Total Variaaion Based Image Restoration with Fr^ee Local Constraints

The two main plagues of image restoration rre oscillatione and smoothing. Tladitiond image reetoration techniques prevent parasitic oscillationg by reeotting to emooth tegularization. Ilence, aingular image features rnd oecillatory textures cannot be reatored. The us€fulness of images oL tained by smooth regularization ir very limited. Regularized faces and characters loee features and are unrecognizably distorted. Oscillatory patterns and texturea are not allowed by regularization methods. Smoothly regularized images are of no us€ in criminal/civil inveetigations and as court evidence. [1]. A new Total Variation based approach was developed in [2] to ov€rcome the basic limitations of all rnooth regularization algorithms, The TV-based technique use the trl norm of the magnitude of a gradient, thue maling discontinuous and nonamooth eolutions poesible (if they belong to the space oI funciions of a bounded total variation). In TV image restoration [3], the solution is obtained by solving a tirne'dependent, nonlinear PDE on a manifold thet satisfies the degradation conetrainta. In practical applications, one asaumes a space.varying blurring keruel and signal-dependent (e.g. multiplicative noise) [4]. The evoIution part of the TV-based PDE turned out to be teloted to the curve shortening equation, but scaled by an inverse lsrodl. I{owever, even with the degradation constraints enforced, restoration may looe too much valuable, singular informatrion. Most notably, adjacent features are still merged and all geometrical Gatnree (such as level eete aud edges) are smoothed out. This is not surprising, since the mean curvature evolution of level eets, even scaled as in the TV method, is essentially Iinear diesipation in the tangential direction. Again, linearity is at the root of the problem. Once more, we seek a solution by nonlinearly minimiaing oscillatione. Bnt this time, rather than focueing on thc oscillations of an irnage inteneity (level sets) we bound the oscillation ofother quantitieo along the teature curvca" and enforce constraints inside the "feature regions". Thefeeture curves and regions may be formed by level e€is aud their interior or by a closed edge and a corresponding region.