Smoothed Functional Algorithms for Stochastic Optimization using q-Gaussian Distributions

Smoothed functional (SF) schemes for gradient estimation are known to be efficient in stochastic optimization algorithms, specially when the objective is to improve the performance of a stochastic system. However, the performance of these methods depends on several parameters, such as the choice of a suitable smoothing kernel. Different kernels have been studied in literature, which include Gaussian, Cauchy and uniform distributions among others. This paper studies a new class of kernels based on the q-Gaussian distribution, that has gained popularity in statistical physics over the last decade. Though the importance of this family of distributions is attributed to its ability to generalize the Gaussian distribution, we observe that this class encompasses almost all existing smoothing kernels. This motivates us to study SF schemes for gradient estimation using the q-Gaussian distribution. Using the derived gradient estimates, we propose two-timescale algorithms for optimization of a stochastic objective function in a constrained setting with projected gradient search approach. We prove the convergence of our algorithms to the set of stationary points of an associated ODE. We also demonstrate their performance numerically through simulations on a queuing model

Noise minimised high resolution digital holographic microscopy applied to surface topography

The topography of surface relief gratings was studied by digital holographic microscopy. The applicability of the method for quantitative measurements of surface microstructure at nanoscale was demonstrated. The method for wavefront reconstruction of surface relief from a digital hologram recorded in off-axis configuration was also applied. The main feature is noise filtration due to the presence of noise in the recorded intensity distribution and the use of all orders of the hologram. Reconstruction results proved a better effectiveness of our approach for topography studying of relief grating patterned on a ChG As2S3 – Se nanomultilayers in comparison with standard Fourier Transform and Atom Force Microscope methods.We express our gratitude to the Materials for Photovoltaic and Photonics Laboratory of the Institute of Applied Physics of the Academy of Sciences of Moldova for the samples preparing. Funding of work: the H2020-TWINN-2015 HOLO-project (687328); the Academy of Finland project 287150, 2015-2019

Methods for depth-map filtering in view-plus-depth 3D video representation

Peer reviewe

MRI noise estimation and denoising using non-local PCA

NOTICE: this is the author’s version of a work that was accepted for publication in Medical Image AnalysisChanges resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Medical Image Analysis, [Volume 22, Issue 1, May 2015, Pages 35–47] DOI 10.1016/j.media.2015.01.004This paper proposes a novel method for MRI denoising that exploits both the sparseness and self-similarity properties of the MR images. The proposed method is a two-stage approach that first filters the noisy image using a non local PCA thresholding strategy by automatically estimating the local noise level present in the image and second uses this filtered image as a guide image within a rotationally invariant non-local means filter. The proposed method internally estimates the amount of local noise presents in the images that enables applying it automatically to images with spatially varying noise levels and also corrects the Rician noise induced bias locally. The proposed approach has been compared with related state-of-the-art methods showing competitive results in all the studied cases.We are grateful to Dr. Matteo Mangioni and Dr. Alessandro Foi for their help on running their BM4D method in our comparisons. We want also to thank Dr. Luis Marti-Bonmati and Dr. Angel Alberich-Bayarri from Quiron Hospital of Valencia for providing the real clinical data used in this paper. This study has been carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Programme IdEx Bordeaux (ANR-10-IDEX-03-02), Cluster of excellence CPU and TRAIL (HR-DTI ANR-10-LABX-57).Manjón Herrera, JV.; Coupé, P.; Buades, A. (2015). MRI noise estimation and denoising using non-local PCA. Medical Image Analysis. 22(1):35-47. doi:10.1016/j.media.2015.01.004S354722

Diffusion Weighted Image Denoising using overcomplete Local PCA

Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffusion imaging. This new filter reduces random noise in multicomponent DWI by locally shrinking less significant Principal Components using an overcomplete approach. The proposed method is compared with state-of-the-art methods using synthetic and real clinical MR images, showing improved performance in terms of denoising quality and estimation of diffusion parameters.This work has been supported by the Spanish grant TIN2011-26727 from Ministerio de Ciencia e Innovacion. This work has been also partially supported by the French grant "HR-DTI" ANR-10-LABX-57 funded by the TRAIL from the French Agence Nationale de la Recherche within the context of the Investments for the Future program. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Manjón Herrera, JV.; Coupé, P.; Concha, L.; Buades, A.; Collins, L.; Robles Viejo, M. (2013). Diffusion Weighted Image Denoising using overcomplete Local PCA. PLoS ONE. 8(9):1-12. https://doi.org/10.1371/journal.pone.0073021S11289Sundgren, P. C., Dong, Q., Gómez-Hassan, D., Mukherji, S. K., Maly, P., & Welsh, R. (2004). Diffusion tensor imaging of the brain: review of clinical applications. Neuroradiology, 46(5), 339-350. doi:10.1007/s00234-003-1114-xJohansen-Berg, H., & Behrens, T. E. (2006). Just pretty pictures? What diffusion tractography can add in clinical neuroscience. 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