Task-driven adaptive statistical compressive sensing of gaussian mixture models

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific sensing protocols specifically and jointly designed for classification and reconstruction. A two-step adaptive sensing paradigm is developed, where online sensing is applied to detect the signal class in the first step, followed by a reconstruction step adapted to the detected class and the observed samples. The approach is based on information theory, here tailored for Gaussian mixture models (GMMs), where an information-theoretic objective relationship between the sensed signals and a representation of the specific task of interest is maximized. Experimental results using synthetic signals, Landsat satellite attributes, and natural images of different sizes and with different noise levels show the improvements achieved using the proposed framework when compared to more standard sensing protocols. The underlying formulation can be applied beyond GMMs, at the price of higher mathematical and computational complexity. © 1991-2012 IEEE.

Assessing variability and long-term trends in burned area by merging multiple satellite fire products

Long term, high quality estimates of burned area are needed for improving both prognostic and diagnostic fire emissions models and for assessing feedbacks between fire and the climate system. We developed global, monthly burned area estimates aggregated to 0.5° spatial resolution for the time period July 1996 through mid-2009 using four satellite data sets. From 2001ĝ€ "2009, our primary data source was 500-m burned area maps produced using Moderate Resolution Imaging Spectroradiometer (MODIS) surface reflectance imagery; more than 90% of the global area burned during this time period was mapped in this fashion. During times when the 500-m MODIS data were not available, we used a combination of local regression and regional regression trees developed over periods when burned area and Terra MODIS active fire data were available to indirectly estimate burned area. Cross-calibration with fire observations from the Tropical Rainfall Measuring Mission (TRMM) Visible and Infrared Scanner (VIRS) and the Along-Track Scanning Radiometer (ATSR) allowed the data set to be extended prior to the MODIS era. With our data set we estimated that the global annual area burned for the years 1997ĝ€ "2008 varied between 330 and 431 Mha, with the maximum occurring in 1998. We compared our data set to the recent GFED2, L3JRC, GLOBCARBON, and MODIS MCD45A1 global burned area products and found substantial differences in many regions. Lastly, we assessed the interannual variability and long-term trends in global burned area over the past 13 years. This burned area time series serves as the basis for the third version of the Global Fire Emissions Database (GFED3) estimates of trace gas and aerosol emissions.

Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.