—A system which embeds watermarks in-dimensional Gaussian data and distributes them in compressed form is studied. The watermarked/compressed data have to satisfy a distortion constraint, and the watermark has to be recoverable in a private scenario (in which the original data are available at the watermark detector). The performance of the system in the… (More)
This thesis is devoted to a range of questions in applied mathematics and signal processing motivated by applications in error correction, compressed sensing, and writing on non-volatile memories. The underlying thread of our results is the use of diverse combinatorial methods originating in coding theory and computer science. The thesis addresses three… (More)
The effects produced in an image by cast shadows can be quite complex, especially when light comes from all directions. This makes it difficult to recover the illumination from a scene and recognize objects from the images. In this paper, we show that such images can be well approximated using much simpler lighting represented by a combination of low… (More)
A popular method for unsupervised classification of high-dimensional data via decision trees is characterized as minimizing the empirical estimate of a concave information functional. It is shown that minimization of such functionals under the true distributions leads to perfect classification.