Sparse coding has become an increasingly popular method in learning and vision for a variety of classification, reconstruction and coding tasks. The canonical approach intrinsically assumes independence between observations during learning. For many natural signals however, sparse coding is applied to sub-elements ( i.e. patches) of the signal, where such an assumption is invalid. Convolutional sparse coding explicitly models local interactions through the convolution operator, however the resulting optimization problem is considerably more complex than traditional sparse coding. In this paper, we draw upon ideas from signal processing and Augmented Lagrange Methods (ALMs) to produce a fast algorithm with globally optimal subproblems and super-linear convergence.

Compressive Sensing has become one of the standard methods of face recognition within the literature. We show, however, that the sparsity assumption which underpins much of this work is not supported by the data. This lack of sparsity in the data means that compressive sensing approach cannot be guaranteed to recover the exact signal, and therefore that sparse approximations may not deliver the robustness or performance desired. In this vein we show that a simple 2 approach to the face recognition problem is not only significantly more accurate than the state-of-theart approach, it is also more robust, and much faster. These results are demonstrated on the publicly available YaleB and AR face datasets but have implications for the application of Compressive Sensing more broadly.

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Maximum consensus is one of the most popular criteria for robust estimation in computer vision. Despite its widespread use, optimising the criterion is still customarily done by randomised sample-and-test techniques, which do not guarantee optimality of the result. Several globally optimal algorithms exist, but they are too slow to challenge the dominance of randomised methods. Our work aims to change this state of affairs by proposing an efficient algorithm for global maximisation of consensus. Under the framework of LP-type methods, we show how consensus maximisation for a wide variety of vision tasks can be posed as a tree search problem. This insight leads to a novel algorithm based on A* search. We propose efficient heuristic and support set updating routines that enable A* search to efficiently find globally optimal results. On common estimation problems, our algorithm is much faster than previous exact methods. Our work identifies a promising direction for globally optimal consensus maximisation.