About Notations in Multiway Array Processing

This paper gives an overview of notations used in multiway array processing. We redefine the vectorization and matricization operators to comply with some properties of the Kronecker product. The tensor product and Kronecker product are also represented with two different symbols, and it is shown how these notations lead to clearer expressions for multiway array operations. Finally, the paper recalls the useful yet widely unknown properties of the array normal law with suggested notations

Spectral Unmixing with Multiple Dictionaries

Spectral unmixing aims at recovering the spectral signatures of materials, called endmembers, mixed in a hyperspectral or multispectral image, along with their abundances. A typical assumption is that the image contains one pure pixel per endmember, in which case spectral unmixing reduces to identifying these pixels. Many fully automated methods have been proposed in recent years, but little work has been done to allow users to select areas where pure pixels are present manually or using a segmentation algorithm. Additionally, in a non-blind approach, several spectral libraries may be available rather than a single one, with a fixed number (or an upper or lower bound) of endmembers to chose from each. In this paper, we propose a multiple-dictionary constrained low-rank matrix approximation model that address these two problems. We propose an algorithm to compute this model, dubbed M2PALS, and its performance is discussed on both synthetic and real hyperspectral images

Cameras in the Courtroom and Due Process: A Proposal for a Qualitative Difference Test

The issue of cameras in the courtroom is at a crossroads. Many criminal defendants tried in the presence of the electronic media have claimed that they were denied due process, yet neither the Washington courts nor the federal courts have adequately defined the standards under which these claims will be evaluated. This failure to reach a definition has left the courts unable to state why cameras will be permitted at one trial and not at another. Creating standards to determine when the presence of cameras denies a defendant due process is not an easy task. The most promising judicial approach to emerge is the qualitative difference test. This test recognizes that the presence of cameras at a trial holds the potential to alter the conduct or outcome of a trial. This test originated in the Florida courts, and is still in its infancy. The qualitative difference test does not yet adequately define or provide a substantive standard courts can rely on to make consistent decisions. Further development is needed before a qualitative difference test can offer governing principles. This comment first reviews the federal law on the role of due process in deciding whether to allow cameras in court. The Washington and Florida experiences with cameras in the courtroom are then examined in an attempt to add substance to the constitutional threshold. By placing the entire issue in the proper context we can chart a course of action that will lead to a useful and workable resolution of lingering problems