Theory, Algorithms, and Applications of Signal Processing with the Sparseness Constraint

CCR-9902961稀疏约束信号处理的理论、算法和应用本研究项目将在几个重要的应用领域研究稀疏约束信号处理问题中出现的理论和计算问题。研究计划包括使用优选化理论来开发和识别合适的多样性度量，其最小化导致稀疏解。然后，为了最大限度地减少这些措施，将开发、分析和应用一类新的优化算法。基于梯度分解表示的算法和基于仿射尺度变换(AST)的内点优化理论方法将是本文工作的起点。为了便于更全面地理解这些方法，并开发出对噪声具有健壮性的方法，将采用贝叶斯框架。研究了多测量向量问题的重要扩展，极大地拓展了应用范围。将开发学习算法，以调整特定应用环境所需的过完备词典，从而提高其整体有效性。理论和算法的开发将以应用程序的要求为指导。将特别关注使用脑磁图(MEG)进行信号表示和神经磁成像的应用(脑磁图是一种潜在的重要的脑成像新方法)。

CCR-9902961RaoTHEORY, ALGORITHMS, AND APPLICATIONS OF SIGNAL PROCESSING WITH THE SPARSENESS CONSTRAINT This research project will examine the theoretical and computational issues that arise in signal processing problems with the sparseness constraint in several important application domains. The research plan includes using majorization theory to develop and identify suitable diversity measures whose minimization leads to sparse solutions. Then, to minimize these measures, a new class of optimization algorithms will be developed, analyzed, and applied. Algorithms based on a factored representation for the gradient along with Affine Scaling Transformation (AST) based methods of interior point optimization theory will be the starting point of this work. To facilitate a more comprehensive understanding of the methods, and to develop methods robust to noise, a Bayesian framework will be employed. The important extension to the multiple measurement vector problem will be studied greatly expanding the range of applications. Learning algorithms will be developed to tune the required overcomplete dictionaries for specific application environments, thereby increasing their overall effectiveness. Theoretical and algorithmic development will be guided by the requirements of the applications. Particular attention will be given to the applications of signal representation and neuromagnetic imaging using Magnetoencephalography (MEG) (a potentially important new modality for the imaging of the brain).