光学成像系统空间移变降质的最小二乘约束复原

对光学成像系统引起图像的空间移变降质，可以根据光学系统的特性函数确定相应的或者近似的逆（复原）函数，以数字图像处理的方法进行恢复，这些复原函数仍然具有空间移变的性质。本文在多项式近似逆滤波图像恢复方法的基础上，提出将空间移变的复原函数分解成空间移不变的基函数及其各次幂的线性组合，给出的基函数可以消除在图像恢复中用数字图像的差分代替图像的导数引入的误差，并在复原函数中引入最小二乘约束，对恢复图像进行规整，得到空间移变降质图像的最小二乘约束复原。获得的复原图像，是降质图像偶数阶差分的线性组合，组合系数由成像系统的点扩散函数、约束算子、复原规整参数和分解基函数确定。对模拟和实际获取的空间移变降质图像的处理结果表明，这种方法对各种信噪比条件下的图像恢复均适用。

Constrained Least-Square Restoration of Space-Variant Blurs Resulting from Optical Imaging Systems

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.