Related papers: Chordal Decomposition for Spectral Coarsening
Hyperspectral imaging offers new perspectives for diverse applications, ranging from the monitoring of the environment using airborne or satellite remote sensing, precision farming, food safety, planetary exploration, or astrophysics.…
The spectral representation separates the contributions of geometrical arrangement (topology) and intrinsic constituent properties in a composite. The aim of paper is to present a numerical algorithm based on the Monte Carlo integration and…
We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…
We propose a new geometric method of IR factorization in sector decomposition. The problem is converted into a set of problems in convex geometry. The latter problems are solved using algorithms in combinatorial geometry. This method…
We consider the global optimization of nonconvex quadratic programs and mixed-integer quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through…
We propose an algorithm for rotational sparse coding along with an efficient implementation using steerability. Sparse coding (also called dictionary learning) is an important technique in image processing, useful in inverse problems,…
Sparse coding (SC) is an automatic feature extraction and selection technique that is widely used in unsupervised learning. However, conventional SC vectorizes the input images, which breaks apart the local proximity of pixels and destructs…
In this paper, we propose a solution for a fundamental problem in computational harmonic analysis, namely, the construction of a multiresolution analysis with directional components. We will do so by constructing subdivision schemes which…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
When it comes to clustering nonconvex shapes, two paradigms are used to find the most suitable clustering: minimum cut and maximum density. The most popular algorithms incorporating these paradigms are Spectral Clustering and DBSCAN. Both…
Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across…
We have developed a method for constructing spectral approximations for convolution operators of Fredholm type. The algorithm we propose is numerically stable and takes advantage of the recurrence relations satisfied by the entries of such…
We present the optimal design of a spectral method widely used to initialize nonconvex optimization algorithms for solving phase retrieval and other signal recovery problems. Our work leverages recent results that provide an exact…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
In this paper, we discuss application of iterative Stochastic Optimization routines to the problem of sparse signal recovery from noisy observation. Using Stochastic Mirror Descent algorithm as a building block, we develop a multistage…
The object recognition is a complex problem in the image processing. Mathematical morphology is Shape oriented operations, that simplify image data, preserving their essential shape characteristics and eliminating irrelevancies. This paper…
We consider the problem of learning a low-dimensional signal model from a collection of training samples. The mainstream approach would be to learn an overcomplete dictionary to provide good approximations of the training samples using…
We consider the problem of approximating the solution of variational problems subject to the constraint that the admissible functions must be convex. This problem is at the interface between convex analysis, convex optimization, variational…
Sparse channel estimation for massive multiple-input multiple-output systems has drawn much attention in recent years. The required pilots are substantially reduced when the sparse channel state vectors can be reconstructed from a few…
Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the…