Theoretically

deteriorated images resuhing from imaging system performances can be recovered in a digital way providing that the optical imaging transfer function is known and its inverse function or the approximate inverse function can be found according to the measurement or the priori knowledge of the imaging transfer function. Basically both the imaging transfer functions and the recovery functions are space-variant. Based on space-variant image recovery by inverse filtering with polynomial approximation

we developed a new approach in which the space-variant recovery function is decomposed as the linear combination of a space-invariant base function and its power functions. The base function is such chosen

in recovery

that it brings no error as it corresponds to difference instead of derivative operations. Furthermore

the least square constraint is introduced to the recovery function for regulating the restoration. By this way

a recovered image is the linear combination of the original image and its even-order differences

where the combining coefficients are determined by the system point-spread function

constraint operator

regulation parameter and the decomposition base function. Detailed analysis and derivation of equations are presented and the processed results for both simulated and practical images show the effectiveness of the proposed scheme for deteriorated images with various signal-to-noise ratios.