Fourier Phase Retrieval with a Single Mask by Douglas-Rachford Algorithm

Douglas-Rachford (DR) algorithm is analyzed for Fourier phase retrieval with a single random phase mask. Local, geometric convergence to a unique fixed point is proved with numerical demonstration of global convergence

A Perfect Match Condition for Point-Set Matching Problems Using the Optimal Mass Transport Approach

We study the performance of optimal mass transport--based methods applied to point-set matching problems. The present study, which is based on the L2 mass transport cost, states that perfect matches always occur when the product of the point-set cardinality and the norm of the curl of the nonrigid deformation field does not exceed some constant. This analytic result is justified by a numerical study of matching two sets of pulmonary vascular tree branch points whose displacement is caused by the lung volume changes in the same human subject. The nearly perfect match performance verifies the effectiveness of this mass transport--based approach.Read More: http://epubs.siam.org/doi/abs/10.1137/12086443

FFTPL: An Analytic Placement Algorithm Using Fast Fourier Transform for Density Equalization

We propose a flat nonlinear placement algorithm FFTPL using fast Fourier transform for density equalization. The placement instance is modeled as an electrostatic system with the analogy of density cost to the potential energy. A well-defined Poisson's equation is proposed for gradient and cost computation. Our placer outperforms state-of-the-art placers with better solution quality and efficiency

Robust Independent Component Analysis viaMinimum γ-Divergence Estimation

Independent component analysis (ICA) has been shown to be useful in many applications. However, most ICA methods are sensitive to data contamination. In this article we introduce a general minimum U-divergence framework for ICA, which covers some standard ICA methods as special cases. Within the U-family we further focus on the γ-divergence due to its desirable property of super robustness for outliers, which gives the proposed method γ-ICA. Statistical properties and technical conditions for recovery consistency of γ-ICA are studied. In the limiting case, it improves the recovery condition of MLE-ICA known in the literature by giving necessary and sufficient condition. Since the parameter of interest in γ-ICA is an orthogonal matrix, a geometrical algorithm based on gradient flows on special orthogonal group is introduced. Furthermore, a data-driven selection for the γ value, which is critical to the achievement of γ-ICA, is developed. The performance, especially the robustness, of γ-ICA is demonstrated through experimental studies using simulated data and image data

WKGM: Weight-K-space Generative Model for Parallel Imaging Reconstruction

Deep learning based parallel imaging (PI) has made great progresses in recent years to accelerate magnetic resonance imaging (MRI). Nevertheless, it still has some limitations, such as the robustness and flexibility of existing methods have great deficiency. In this work, we propose a method to explore the k-space domain learning via robust generative modeling for flexible calibration-less PI reconstruction, coined weight-k-space generative model (WKGM). Specifically, WKGM is a generalized k-space domain model, where the k-space weighting technology and high-dimensional space augmentation design are efficiently incorporated for score-based generative model training, resulting in good and robust reconstructions. In addition, WKGM is flexible and thus can be synergistically combined with various traditional k-space PI models, which can make full use of the correlation between multi-coil data and realizecalibration-less PI. Even though our model was trained on only 500 images, experimental results with varying sampling patterns and acceleration factors demonstrate that WKGM can attain state-of-the-art reconstruction results with the well-learned k-space generative prior.Comment: 11pages, 12 figure