Mathematics for demosaicking

Digital color cameras sample the continuous color spectrum using three or more filters; however, each pixel represents a sample of only one of the color bands. This arrangement is called a mosaic. To produce a full-resolution color image, the recorded image must be processed to estimate the values of the pixels for all the other color bands. This restoration process is often called demosaicking. This paper uses stacked notation to represent the mosaicked image capture and derives the minimum mean square error (MMSE) estimator for the demosaicked image. By making common assumptions, the restoration can be computed in a cost-effective manner. Extensions to the linear method are proposed to allow adaptive behavior.