Image Processing Algorithms for Resolution Enhancement

In this project, iterative algorithms for image resolution enhancement are developed, considering non-ideal sampling (i.e. presence of an acquisition system before sampling) and continuous domain reconstruction (synthesis function); a variational approach is used. Using linear multigrid concepts, a fast linear magnification algorithm which handles data weighting terms is developed; in some cases, convergence rates outperform those of standard iterative methods by several orders of magnitude. This algorithm is notably able to magnify an image from a limited subset of its samples (Figs. 1 and 2).

The second developed algorithm is a non-linear one; it minimizes a convex (non-quadratic) functional, using a Huber-type potential (closely related to Total-Variation) as a regularization term. Qualitatively speaking, this will tend to minimize a combination of the L1 and L2 norms of the output image gradient. The solving approach consists in minimizing successive quadratic terms which all major the functional (min-max approach), this minimization being carried out by the Conjugate-Gradient method. The advantage of this algorithm is simultaneous preservation of the image contours as well as textures during magnification, as can be seen on the corresponding images (Figs. 3 and 4).

Potential further work can include use of the same multigrid concepts mentioned above in view of accelerating convergence rates of the non-linear algorithm, considering the minimization of the local quadratic expressions.

Fig. 1 : On the left, crop of the standard image "Lena"; on the right, its masked counterpart

Fig. 2 : 4x magnification of the masked samples from Fig. 1 by the linear algorithm

Fig. 3 : Crop of the standard image "house"

Fig. 4 : 4x magnification of the samples from Fig. 3 by the non-linear algorithm