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We address the problem of Compressed Sensing (CS) with side information. Namely, when reconstructing a target CS signal, we assume access to a similar signal. This additional knowledge, the side information, is integrated into CS via ℓ1-ℓ1 and ℓ1-ℓ2 minimization. We then provide lower bounds on the number of measurements that these problems require for successful reconstruction of the target signal...
Alternating minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems. Theoretical guarantees for alternating minimization have been hard to come by and are still poorly understood. This is in part because the heuristic is iterative and non-convex in nature. We give a new algorithm based on alternating minimization that provably...
This paper addresses the problem of computing the intersection of regular languages in a privacy-preserving fashion. Private set intersection has been addressed earlier in the literature, but for finite sets only. We discuss the various possibilities for solving the problem efficiently, and argue for an approach based on minimal deterministic finite automata (DFA) as a suitable, non-leaking representation...
Network resource allocation problems are concerned with the allocation of limited resources among competing entities so as to respect some fairness rules while looking for the overall efficiency. This paper presents the methodology of fair optimization representing inequality averse optimization rather than strict inequality minimization as foundation of fairness in resource allocation. Commonly applied...
Spectrum cartography is the process of constructing a map showing Radio Frequency signal strength over a finite geographical area. In our previous work we formulated spectrum cartography as a compressive sensing problem and we illustrated how cartography can be used in the context of discovering spectrum holes in space that can be exploited locally in cognitive radio networks. This paper investigates...
Motivated by a variational formulation of the motion segmentation problem, we propose a fully implicit variant of the (linearized) alternating direction method of multipliers for the minimization of convex functionals over a convex set. The new scheme does not require a step size restriction for stability and thus approaches the minimum using considerably fewer iterates. In numerical experiments on...
Reduction of the out-of-band (OOB) emission is essential for Cognitive Radio (CR) systems to enable coexistence with licensed (primary) systems operating in the adjacent frequency bands. This paper proposes an algorithm for the Non Contiguous Orthogonal Frequency Division Multiplexing (NC-OFDM)-based CR, to reduce the interference caused by both OOB radiation and by non-ideal frequency selectivity...
In this paper, we consider using total variation minimization to recover signals whose gradients have a sparse support, from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV) minimization in recovering one-dimensional signal with sparse gradient support. This partially answers the open problem of proving the fidelity of total variation minimization...
Our work is motivated by energy minimization in the space of rigid affine transformations of macromolecules, an essential step in computational protein-protein docking. We introduce a novel representation of rigid body motion that leads to a natural formulation of the energy minimization problem as an optimization on the SO(3)×ℜ3 manifold, rather than the commonly used SE(3). The new representation...
Using an intelligent supplier selection support structure to determine optimal suppliers, as based on the future development strategies of a company, is very important to the members of the chain restaurant industry in the current consumer demand-oriented market. Hence, this study conducted research in the following four parts: 1) supplier specification design, 2) the clustering design of the modified...
In this paper we focus on the problem of visual odometry, i.e., the task of tracking the pose of a moving platform using visual measurements. In recent years, several VO algorithms have been proposed that employ nonlinear minimization in a sliding window of poses for this task. Through the use of iterative re-linearization, these methods are capable of successfully addressing the nonlinearity of the...
We propose a new algorithm to recover a sparse signal from a system of linear measurements. By projecting the measured signal onto a properly chosen subspace, we can use the projection to zero in on a low-sparsity portion of our original signal, which we can recover using ℓ1-minimization. We can then recover the remaining portion of our signal from an overdetermined system of linear equations. We...
In this paper, we propose an adaptive compressed sensing scheme that utilizes a support estimate to focus the measurements on the large valued coefficients of a compressible signal. We embed a “sparse-filtering” stage into the measurement matrix by weighting down the contribution of signal coefficients that are outside the support estimate. We present an application which can benefit from the proposed...
In the field of computer vision, pyramid matching by minimization has gained increasing popularity. This paper points out and discusses an inherent anomaly in pyramid matching by minimization that can affect the performance of classification approaches based on this type of matching. As a solution, a new multiresolution measure, called Manhattan-Pyramid Distance (MPD), is proposed. Systematic evaluations...
We present a preprocessing algorithm to make certain polynomial algorithms strongly polynomial. The running time of some of the known combinatorial optimization algorithms depends on the size of the objective function w. Our preprocessing algorithm replaces w by an integral valued w whose size is polynomially bounded in the size of the combinatorial structure and which yields the same set of optimal...
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