The Image Inverse Filtering with Polynomial Approximation and the Image Recovery in Spatially Variant Systems
用多项式近似的图象逆滤波及空间移变系统图象的恢复

The deteriorated image resulting from imaging system performances can be recovered with inverse filtering by multiplying the inverse filtering function and the Fourier transform of the acquired image providing that the optical imaging transfer function is known and its inverse function or the corresponding i inverse filtering function can be found according to the measure or the priori knowledge of the imaging transferl function. If the inverse function is continuous about the origin it may actually be represented as the Tailor series. The inverse Fourier transform operation of the polynomial series is differentiation of orders corresponding no degrees in the polynomial. Consequently, the inverse Fourier transform of the recovered image is approximately realized in spatial domain by the linear combinations of the image and its derivatives rather than by complicated deoonvolution. It is considerable for the recovery of the spatially variant deterioration, such as the deterioration resulting from curvature of field. For images of space-variant degradation, the linear combining coefficients rare functions of spatial coordinates specified by the spatial variance. Detailed analysis and derivation of equations are presented. Finally, the processing results both in spatial invariant and variant systems are given.