Related papers: Total variation on a tree
Although much research has been devoted to the problem of restoring Poissonian images, namely in the fields of medical and astronomical imaging, applying the state of the art regularizers (such as those based on wavelets or total variation)…
We present a parallelized primal-dual algorithm for solving constrained convex optimization problems. The algorithm is "block-based," in that vectors of primal and dual variables are partitioned into blocks, each of which is updated only by…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
Total variation has proved its effectiveness in solving inverse problems for compressive sensing. Besides, the nonlocal means filter used as regularization preserves texture better for recovered images, but it is quite complex to implement.…
The total variation filtering technique emerges as a highly effective strategy for restoring signals with discontinuities in various parts of their structure. This study presents and implements a one-dimensional signal filtering algorithm…
Our work considers the optimization of the sum of a non-smooth convex function and a finite family of composite convex functions, each one of which is composed of a convex function and a bounded linear operator. This type of problem is…
We consider curvature depending variational models for image regularization, such as Euler's elastica. These models are known to provide strong priors for the continuity of edges and hence have important applications in shape-and image…
We develop new adaptive algorithms for variational inequalities with monotone operators, which capture many problems of interest, notably convex optimization and convex-concave saddle point problems. Our algorithms automatically adapt to…
To overcome the weakness of a total variation based model for image restoration, various high order (typically second order) regularization models have been proposed and studied recently. In this paper we analyze and test a fractional-order…
Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
Capturing complex high-order interactions among data is an important task in many scenarios. A common way to model high-order interactions is to use hypergraphs whose topology can be mathematically represented by tensors. Existing methods…
In this paper we propose a global optimization-based approach to jointly matching a set of images. The estimated correspondences simultaneously maximize pairwise feature affinities and cycle consistency across multiple images. Unlike…
The joint problem of reconstruction / feature extraction is a challenging task in image processing. It consists in performing, in a joint manner, the restoration of an image and the extraction of its features. In this work, we firstly…
An algorithm on weighted graphs is called universally optimal if it is optimal for every input graph, in the worst case taken over all weight assignments. Informally, this means the algorithm is competitive even with algorithms that are…
Energy minimization has been an intensely studied core problem in computer vision. With growing image sizes (2D and 3D), it is now highly desirable to run energy minimization algorithms in parallel. But many existing algorithms, in…
In this paper, we investigate adaptive nonlinear regression and introduce tree based piecewise linear regression algorithms that are highly efficient and provide significantly improved performance with guaranteed upper bounds in an…
In this paper, we propose a new Fully Composite Formulation of convex optimization problems. It includes, as a particular case, the problems with functional constraints, max-type minimization problems, and problems of Composite…
We propose an adaptive refinement algorithm to solve total variation regularized measure optimization problems. The method iteratively constructs dyadic partitions of the unit cube based on i) the resolution of discretized dual problems and…