Inverse Obstacle Scattering and Linear Classification

TAOS (two-dimensional angle-resolved optical scattering) is an experimental method to detect single, micrometer-sized airborne material particles, illuminate them by a single pulse of laser (${\mit\lambda} = 532$nm, pulse duration = 30ns) and record their scattered light intensity patterns over the angular sector $\{75^\circ\le{\mit\theta}\le 135^\circ\}\times\{0^\circ\le{\mit\varphi}\le 360^\circ\}$ at high resolution (one pattern $\doteq1024^2$ pixels). Particles of reference materials and from outdoor environmental sampling have been analyzed and thousands of scattering patterns (TAOS patterns, hereinafter) have been stored . One of the goals of classification is the discrimination of bacterial spore patterns ($Bq$). A typical result is: a set of 957 $K5$ (outdoor dust) patterns is analysed; 98 patterns (10\%) are falsely recognised as $Bq$ (lower halfplane), whereas the remainder is assigned to the other two training classes, $Fq$ (top) and $Pq$ (middle).