In a previous work, the authors presented a method to correct the image blurring that occurs prior to the geometric transformation of video images. As the authors indicate, this happens when the dominating blur is either atmospheric turbulence blur or object-image relative motion blur, for example, in satellite imaging, when there is a considerable distance between the object and a high-quality video camera. The authors previously worked with this model with camera motion free images, where they proposed a method based on the following steps: first, image registration (several low-resolution (LR) frames are matched); second, image interpolation and noise filtering (to obtain a blurred and noise filtered high-resolution (HR) image from low-resolution images); and, third, image restoration (deblurring the HR image). So, in this initial scheme, the interpolation is followed by restoration (noise filtering, blur estimation, and deblurring).

This paper presents a method for the reconstruction of HR images from several blurred LR image frames. The models for camera motion free observed images are described, and two other mathematical models are presented and used to characterize medium field photography. The first model assumes that the HR image is first blurred by the atmosphere (far field blurring), and then degraded by the optical devices (initially it is down-sampled, and then the near field blur and noise are added). The authors present the solution to this problem by determining the coefficient matrix of a linear system, and suggest an algorithm to solve the system efficiently. The coefficient matrix is divided into two parts: one is the blurring and down-sampling matrix, and the other is the regularization matrix. The second model assumes that the HR image is first blurred by the atmosphere (far field blurring), then blurred by the optical device (near field blurring), and, finally, down-sampled with noise added. The authors present the solution for this problem by determining the coefficient matrix of a linear system, and suggest an algorithm to solve the system efficiently. They also present the complexity analysis of the proposed algorithm, estimating the cost of the method used in the matrix computation.

The paper concludes with some numerical results obtained from experiments using simulated blurred images. It is important to note that the results are obtained using only a single observed image that is artificially blurred, obtaining a single observed blurred image (first experiment) or three observed blurred images with different blurring coefficients (second experiment). The experiments demonstrate the application of the first and second models, described above, for camera motion free observed images that are artificially degraded according to the corresponding model. Experimental results demonstrate that the proposed methods are quite efficient, as well as effective when using a few images (namely, motion free artificial blurred and decimated images). The proposed method should be extended to incorporate camera motion since it does not support geometric transformations mixed (after or before) with the blurring process.