An Efficient Algorithm for Video Super-Resolution Based On a Sequential Model

In this work, we propose a novel procedure for video super-resolution, that is the recovery of a sequence of high-resolution images from its low-resolution counterpart. Our approach is based on a "sequential" model (i.e., each high-resolution frame is supposed to be a displaced version of the preceding one) and considers the use of sparsity-enforcing priors. Both the recovery of the high-resolution images and the motion fields relating them is tackled. This leads to a large-dimensional, non-convex and non-smooth problem. We propose an algorithmic framework to address the latter. Our approach relies on fast gradient evaluation methods and modern optimization techniques for non-differentiable/non-convex problems. Unlike some other previous works, we show that there exists a provably-convergent method with a complexity linear in the problem dimensions. We assess the proposed optimization method on {several video benchmarks and emphasize its good performance with respect to the state of the art.}Comment: 37 pages, SIAM Journal on Imaging Sciences, 201

Accelerated Projected Gradient Method for Linear Inverse Problems with Sparsity Constraints

Regularization of ill-posed linear inverse problems via $\ell_1$ penalization has been proposed for cases where the solution is known to be (almost) sparse. One way to obtain the minimizer of such an $\ell_1$ penalized functional is via an iterative soft-thresholding algorithm. We propose an alternative implementation to $\ell_1$-constraints, using a gradient method, with projection on $\ell_1$-balls. The corresponding algorithm uses again iterative soft-thresholding, now with a variable thresholding parameter. We also propose accelerated versions of this iterative method, using ingredients of the (linear) steepest descent method. We prove convergence in norm for one of these projected gradient methods, without and with acceleration.Comment: 24 pages, 5 figures. v2: added reference, some amendments, 27 page

Light Field Super-Resolution Via Graph-Based Regularization

Light field cameras capture the 3D information in a scene with a single exposure. This special feature makes light field cameras very appealing for a variety of applications: from post-capture refocus, to depth estimation and image-based rendering. However, light field cameras suffer by design from strong limitations in their spatial resolution, which should therefore be augmented by computational methods. On the one hand, off-the-shelf single-frame and multi-frame super-resolution algorithms are not ideal for light field data, as they do not consider its particular structure. On the other hand, the few super-resolution algorithms explicitly tailored for light field data exhibit significant limitations, such as the need to estimate an explicit disparity map at each view. In this work we propose a new light field super-resolution algorithm meant to address these limitations. We adopt a multi-frame alike super-resolution approach, where the complementary information in the different light field views is used to augment the spatial resolution of the whole light field. We show that coupling the multi-frame approach with a graph regularizer, that enforces the light field structure via nonlocal self similarities, permits to avoid the costly and challenging disparity estimation step for all the views. Extensive experiments show that the new algorithm compares favorably to the other state-of-the-art methods for light field super-resolution, both in terms of PSNR and visual quality.Comment: This new version includes more material. In particular, we added: a new section on the computational complexity of the proposed algorithm, experimental comparisons with a CNN-based super-resolution algorithm, and new experiments on a third datase

SNR Enhancement in Brillouin Microspectroscopy using Spectrum Reconstruction

Brillouin imaging suffers from intrinsically low signal-to-noise ratios (SNR). Such low SNRs can render common data analysis protocols unreliable, especially for SNRs below $\sim10$. In this work we exploit two denoising algorithms, namely maximum entropy reconstruction (MER) and wavelet analysis (WA), to improve the accuracy and precision in determination of Brillouin shifts and linewidth. Algorithm performance is quantified using Monte-Carlo simulations and benchmarked against the Cram\'er-Rao lower bound. Superior estimation results are demonstrated even at low SNRS ($\geq 1$). Denoising was furthermore applied to experimental Brillouin spectra of distilled water at room temperature, allowing the speed of sound in water to be extracted. Experimental and theoretical values were found to be consistent to within $\pm1\%$ at unity SNR

Development Of A High Performance Mosaicing And Super-Resolution Algorithm

In this dissertation, a high-performance mosaicing and super-resolution algorithm is described. The scale invariant feature transform (SIFT)-based mosaicing algorithm builds an initial mosaic which is iteratively updated by the robust super resolution algorithm to achieve the final high-resolution mosaic. Two different types of datasets are used for testing: high altitude balloon data and unmanned aerial vehicle data. To evaluate our algorithm, five performance metrics are employed: mean square error, peak signal to noise ratio, singular value decomposition, slope of reciprocal singular value curve, and cumulative probability of blur detection. Extensive testing shows that the proposed algorithm is effective in improving the captured aerial data and the performance metrics are accurate in quantifying the evaluation of the algorithm

Collaborative patch-based super-resolution for diffusion-weighted images

In this paper, a new single image acquisition super-resolution method is proposed to increase image resolution of diffusion weighted (DW) images. Based on a nonlocal patch-based strategy, the proposed method uses a non-diffusion image (b0) to constrain the reconstruction of DW images. An extensive validation is presented with a gold standard built on averaging 10 high-resolution DW acquis itions. A comparison with classical interpo- lation methods such as trilinear and B-spline demonstrates the competitive results of our proposed approach in termsofimprovementsonimagereconstruction,fractiona lanisotropy(FA)estimation,generalizedFAandangular reconstruction for tensor and high angular resolut ion diffusion imaging (HARDI) models. Besides, fi rst results of reconstructed ultra high resolution DW images are presented at 0.6 × 0.6 × 0.6 mm 3 and0.4×0.4×0.4mm 3 using our gold standard based on the average of 10 acquisitions, and on a single acquisition. Finally, fi ber tracking results show the potential of the proposed super-resolution approach to accurately analyze white matter brain architecture.We thank the reviewers for their useful comments that helped improve the paper. We also want to thank the Pr Louis Collins for proofreading this paper and his fruitful comments. Finally, we want to thank Martine Bordessoules for her help during image acquisition of DWI used to build the phantom. This work has been 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. This work has been also partially supported by the French National Agency for Research (Project MultImAD; ANR-09-MNPS-015-01) and by the Spanish grant TIN2011-26727 from the Ministerio de Ciencia e Innovacion. This work benefited from the use of FSL (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/), FiberNavigator (code.google.com/p/fibernavigator/), MRtrix software (http://www. brain.org.au/software/mrtrix/) and ITKsnap (www.itk.org).Coupé, P.; Manjón Herrera, JV.; Chamberland, M.; Descoteaux, M.; Hiba, B. (2013). Collaborative patch-based super-resolution for diffusion-weighted images. NeuroImage. 83:245-261. https://doi.org/10.1016/j.neuroimage.2013.06.030S2452618

Super-Resolution of Positive Sources: the Discrete Setup

In single-molecule microscopy it is necessary to locate with high precision point sources from noisy observations of the spectrum of the signal at frequencies capped by $f_c$, which is just about the frequency of natural light. This paper rigorously establishes that this super-resolution problem can be solved via linear programming in a stable manner. We prove that the quality of the reconstruction crucially depends on the Rayleigh regularity of the support of the signal; that is, on the maximum number of sources that can occur within a square of side length about $1/f_c$. The theoretical performance guarantee is complemented with a converse result showing that our simple convex program convex is nearly optimal. Finally, numerical experiments illustrate our methods.Comment: 31 page, 7 figure