This paper proposes a new regularization method based on the MDL (Minimum Description Length) principle. An adequate precision weight vector is trained by approximately truncating the maximum likelihood weight vector. The main advantage of the proposed regularizer over existing ones is that it automatically determines a regularization factor without assuming any specific prior distribution with...

This paper presents an image interpolation model with nonlocal p-Laplacian regularization. The nonlocal p-Laplacian regularization overcomes the drawback of the partial differential equation PDE proposed by Belahmidi and Guichard 2004 that image density diffuses in the directions pointed by local gradient. The grey values of images diffuse along image feature direction not gradient direction un...

In this thesis (higher order) total variation regularization methods are examined in the context of image reconstruction and denoising. Therefore, variational schemes consisting of a data fidelity term and a regularization term, additionally weighted with a constant, are considered. With the staircasing effect and the loss of contrast, two well known drawbacks of the total variation (TV) as reg...

Segmentation plays an important role in many preprocessing stages in image processing. Recently, convex relaxation methods for image multi-labeling were proposed in the literature. Often these models involve the total variation (TV) semi-norm as regularizing term. However, it is well-known that the TV functional is not optimal for the segmentation of textured regions. In recent years directiona...

We propose a convex, lower semi-continuous, coercive approximation of Euler’s elastica energy for images, which is thus very well-suited as a regularizer in image processing. The approximation is not quite the convex relaxation, and we discuss its close relation to the exact convex relaxation as well as the difficulties associated with computing the latter. Interestingly, the convex relaxation ...

This thesis addresses the problem of performing image magnification to achieve higher perceived resolution for grey-scale and color images. A new perspective on the problem is introduced through the new concept of a theoretical camera that can acquire an ideal high resolution image. A new formulation of the problem is then introduced using two ingredients: a newly designed observation model and...

Aerial images are often degraded by space-varying motion blur and simultaneous uneven illumination. To recover high-quality aerial image from its non-uniform version, we propose a novel patch-wise restoration approach based on a key observation that the degree of blurring is inevitably affected by the illuminated conditions. A nonlocal Retinex model is developed to accurately estimate the refle...

Abstract This paper considers large-scale linear ill-posed inverse problems whose solutions can be represented as sums of smooth and piecewise constant components. To solve such we consider regularizers consisting two terms that must balanced. Namely, a Tikhonov term guarantees the smoothness solution component, while total-variation (TV) regularizer promotes blockiness non-smooth component. A ...

Aimed at achieving the accurate restoration of Poissonian images that exhibit neat edges and no staircase effect, this article develops a novel hybrid nonconvex double regularizer model. The proposed scheme closely takes advantages total variation with overlapping group sparsity high-order priors. is adopted to globally suppress artifacts, while regularization plays role locally preserving sign...

Abstract We establish an equivalence between a family of adversarial training problems for non-parametric binary classification and regularized risk minimization where the regularizer is nonlocal perimeter functional. The resulting admit exact convex relaxations type $L^1+\text{(nonlocal)}\operatorname{TV}$, form frequently studied in image analysis graph-based learning. A rich geometric struct...