Numerous tasks at the core of statistics, learning and vision areas are specific cases of ill-posed inverse problems. Recently, learning-based (e.g., deep) iterative methods have been empirically shown to be useful for these problems. Nevertheless, integrating learnable structures into iterations is still a laborious process, which can only be guided by intuitions or empirical insights. Moreover, there is a lack of rigorous analysis about the convergence behaviors of these reimplemented iterations, and thus the significance of such methods is a little bit vague. This paper moves beyond these limits and proposes Flexible Iterative Modularization Algorithm (FIMA), a generic and provable paradigm for nonconvex inverse problems. Our theoretical analysis reveals that FIMA allows us to generate globally convergent trajectories for learning-based iterative methods. Meanwhile, the devised scheduling policies on flexible modules should also be beneficial for classical numerical methods in the nonconvex scenario. Extensive experiments on real applications verify the superiority of FIMA.

The Next Release Problem (NRP) aims to optimize customer profits and requirements selection for the software releases. The research on the NRP is restricted by the growing scale of requirements. In this paper, we propose a Backbone-based Multilevel Algorithm (BMA) to address the large scale NRP. In contrast to direct solving approaches, the BMA employs multilevel reductions to downgrade the problem scale and multilevel refinements to construct the final optimal set of customers. In both reductions and refinements, the backbone is built to fix the common part of the optimal customers. Since it is intractable to extract the backbone in practice, the approximate backbone is employed for the instance reduction while the soft backbone is proposed to augment the backbone application. In the experiments, to cope with the lack of open large requirements databases, we propose a method to extract instances from open bug repositories. Experimental results on 15 classic instances and 24 realistic instances demonstrate that the BMA can achieve better solutions on the large scale NRP instances than direct solving approaches. Our work provides a reduction approach for solving large scale problems in search-based requirements engineering.

Rain streaks removal is an important issue of the outdoor vision system and recently has been investigated extensively. In the past decades, maximum a posterior and network-based architecture have been attracting considerable attention for this problem. However, it is challenging to establish effective regularization priors and the cost function with complex prior is hard to optimize. On the other hand, it is still hard to incorporate data-dependent information into conventional numerical iterations. To partially address the above limits and inspired by the leader-follower gaming perspective, we introduce an unrolling strategy to incorporate data-dependent network architectures into the established iterations, i.e., a learning bilevel layer priors method to jointly investigate the learnable feasibility and optimality of rain streaks removal problem. Both visual and quantitative comparison results demonstrate that our method outperforms the state of the art.

We address the challenging issue of reconstructing a 3D face from one single image under various expressions and illuminations, which is widely applied in multimedia tasks. Methods built upon classical parametric morphable models (3DMMs) gain success on reconstructing the global geometry of a 3D face, but fail to precisely characterize local facial details. Recently, deep neural networks (DNN) have been applied to the reconstruction that directly predicts depth maps, showing compelling performance on detail recovery. Unfortunately, their reconstruction is prone to structural distortions owing to the lack of explicit prior constraints. In this paper, we propose dual neural networks that optimize one energy coupling data fitting with local explicit geometric prior. Specifically, we build one residual network upon traditional convolution layers in order to directly predict 3D structures by fitting an input image. Meanwhile, we devise a novel architecture stacking shallow networks to refine 3D clouds with geometric priors given by Markov random fields (MRFs). Quantitative evaluations demonstrate the superior performance of the dual networks over either end-to-end DNNs or parametric models. Comparisons with the state-of-the-art also show competitive reconstruction quality on various conditions.