Investigating Task-driven Latent Feasibility for Nonconvex Image Modeling

Properly modeling latent image distributions plays an important role in a variety of image-related vision problems. Most exiting approaches aim to formulate this problem as optimization models (e.g., Maximum A Posterior, MAP) with handcrafted priors. In recent years, different CNN modules are also considered as deep priors to regularize the image modeling process. However, these explicit regularization techniques require deep understandings on the problem and elaborately mathematical skills. In this work, we provide a new perspective, named Task-driven Latent Feasibility (TLF), to incorporate specific task information to narrow down the solution space for the optimization-based image modeling problem. Thanks to the flexibility of TLF, both designed and trained constraints can be embedded into the optimization process. By introducing control mechanisms based on the monotonicity and boundedness conditions, we can also strictly prove the convergence of our proposed inference process. We demonstrate that different types of image modeling problems, such as image deblurring and rain streaks removals, can all be appropriately addressed within our TLF framework. Extensive experiments also verify the theoretical results and show the advantages of our method against existing state-of-the-art approaches.Comment: 11 pages, Accepted at IEEE TI

Robust Algorithms for Low-Rank and Sparse Matrix Models

Data in statistical signal processing problems is often inherently matrix-valued, and a natural first step in working with such data is to impose a model with structure that captures the distinctive features of the underlying data. Under the right model, one can design algorithms that can reliably tease weak signals out of highly corrupted data. In this thesis, we study two important classes of matrix structure: low-rankness and sparsity. In particular, we focus on robust principal component analysis (PCA) models that decompose data into the sum of low-rank and sparse (in an appropriate sense) components. Robust PCA models are popular because they are useful models for data in practice and because efficient algorithms exist for solving them. This thesis focuses on developing new robust PCA algorithms that advance the state-of-the-art in several key respects. First, we develop a theoretical understanding of the effect of outliers on PCA and the extent to which one can reliably reject outliers from corrupted data using thresholding schemes. We apply these insights and other recent results from low-rank matrix estimation to design robust PCA algorithms with improved low-rank models that are well-suited for processing highly corrupted data. On the sparse modeling front, we use sparse signal models like spatial continuity and dictionary learning to develop new methods with important adaptive representational capabilities. We also propose efficient algorithms for implementing our methods, including an extension of our dictionary learning algorithms to the online or sequential data setting. The underlying theme of our work is to combine ideas from low-rank and sparse modeling in novel ways to design robust algorithms that produce accurate reconstructions from highly undersampled or corrupted data. We consider a variety of application domains for our methods, including foreground-background separation, photometric stereo, and inverse problems such as video inpainting and dynamic magnetic resonance imaging.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143925/1/brimoor_1.pd