Multichannel Blind Restoration of Images with Space-Variant Degradations

In this thesis, we cover the related problems of image restoration and depth map estimation from two or more space-variantly blurred images of the same scene in situations, where the extent of blur depends on the distance of scene from camera. This includes out-of-focus blur and the blur caused by camera motion. The latter is typical when photographing in low-light conditions. Both out-of-focus blur and camera motion blur can be modeled by convolution with a spatially varying point spread function (PSF). There exist many methods for restoration with known PSF. In our case, the PSF is unknown as it depends on depth map of the scene and camera motion. Such a problem is ill-posed if only one degraded image is available. We consider multichannel case, when at least two images of the same scene are available, which gives us additional information that makes the problem tractable. The main contribution of this thesis, Algorithm I, belongs to the group of variational methods that estimate simultaneously sharp image and depth map, based on the minimization of a cost functional. Compared to other existing methods, it works for much broader class of PSFs. In case of out-of-focus blur, the algorithm is able to consider optical aberrations. As for camera motion blur, we are concerned mainly with the special case when the camera moves in one plane perpendicular to the optical axis without any rotations. In this case the algorithm needs to know neither camera motion nor camera parameters. This model can be valid in industrial applications with camera mounted on vibrating or moving devices. In addition, we discuss the possibility to extend the described algorithm to general camera motion. In this case, the knowledge of camera motion is indispensable. In practice, information about the motion could be provided by inertial sensors mounted on the camera. Besides, we present two filter-based methods for depth map estimation based on the measurement of the local level of blur. Algorithm II is a fast method working for arbitrary sufficiently symmetrical blurs using only two convolutions. Algorithm III places no constraints on the shape of PSF at the expense of higher time requirements. Finally, we propose an extension of Algorithms I and III to color images.