Principal Components Analysis as enhancement Operator and Compression factor

Principal components analysis (PCA) is effective at compressing information in multivariate data sets by computing orthogonal projections that maximize the amount of data variance. Unfortunately, information content in hyper spectral images does not always coincide with such projections. We propose an application of projection pursuit (pp), which seeks to find a set of projections that are "interesting" in the sense that they deviate from the Gaussian distribution assumption. Once these projections are obtained, they can be used for image compression, segmentation, or enhancement for visual analysis. To find these projections, a two –step iterative process is followed where we first search for a projection that maximizes a projection index based on the information divergence of the projections estimated probability distribution from the Gaussian distribution and then reduce the rank by projections the data on to the subspace orthogonal to the previous projection . To calculate each projections, we use a simplified approach to maximizing the projection index, which does not require optimization algorithm. It searches for a solution by obtaining a set of candidate projections from the data and choosing the one with the highest projection index. The effectiveness of the method is demonstrated through simulated examples as well as data from the hyper spectral digital imagery collection experiment and the spatially enhanced broadband and array spectrograph system.

On Remotest set and Random controls in Kaczmarz algorithm

In this paper we analyse the Kaczmarz projection algorithm with Remotest set and Random control of projection indices and provide a suficient condition such that each projection index appears infinitely many times during the iterations.