1. An image processing system characterized by comprising: a hardware including a processor; an error-function determining unit, implemented by the processor, for making use of a blur function serving as a function representing the degree of blurring of a blurred input image and a geometrical-deformation matrix serving as a matrix for restricting an operation to lay out a 2-dimensional code shown by the input image on cells each serving as a configuration unit, implemented by the processor, of the 2-dimensional code in order to determine an error function serving as a function satisfying a relation that, the smaller the error between the input image and an image obtained by adding geometrical deformations and blurs to a recovered image obtained from a recovering process, the more the approach to a result determined in advance; a pixel-value restricting unit, implemented by the processor, for determining pixel-value restriction information prescribing a restriction condition for a restriction imposed on a predetermined pixel value obtained from discretization of pixel values of the 2-dimensional code to be recovered; an objective-function determining unit, implemented by the processor, for making use of the error function and the pixel-value restriction information as a basis for determining an objective function serving as a function satisfying a relation that, the closer the recovered image to the true image, the more the approach to a result determined in advance; and an objective-function optimizing unit, implemented by the processor, for determining a recovered image which optimizes the objective function.