— New bounds on the rate distortion function of certain non-Gaussian sources, with a proportional-weighted mean-square error (MSE) distortion measure, are given. The growth, g, of the rate distortion function, as a result of changing from a non-weighted MSE distortion measure to a proportional-weighted distortion criterion is analyzed. It is shown that for a small distortion, d, the growth, g, ...

Gaussian convolution is of fundamental importance in linear scale-space theory and in numerous applications. We introduce iterated extended box filtering as an efficient and highly accurate way to compute Gaussian convolution. Extended box filtering approximates a continuous box filter of arbitrary non-integer standard deviation. It provides a much better approximation to Gaussian convolution t...

The explicit form of the rate-distortion function has rarely been obtained, except for few cases where the Shannon lower bound coincides with the rate-distortion function for the entire range of the positive rate. From an information geometrical point of view, the evaluation of the rate-distortion function is achieved by a projection to the mixture family defined by the distortion measure. In t...

We show tight bounds for both online integer multiplication and convolution in the cell-probe model with word size w. For the multiplication problem, one pair of digits, each from one of two n digit numbers that are to be multiplied, is given as input at step i. The online algorithm outputs a single new digit from the product of the numbers before step i + 1. We give a Θ (

Digital signals are complex-valued functions on Zn. Signal sets with certain properties are required in various communication systems. Traditional signal sets consider only the time distortion during transmission. Recently, signal sets against both the time and phase distortion have been studied, and are called time-phase signal sets. Several constructions of time-phase signal sets are availabl...

We obtain estimates for derivative and cross–ratio distortion for C (any η > 0) unimodal maps with non–flat critical points. We do not require any ‘Schwarzian–like’ condition. For two intervals J ⊂ T , the cross–ratio is defined as the value B(T, J) := |T ||J | |L||R| where L, R are the left and right connected components of T \J respectively. For an interval map g such that gT : T → R is a dif...

In recent years attention has been turned to the use of neural network-derived algorithms to restore images using a model-based approach. Considering an M by M input image, in most cases the image degradation model is a spatially and temporally invariant linear distortion described by the equation (Pratt [1]) (Andrews and Hunt [2]): Where f and g are the M2 by 1 lexicographically organized orig...

We compared cortical folding patterns between patients with schizophrenia and demographically-matched healthy controls in prefrontal and temporal regions of interest. Using the Freesurfer (http://surfer.nmr.mgh.harvard.edu) cortical surface-based reconstruction methodology, we indirectly ascertained cortical displacement and convolution, together, by measuring the degree of metric distortion re...

Article history: Received 24 January 2008 Received in revised form 6 May 2008 Available online 20 May 2008 Communicated by C. Scheideler