On MMSE and MAP Denoising Under Sparse Representation Modeling Over a Unitary Dictionary

Among the many ways to model signals, a recent approach that draws considerable attention is sparse representation modeling. In this model, the signal is assumed to be generated as a random linear combination of a few atoms from a pre-specified dictionary. In this work we analyze two Bayesian denoising algorithms -- the Maximum-Aposteriori Probability (MAP) and the Minimum-Mean-Squared-Error (MMSE) estimators, under the assumption that the dictionary is unitary. It is well known that both these estimators lead to a scalar shrinkage on the transformed coefficients, albeit with a different response curve. In this work we start by deriving closed-form expressions for these shrinkage curves and then analyze their performance. Upper bounds on the MAP and the MMSE estimation errors are derived. We tie these to the error obtained by a so-called oracle estimator, where the support is given, establishing a worst-case gain-factor between the MAP/MMSE estimation errors and the oracle's performance. These denoising algorithms are demonstrated on synthetic signals and on true data (images).Comment: 29 pages, 10 figure

Compact Network Training for Person ReID

The task of person re-identification (ReID) has attracted growing attention in recent years leading to improved performance, albeit with little focus on real-world applications. Most SotA methods are based on heavy pre-trained models, e.g. ResNet50 (~25M parameters), which makes them less practical and more tedious to explore architecture modifications. In this study, we focus on a small-sized randomly initialized model that enables us to easily introduce architecture and training modifications suitable for person ReID. The outcomes of our study are a compact network and a fitting training regime. We show the robustness of the network by outperforming the SotA on both Market1501 and DukeMTMC. Furthermore, we show the representation power of our ReID network via SotA results on a different task of multi-object tracking