Introduction

Global flow diagnostics are essentially image-based measurements of the fundamental physical quantities in fluid mechanics and aerodynamics, including velocity, pressure, temperature, density, concentration of species, skin friction, and surface heat flux. In experiments, these fundamental quantities are related to some observable quantities in flow visualizations. The observable information is presented in digital flow visualization images, including scattering particle images in particle image velocimetry (PIV), fluorescent images in planar laser-induced fluorescence (PLIF) visualizations, Schlieren and shadowgraph images of density-varying flows, transmittance images (X-ray and neutron radiography images), pressure- and temperature-sensitive paint images (PSP and TSP images), surface luminescent oil-film images, and multispectral images of clouds and oceans taken by satellites and spacecraft. From a standpoint of image/data processing, a key problem is how to determine required physical quantities from observable quantities that are represented by the image intensity in flow visualizations. This is an inverse problem that belongs to a large class of ill-posed inverse problems in various scientific and engineering fields (Tikhonov and Arsenin 1977; Ramm 2004).