This paper proposes a general framework for reconstructing sparse images from undersampled (squared)-magnitude data corrupted with outliers and noise. This phase retrieval method uses a layered approach, combining repeated minimization of a convex majorizer (surrogate for a nonconvex objective function), and iterative optimization of that majorizer using a preconditioned variant of the alternating direction method of multipliers (ADMM). Since phase retrieval is nonconvex, this implementation uses multiple initial majorization vectors. The introduction of a robust 1-norm data fit term that is better adapted to outliers exploits the generality of this framework. The derivation also describes a normalization scheme for the regularization parameter and a known adaptive heuristic for the ADMM penalty parameter. Both 1D Monte Carlo tests and 2D image reconstruction simulations suggest the proposed framework, with the robust data fit term, reduces the reconstruction error for data corrupted with both outliers and additive noise, relative to competing algorithms having the same total computation.

Fig. 1: Viewpoint estimation. Given an image containing objects from known categories, our model estimates the viewpoints (azimuth) of the objects. The image to the right is an animation that may be viewed in Adobe Acrobat Reader.Abstract. This paper addresses the problem of viewpoint estimation of an object in a given image. It presents five key insights that should be taken into consideration when designing a CNN that solves the problem. Based on these insights, the paper proposes a network in which (i) The architecture jointly solves detection, classification, and viewpoint estimation. (ii) New types of data are added and trained on. (iii) A novel loss function, which takes into account both the geometry of the problem and the new types of data, is propose. Our network improves the state-of-the-art results for this problem by 9.8%.

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