to-time mapping of multimode light. Nat. Commun. 8, 14080 (2017).Wadsworth, W. J. et al. Very high numerical aperture fibers. Photon. Technol. Lett. 16, 843–845 (2004).Pesquet, J.-C. & Repetti, A. A class of randomized primal-dual algorithms for distributed optimization. J. Nonlinear Convex Anal. 16, 2353–2490 (2015).Chambolle, A., Ehrhardt, M. J., Richtárik, P. & Schönlieb, C.-B. Stochastic primal-dual hybrid gradient algorithm with arbitrary sampling and imaging applications. SIAM J. Optim. 28, 2783–2808 (2018).Bolte, J., Sabach, S. & Teboulle, M. Proximal alternating linearized minimization for nonconvex and nonsmooth problems. Math. Program. 146, 459–494 (2014).Chouzenoux, E., Pesquet, J.-C. & Repetti, A. A block coordinate variable metric forward-backward algorithm. J. Glob. Optim. 66, 457–485 (2016).Flusberg, B. A. et al. Fiber-optic fluorescence imaging. Nat. Methods 2, 941–950 (2005).Tsvirkun, V. et al. Bending-induced inter-core group delays in multicore fibers. Opt. Express 25, 31863–31875 (2017).Candès, E. J., Wakin, M. B. & Boyd, S. Enhancing sparsity by reweighted l1 minimization. J. Fourier Anal. Appl. 14, 877–905 (2008).Condat, L. A primal–dual splitting method for convex optimization involving lipschitzian, proximable and linear composite terms. J. Optim. Theory Appl. 158, 460–479 (2013).Vu, B. C. A splitting algorithm for dual monotone inclusions involving cocoercive operators. Adv. Comp. Math. 38, 667–681 (2013)