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“Digital Color Image Restoration”
by Clanton E. Mancill
August 1975
The restoration of color errors in digitally recorded color images is considered in this dissertation. A vector space model of a general digital color image recording system is derived and the equations representing the model and the equations of colorimetry are expressed in matrix form. Computer algorithms are derived which correct color errors introduced by imperfections in the color recording system The sources of color error which are considered include sensor spectral responses which depart from ideal color matching curves, crosstalk between color signal channels, and system nonlinearities. The special case of a color film-digital scanner system is examined in detail, although the methods derived apply to a wider class of color or multispectral sensing and recording systems. The success of the correction algorithms is demonstrated using a computer simulation of the film-scanner system. The algorithms for correction of spectrally created six band multispectral test image.
The generalized matrix inverse is used extensively in this report. Least squares, minimum norm, and Wiener estimation algorithms, in the form of generalized inverses, are applied to the correction of sensor imperfections. The utility of the generalized inverse in the spectral domain is also demonstrated by applying it to some related color problems. These include the estimation of the spectral response of a sensor from sample readings, and computer generation of spectral waveforms with desired colorimetric properties.