Resolution beyond the diffraction limit for regularized object restoration

We propose a new formulation of Miller's regularization theory, which is particularly suitable for object restoration problems. By means of simple geometrical arguments, we obtain upper and lower bounds for the errors on regularized solutions. This leads to distinguish between ' Holder continuity ' which is quite good for practical computations and ` logarithmic continuity ' which is very poor. However, in the latter case, one can reconstruct local weighted averages of the solution. This procedure allows for precise valuations of the resolution attainable in a given problem. Numerical computations, made for object restoration beyond the diffraction limit in Fourier optics, show that, when logarithmic continuity holds, the resolution is practically independent of the data noise level. © 1980 Taylor & Francis Group, LLC.

Global carbon dioxide emissions from inland waters

Carbon dioxide (CO2) transfer from inland waters to the atmosphere, known as CO2 evasion, is a component of the global carbon cycle. Global estimates of CO2 evasion have been hampered, however, by the lack of a framework for estimating the inland water surface area and gas transfer velocity and by the absence of a global CO2 database. Here we report regional variations in global inland water surface area, dissolved CO2 and gas transfer velocity. We obtain global CO2 evasion rates of 1.8petagrams of carbon (Pg C) per year from streams and rivers and 0.32Pg Cyr-1 from lakes and reservoirs, where the upper and lower limits are respectively the 5th and 95th confidence interval percentiles. The resulting global evasion rate of 2.1 Pg Cyr-1 is higher than previous estimates owing to a larger stream and river evasion rate. Our analysis predicts global hotspots in stream and river evasion, with about 70 per cent of the flux occurring over just 20 per cent of the land surface. The source of inland water CO2 is still not known with certainty and new studies are needed to research the mechanisms controlling CO2 evasion globally. © 2013 Macmillan Publishers Limited. All rights reserved.