Underwater images typically exhibit color distortion and low contrast as a result of the exponential decay that light suffers as it travels. Moreover, colors associated to different wavelengths have different attenuation rates, being the red wavelength the one that attenuates the fastest. To restore underwater images, we propose a Red Channel method, where colors associated to short wavelengths are recovered, as expected for underwater images, leading to a recovery of the lost contrast. The Red Channel method can be interpreted as a variant of the Dark Channel method used for images degraded by the atmosphere when exposed to haze. Experimental results show that our technique handles gracefully artificially illuminated areas, and achieves a natural color correction and superior or equivalent visibility improvement when compared to other state-of-the-art methods.David Pardo was partially funded by the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2013-40824-P, the BCAM "Severo Ochoa" accreditation of excellence SEV-2013-0323, the CYTED 2011 Project 712RT0449, and the Basque Government Consolidated Research Group Grant IT649-13 on "Mathematical Modeling, Simulation, and Industrial Applications (M2SI)"

In this paper we study how the use of a more continuous set of basis functions affects the cost of solving systems of linear equations resulting from a discretized Galerkin weak form. Specifically, we compare performance of linear solvers when discretizing using $C^0$ B-splines, which span traditional finite element spaces, and $C^{p-1}$ B-splines, which represent maximum continuity. We provide theoretical estimates for the increase in cost of the matrix-vector product as well as for the construction and application of black-box preconditioners. We accompany these estimates with numerical results and study their sensitivity to various grid parameters such as element size $h$ and polynomial order of approximation $p$ in addition to the aforementioned continuity of the basis. Finally, we present timing results for a range of preconditioning options for the Laplace problem. We conclude that the matrix-vector product operation is at most $\left.{33p^2}\middle/{8}\right.$ times more expensive for the more continuous space, although for moderately low $p$, this number is significantly reduced. Moreover, if static condensation is not employed, this number further reduces to at most a value of 8, even for high $p$. Preconditioning options can be up to $p^3$ times more expensive to set up, although this difference significantly decreases for some popular preconditioners such as incomplete LU factorization.

Images obtained under adverse weather conditions, such as haze or fog, typically exhibit low contrast and faded colors, which may severely limit the visibility within the scene. Unveiling the image structure under the haze layer and recovering vivid colors out of a single image remains a challenging task, since the degradation is depth-dependent and conventional methods are unable to overcome this problem. In this work, we extend a well-known perception-inspired variational framework for single image dehazing. Two main improvements are proposed. First, we replace the value used by the framework for the gray-world hypothesis by an estimation of the mean of the clean image. Second, we add a set of new terms to the energy functional for maximizing the interchannel contrast. Experimental results show that the proposed enhanced variational image dehazing (EVID) method outperforms other state-of-the-art methods both qualitatively and quantitatively. In particular, when the illuminant is uneven, our EVID method ...

We have developed an efficient inversion method to estimate layer-by-layer electric resistivity from logging-while-drilling electromagnetic induction measurements. The method assumes a 1D model based on planarly layered transversely isotropic formations with known bed boundaries, penetrated by arbitrary well trajectories. Forward simulations are based on a 1D reduced model in which borehole and mandrel effects are assumed to be negligible. The stopping criteria, regularization term, regularization parameter, the Jacobian matrix, and inversion variables are automatically estimated by the inversion algorithm, thereby minimizing the required user interaction and expertise. Numerical inversion results of challenging synthetic and field data confirmed the high stability and superior approximation properties of the developed inversion algorithm. We evaluated results indicating that triaxial induction measurements provide significantly more stable inversion results than conventional coaxial measurements, especially in the presence of anisotropic formations.