| Popis: |
Most signals reaching the mammalian brain are noisy, weak, and degraded so that the corresponding data that are carried by the signals are themselves incomplete and overlapping, and, more likely that not, the product of convolution with nonlinear sources. The attempt to deconvolve these signals so as extracts the maximum meaningful information and make the best possible decisions usually leads to problems that are mathematically known as ill-possible and ill-conditioned. That is, there may exist insufficient information from which to draw unique conclusions, and simultaneously, small uncertainties within the datasets may lead to mutual inconsistencies within the competing hypotheses. How the brain processes signals and attemts to learn from them is a mystery. Under the best of circumstances, the brain can usually perform well when solving problems involving deductive inferencing. However, when attempting to form decisions from incomplete or ambigous pieces of information, if often falls prey to what is referred to as “cognitive illusions”. This article illustrates the potential for powerful artificial intelligence (AI) techniques when used in the analysis not only of the formidable problems that now exist in the NASA earth science programs, but also those to be encountered in the future Mission to Planet Earth (MTPE) and Earth Observing System (EOS) programs. These techniques, based on the logical and probabilistic reasoning aspects of plausible inference, stongly emphasize the synergetic relation between data and information. In particular, we address a complex, nonlinear system of under-determined and ill-conditioned equations that arise from the conditions of insufficient and overlapping data. The specific problem involves the estimation of the earth's vertical atmospheric ozone profile over 92 layers from 12 solar backscattered ultraviolet (SBUV) radiation data values. To accomplish this, we employ a given atmospheric radiative transfer function to transform a known ozone profile into SBUV equivalent, single-scattering data values ranging from 255.7 to 339.9 nm. We then use these simulated data values together with the known total ozone value and the radiative transfer function, to retrieve the known ozone profile. An analysis of this problem shows that while the data may fully specify the likelihood of a profile, the a priori information is often dismissed as being not as fully cogent as the data. In this application, a maximum entropy-derived Bayesian method is introduced. This method fully utilizes the evidence of prior information and makes logical assignments of numerical values to probabilities from the measured data. Since the number of levels over which the ozone is distributed is greater than the number of measured radiances, the problem of inferring the profile is nonlinear, and since the is an ill-posed one. In addition, the given profile is nonlinear, and since the transfer function is itself dependent on the profile, the information passed from the profile plane to the data plane is expressed as a Fredholm integral equation of the first kind. The results obtained are seen to compare favorably with those determined by the standard optimal statistical technique used by atmospheric chemists. Ozones retrieval appears to be well suited to an induction inference analysis that encompasses both logical and probability-based reasoning. |
