Reproducibility of Pansharpening Methods and Quality Indexes versus Data Formats

In this work, we investigate whether the performance of pansharpening methods depends on their input data format; in the case of spectral radiance, either in its original floating-point format or in an integer-packed fixed-point format. It is theoretically proven and experimentally demonstrated that methods based on multiresolution analysis are unaffected by the data format. Conversely, the format is crucial for methods based on component substitution, unless the intensity component is calculated by means of a multivariate linear regression between the upsampled bands and the lowpass-filtered Pan. Another concern related to data formats is whether quality measurements, carried out by means of normalized indexes depend on the format of the data on which they are calculated. We will focus on some of the most widely used with-reference indexes to provide a novel insight into their behaviors. Both theoretical analyses and computer simulations, carried out on GeoEye-1 and WorldView-2 datasets with the products of nine pansharpening methods, show that their performance does not depend on the data format for purely radiometric indexes, while it significantly depends on the data format, either floating-point or fixed-point, for a purely spectral index, like the spectral angle mapper. The dependence on the data format is weak for indexes that balance the spectral and radiometric similarity, like the family of indexes, Q2n, based on hypercomplex algebra.

22.—Analytic, Generalized, Hyperanalytic Function Theory and an Application to Elasticity

SynopsisThough it is still an open problem for which class of first-order elliptic systems Carleman's theorem holds, this is proven here for a certain class of systems (with analytic coefficients) for which Douglis introduced the hypercomplex algebra and hyperanalytic functions. The proof is based on a representation formula generalising Vekua's approach with Volterra integral equations in C2 to more than two unknowns. The representation formula is of its own interest because it provides the generation of complete families of solutions. The equations of plane inhomogeneous elasticity problems lead to a system of the desired class.

The algebra of meson matrices

In an interesting recent paper Schrödinger(5) contributes much new information on the properties of the hypercomplex algebra used in meson theory(1, 2, 4, 6, 7) which is defined by the relations(3)