Automating a Dehazing System by Self-Calibrating on Haze Conditions

Existing image dehazing algorithms typically rely on a two-stage procedure. The medium transmittance and lightness are estimated in the first stage, and the scene radiance is recovered in the second by applying the simplified Koschmieder model. However, this type of unconstrained dehazing is only applicable to hazy images, and leads to untoward artifacts in haze-free images. Moreover, no algorithm that can automatically detect the haze density and perform dehazing on an arbitrary image has been reported in the literature to date. Therefore, this paper presents an automated dehazing system capable of producing satisfactory results regardless of the presence of haze. In the proposed system, the input image simultaneously undergoes multiscale fusion-based dehazing and haze-density-estimating processes. A subsequent image blending step then judiciously combines the dehazed result with the original input based on the estimated haze density. Finally, tone remapping post-processes the blended result to satisfactorily restore the scene radiance quality. The self-calibration capability on haze conditions lies in using haze density estimate to jointly guide image blending and tone remapping processes. We performed extensive experiments to demonstrate the superiority of the proposed system over state-of-the-art benchmark methods.

Applications of analytic newvectors for $$\mathrm {GL}(n)$$

We provide a few natural applications of the analytic newvectors, initiated in Jana and Nelson (Analytic newvectors for $$\text {GL}_n(\mathbb {R})$$ GL n ( R ) , arXiv:1911.01880 [math.NT], 2019), to some analytic questions in automorphic forms for $$\mathrm {PGL}_n(\mathbb {Z})$$ PGL n ( Z ) with $$n\ge 2$$ n ≥ 2 , in the archimedean analytic conductor aspect. We prove an orthogonality result of the Fourier coefficients, a density estimate of the non-tempered forms, an equidistribution result of the Satake parameters with respect to the Sato–Tate measure, and a second moment estimate of the central L-values as strong as Lindelöf on average. We also prove the random matrix prediction about the distribution of the low-lying zeros of automorphic L-function in the analytic conductor aspect. The new ideas of the proofs include the use of analytic newvectors to construct an approximate projector on the automorphic spectrum with bounded conductors and a soft local (both at finite and infinite places) analysis of the geometric side of the Kuznetsov trace formula.

Analytical modelling and joint inversion of surface displacements and gravity changes at volcanoes

<p>Gravity change observations at volcanoes provide information on the location and mass change of intruded magma bodies. Gravity change and surface displacement observations are often combined in order to infer the density of the intruded materials. Previous studies have highlighted that it is crucial to account for magma compressibility and the shape of the gravity change and deformation source to avoid large biases in the density estimate. Currently, an analytical model for the deformation field and gravity change due to a source of arbitrary shape is lacking, affecting our ability to perform rapid inversions and assess the nature of volcanic unrest.  </p><p>Here, we propose an efficient approach for rapid joint-inversions of surface displacement and gravity change observations associated with underground pressurized reservoirs. We derive analytical solutions for deformations and gravity changes due to the volume changes of triaxial point-sources in an isotropic elastic half-space. The method can be applied to  volcanic reservoirs that are deep compared to their size (far field approximation). We show that the gravity changes not only allow inferring mass changes within the reservoirs, but also help better constrain location, shape and the volume change of the source. We discuss how the inherent uncertainties in the realistic shape of volcanic reservoirs are reflected in large uncertainties on the density estimates. We apply our approach to the surface displacements and gravity changes at Long Valley caldera over the 1985-1999 time period. We show that gravity changes together with only vertical displacements are sufficient to constrain the mass change and all the other source parameters. We also show that while mass change is well constrained by gravity change observations the density estimate is more uncertain even if the magma compressibility is accounted for in the model.</p>