Foveated, log-polar, or space-variant image architectures provide a high resolution and wide field workspace, while providing a small pixel computation load. These characteristics are ideal for mobile robotic and active vision applications, but have been little used due to the general lack of image processing tools that are applicable to the log-polar coordinate system. Recently, we have descri...

A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum algorithms. We present a divide-and-conquer approach to the design of various quantum algorithms. The class of algorithm includes many transforms which are well-k...

We discuss interplays between log-concave functions and log-concave sequences. We prove a Bernstein-type theorem, which characterizes the Laplace transform of logconcave measures on the half-line in terms of log-concavity of the alternating Taylor coefficients. We establish concavity inequalities for sequences inspired by the PrékopaLeindler and the Walkup theorems. One of our main tools is a s...

The Reciprocal-Wedge Transform (RWT) is presented as an alternative to the log-polar transform which has been a popular model for space-variant sensing in computer vision. The log-polar transform provides efficient data reduction. It simplifies the centric rotational and scaling image transformations. However, it adversely complicates the linear features and translational transformations. The R...

Well log is a data manifestation of geographical, chemical, physical and other information detected in different geological environment and formation condition by means of different well log methods. Aiming at the noise existing in well log signal and the property of its morphological characteristics and combining and analyzing bilinear interpolation algorithm and the theory of wavelet transfor...

We prove that the Fenchel dual of the log-Laplace transform of the uniform measure on a convex body in Rn is a (1 + o(1))n-self-concordant barrier. This gives the first construction of a universal barrier for convex bodies with optimal self-concordance parameter. The proof is based on basic geometry of log-concave distributions, and elementary duality in exponential families.

The generalized Motzkin numbers are common generalizations of the Motzkin numbers and the Catalan numbers. We investigate their combinatorial properties, including the combinatorial interpretation, the recurrence relation, the binomial transform, the Hankel transform, the log-convexity, the continued fraction of the generating function, and the total positivity of the corresponding Hankel matrix.