Variable Weighted Ordered Subset Image Reconstruction Algorithm

We propose two variable weighted iterative reconstruction algorithms (VW-ART and VW-OS-SART) to improve the algebraic reconstruction technique (ART) and simultaneous algebraic reconstruction technique (SART) and establish their convergence. In the two algorithms, the weighting varies with the geometrical direction of the ray. Experimental results with both numerical simulation and real CT data demonstrate that the VW-ART has a significant improvement in the quality of reconstructed images over ART and OS-SART. Moreover, both VW-ART and VW-OS-SART are more promising in convergence speed than the ART and SART, respectively

Model-based X-ray CT Image and Light Field Reconstruction Using Variable Splitting Methods.

Model-based image reconstruction (MBIR) is a powerful technique for solving ill-posed inverse problems. Compared with direct methods, it can provide better estimates from noisy measurements and from incomplete data, at the cost of much longer computation time. In this work, we focus on accelerating and applying MBIR for solving reconstruction problems, including X-ray computed tomography (CT) image reconstruction and light field reconstruction, using variable splitting based on the augmented Lagrangian (AL) methods. For X-ray CT image reconstruction, we combine the AL method and ordered subsets (OS), a well-known technique in the medical imaging literature for accelerating tomographic reconstruction, by considering a linearized variant of the AL method and propose a fast splitting-based ordered-subset algorithm, OS-LALM, for solving X-ray CT image reconstruction problems with penalized weighted least-squares (PWLS) criterion. Practical issues such as the non-trivial parameter selection of AL methods and remarkable memory overhead when considering the finite difference image variable splitting are carefully studied, and several variants of the proposed algorithm are investigated for solving practical model-based X-ray CT image reconstruction problems. Experimental results show that the proposed algorithm significantly accelerates the convergence of X-ray CT image reconstruction with negligible overhead and greatly reduces the noise-like OS artifacts in the reconstructed image when using many subsets for OS acceleration. For light field reconstruction, considering decomposing the camera imaging process into a linear convolution and a non-linear slicing operations for faster forward projection, we propose to reconstruct light field from a sequence of photos taken with different focus settings, i.e., a focal stack, using an alternating direction method of multipliers (ADMM). To improve the quality of the reconstructed light field, we also propose a signal-independent sparsifying transform by considering the elongated structure of light fields. Flatland simulation results show that our proposed sparse light field prior produces high resolution light field with fine details compared with other existing sparse priors for natural images.PhDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/108981/1/hungnien_1.pd

Optimizing Ranking Measures for Compact Binary Code Learning

Hashing has proven a valuable tool for large-scale information retrieval. Despite much success, existing hashing methods optimize over simple objectives such as the reconstruction error or graph Laplacian related loss functions, instead of the performance evaluation criteria of interest---multivariate performance measures such as the AUC and NDCG. Here we present a general framework (termed StructHash) that allows one to directly optimize multivariate performance measures. The resulting optimization problem can involve exponentially or infinitely many variables and constraints, which is more challenging than standard structured output learning. To solve the StructHash optimization problem, we use a combination of column generation and cutting-plane techniques. We demonstrate the generality of StructHash by applying it to ranking prediction and image retrieval, and show that it outperforms a few state-of-the-art hashing methods.Comment: Appearing in Proc. European Conference on Computer Vision 201

Random sampling of bandlimited signals on graphs

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than O(k log(k)) measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques