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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…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
The Kaczmarz algorithm is popular for iteratively solving an overdetermined system of linear equations. The traditional Kaczmarz algorithm can approximate the solution in few sweeps through the equations but a randomized version of the…
This paper proposes low-complexity algorithms for finding approximate second-order stationary points (SOSPs) of problems with smooth non-convex objective and linear constraints. While finding (approximate) SOSPs is computationally…
This paper studies the copositive optimization problem whose objective is a sparse polynomial, with linear constraints over the nonnegative orthant. We propose sparse Moment-SOS relaxations to solve it. Necessary and sufficient conditions…
Computational problem certificates are additional data structures for each output, which can be used by a-possibly randomized-verification algorithm that proves the correctness of each output. In this paper, we give an algorithm that…
This paper presents new efficient solutions to the rolling shutter camera absolute pose problem. Unlike the state-of-the-art polynomial solvers, we approach the problem using simple and fast linear solvers in an iterative scheme. We present…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
This paper introduces a framework for super-resolution of scalable video based on compressive sensing and sparse representation of residual frames in reconnaissance and surveillance applications. We exploit efficient compressive sampling…
Sparse polynomial interpolation, sparse linear system solving or modular rational reconstruction are fundamental problems in Computer Algebra. They come down to computing linear recurrence relations of a sequence with the Berlekamp-Massey…
We study sparsity in the max-plus algebraic setting. We seek both exact and approximate solutions of the max-plus linear equation with minimum cardinality of support. In the former case, the sparsest solution problem is shown to be…
We show how to construct sparse polynomial systems that have non-trivial lower bounds on their numbers of real solutions. These are unmixed systems associated to certain polytopes. For the order polytope of a poset P this lower bound is the…
Utilizing a ray-tracing program, we have modeled the angular resolution of a short focal length (~2m), large field-of-view (3.1 square degrees), grazing incidence mirror shell. It has been previously shown in the literature that the…
We propose a stochastic variance reduced optimization algorithm for solving sparse learning problems with cardinality constraints. Sufficient conditions are provided, under which the proposed algorithm enjoys strong linear convergence…
The Extended Randomized Kaczmarz method is a well known iterative scheme which can find the Moore-Penrose inverse solution of a possibly inconsistent linear system and requires only one additional column of the system matrix in each…
Recovering matrices from compressive and grossly corrupted observations is a fundamental problem in robust statistics, with rich applications in computer vision and machine learning. In theory, under certain conditions, this problem can be…
This paper presents a weakly intrusive strategy for computing a low-rank approximation of the solution of a system of nonlinear parameter-dependent equations. The proposed strategy relies on a Newton-like iterative solver which only…
In our recent work \cite{StojnicCSetam09,StojnicUpper10} we considered solving under-determined systems of linear equations with sparse solutions. In a large dimensional and statistical context we proved results related to performance of a…
This paper deals with robust regression and subspace estimation and more precisely with the problem of minimizing a saturated loss function. In particular, we focus on computational complexity issues and show that an exact algorithm with…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…