ABSTRACT

This chapter illustrates two applications, in mathematical statistics (linear regression) and automatic control (feedback compensation problem). It argues that these two applications illustrate the richness and potential of the generalized inverses. The chapter deals with the renewal of damaged digital images provided by use camera or camcorder. Restoration process is of fundamental importance to obtain sharpness and clarity of images. One of the challenges of the restoration of paintings is to design efficient and reliable algorithm to obtain as much information as possible about the original image, on the basis of the data provided. The chapter considers just this problem with images in which there has been a blur due to the uniform linear motion camera. Due to the relative motion between the camera and the object that should be photographed blurring caused by motion. For uniform linear motion to the core blur, can be represented by means of a characteristic Toeplitz's matrices.