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We present a family of online algorithms for real-time factorization-based structure from motion, leveraging a relationship between the incremental singular value decomposition and recent work in online matrix completion. Our methods are orders of magnitude faster than previous state of the art, can handle missing data and a variable number of feature points, and are robust to noise and sparse outliers...
We discuss inherent robust stability properties of discrete-time nonlinear systems controlled by Model Predictive Control (MPC) algorithms that do not necessarily attain the global minimum of the optimization problem solved at each sample time. For these implementable suboptimal MPC algorithms, we prove nominal exponential stability of the origin of the closed-loop system. The stability property is...
This paper studies the problem of simultaneously aligning a batch of linearly correlated images despite gross corruption (such as occlusion). Our method seeks an optimal set of image domain transformations such that the matrix of transformed images can be decomposed as the sum of a sparse matrix of errors and a low-rank matrix of recovered aligned images. We reduce this extremely challenging optimization...
This paper studies algorithms for solving the problem of recovering a low-rank matrix with a fraction of its entries arbitrarily corrupted. This problem can be viewed as a robust version of classical PCA, and arises in a number of application domains, including image processing, web data ranking, and bioinformatic data analysis. It was recently shown that under surprisingly broad conditions, it can...
We consider the problem of estimating a state x from noisy and corrupted linear measurements y = Ax + z + e, where z is a dense vector of small-magnitude noise and e is a relatively sparse vector whose entries can be arbitrarily large. We study the behavior of the lscr1 estimator xcirc = arg minx ||y - Ax||1, and analyze its breakdown point with respect to the number of corrupted measurements ||e||...
We consider the problem of automatically recognizing human faces from frontal views with varying expression and illumination, as well as occlusion and disguise. We cast the recognition problem as one of classifying among multiple linear regression models and argue that new theory from sparse signal representation offers the key to addressing this problem. Based on a sparse representation computed...
This work builds on the method of to create a prototype access control system, capable of handling variations in illumination and expression, as well as significant occlusion or disguise. Our demonstration will allow participants to interact with the algorithm, gaining a better understanding strengths and limitations of sparse representation as a tool for robust recognition.
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