OEM for least squares problems Xiong, Shifeng; Dai, Bin; Qian, Peter Z G
arXiv (Cornell University),
08/2013
Paper, Journal Article
Odprti dostop
We propose an algorithm, called OEM (a.k.a. orthogonalizing EM), intended for var- ious least squares problems. The first step, named active orthogonization, orthogonalizes an arbi- trary regression ...matrix by elaborately adding more rows. The second step imputes the responses of the new rows. The third step solves the least squares problem of interest for the complete orthog- onal design. The second and third steps have simple closed forms, and iterate until convergence. The algorithm works for ordinary least squares and regularized least squares with the lasso, SCAD, MCP and other penalties. It has several attractive theoretical properties. For the ordinary least squares with a singular regression matrix, an OEM sequence converges to the Moore-Penrose gen- eralized inverse-based least squares estimator. For the SCAD and MCP, an OEM sequence can achieve the oracle property after sufficient iterations for a fixed or diverging number of variables. For ordinary and regularized least squares with various penalties, an OEM sequence converges to a point having grouping coherence for fully aliased regression matrices. Convergence and convergence rate of the algorithm are examined. These convergence rate results show that for the same data set, OEM converges faster for regularized least squares than ordinary least squares. This provides a new theoretical comparison between these methods. Numerical examples are provided to illustrate the proposed algorithm.
Segmentation is one of the most challenging problems in the field of medical image analysis, and blood vessels are especially difficult to extract. In this paper, we propose a novel method for ...segmentation of cerebral blood vessels from magnetic resonance angiography (MRA) images based on Boltzmann theory. The method is composed of three major steps: first, power-law transformation is applied to enhance blood vessels for their weak local contrast. Then a threshold value selected from a histogram analysis with a polyline splitting algorithm is employed to process the enhanced images in order to segment blood vessel regions. Then class region growing algorithm based on Boltzmann theory is adopted to extract blood vessels from background. Results on head MRA datasets demonstrate the availability of the method.
Software-Defined Satellite Payloads Based on Microwave Photonics! Satellite communication offers a number of distinct features that are not readily available with other means of communication, such ...as seamless coverage of remote and sparsely populated areas, reliable data relay for deep-space exploration, inherent multicasting and broadcasting capabilities, and reliable performance in extreme conditions (e.g., war, earthquakes, and other adverse events) 1, 2. In recent years, the steep rise in mobile multimedia applications and increased space exploration activity have created unprecedented opportunities for innovative satellite communication. According to a report provided by the Satellite Industry Association in September 2014, the global revenue of the satellite communication industry for 2013 reached US189.2 billion-60% of global space revenue and 4% of global telecommunications revenue 3. Apple, Google, Amazon, Facebook, and many other large technology companies are currently seeking to bolster their satellite communication systems in the next five to ten years, fostering a continuous increase of revenue in this area.
