Related papers: Harnessing Sparsity over the Continuum: Atomic Nor…
In a plethora of applications dealing with inverse problems, e.g. in image processing, social networks, compressive sensing, biological data processing etc., the signal of interest is known to be structured in several ways at the same time.…
Sparse coding consists in representing signals as sparse linear combinations of atoms selected from a dictionary. We consider an extension of this framework where the atoms are further assumed to be embedded in a tree. This is achieved…
Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…
In the context of optical interferometry, only undersampled power spectrum and bispectrum data are accessible. It poses an ill-posed inverse problem for image recovery. Recently, a tri-linear model was proposed for monochromatic imaging,…
A simple, yet general, formalism for the optimized linear combination of astrophysical images is constructed and demonstrated. The formalism allows the user to combine multiple undersampled images to provide oversampled output at high…
Super-resolution is a fundamental problem in computer vision which aims to overcome the spatial limitation of camera sensors. While significant progress has been made in single image super-resolution, most algorithms only perform well on…
The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…
Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the…
A major challenge in single particle reconstruction from cryo-electron microscopy is to establish a reliable ab-initio three-dimensional model using two-dimensional projection images with unknown orientations. Common-lines based methods…
This paper introduces and studies the convergence properties of a new class of explicit $\epsilon$-subgradient methods for the task of minimizing a convex function over the set of minimizers of another convex minimization problem. The…
Compressed sensing aims at reconstructing sparse signals from significantly reduced number of samples, and a popular reconstruction approach is $\ell_1$-norm minimization. In this correspondence, a method called orthonormal expansion is…
For the general problem of minimizing a convex function over a compact convex domain, we will investigate a simple iterative approximation algorithm based on the method by Frank & Wolfe 1956, that does not need projection steps in order to…
We consider the problem of recovering a lowrank matrix M from a small number of random linear measurements. A popular and useful example of this problem is matrix completion, in which the measurements reveal the values of a subset of the…
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ…
Composite minimization is a powerful framework in large-scale convex optimization, based on decoupling of the objective function into terms with structurally different properties and allowing for more flexible algorithmic design. We…
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…
We consider the constrained Linear Inverse Problem (LIP), where a certain atomic norm (like the $\ell_1 $ norm) is minimized subject to a quadratic constraint. Typically, such cost functions are non-differentiable, which makes them not…
The problem of super-resolution is concerned with the reconstruction of temporally/spatially localized events (or spikes) from samples of their convolution with a low-pass filter. Distinct from prior works which exploit sparsity in…
We consider the problem of recovering a signal consisting of a superposition of point sources from low-resolution data with a cut-off frequency f. If the distance between the sources is under 1/f, this problem is not well posed in the sense…
In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…