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This paper proposes a class of nonlinear methods, called Set-Theoretic Deconvolution (STD), developed for joint restoration of M(M >1) monochrome distorted 2-dimensional images (snapshots) of an unknown extended object, being viewed through the optical channel with unknown PSF, whose true monochrome brightness profiles look distinct at M(M>!) slightly different wavelengths chosen. The presented method appeals to the generalized Projection Onto Convex Sets (POCS) formalism, so that the proper projective metric is introduced and then minimized. Thus, a number of operators is derived in closed form and cyclically applied to M-dimensional functional vector built up from estimates for combinations of monochrome images. During the projecting of vector onto convex sets one attempts to avoid non-physical inversion and to correctly form a feasible solution (fixed point) consistent with qualitative not quantitative information being assumed to be known in advance. Computer simulation demonstrates that the resulting improved monochrome images reveal fine details which could not easily be discerned in the original distorted images. This technique recovers fairly reliably the total multichromatic 2-D portrait of an arbitrary compact object whose monochrome brightness distributions have discontinuities and are highly nonconvex plus multiply connected ones. Originally developed for the deblurring of passively observed objects, the STD approach can be carried over to scenario with actively irradiated objects (f.e., near-Earth space targets). Under advanced conditions, such as spatio-spectrally diversified laser illumination or coherent Doppler imaging implementation, the synthesized loop deconvolver could be universal tool in object feature extraction by means of occasionally aberrated space-borne telescope or turbulence-affected ground/air-based large aperture optical systems.
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