Ruscheweyh and Sheil-Small proved that convexity is preserved under the convolution of univalent analytic mappings in K. However, when we consider the convolution of univalent harmonic convex mappings in K H , this property does not hold. In fact, such convolutions may not be univalent. We establish some results concerning the convolution of univalent harmonic convex mappings provided that it i...

Convolution is a fundamental operation in many signal and image processing applications. Since the computation and communication pattern in a convolution operation is regular, a number of special architectures have been designed and implemented for this operator. The Von Neuman architectures cannot meet the real-time requirements of applications that use convolution as an intermediate step. We ...

We introduce and study a new type of convolution of probability measures called the orthogonal convolution, which is related to the monotone convolution. Using this convolution, we derive alternating decompositions of the free additive convolution μ` ν of compactly supported probability measures in free probability. These decompositions are directly related to alternating decompositions of the ...

In this session we want to review the basic concepts introduced in class for convolution in continuous-time. It has been proved that in order to determine the characteristics of a linear, time-invariant (LTI) system we need to know the impulse response of the system. When we apply an input x(t) to a system that has h(t) as its impulse response, we obtain an output y(t) (see Figure 1). One of th...

Many image processing algorithms exist in pairs: a forward mapping version and a reverse mapping version [9], [10]. In this paper we show that the forward and reverse versions of spatially-varying convolution filters are transpose to each other. We will then show how an implementation of a function that operates linearly on a set of variables may be transformed into an implementation of its tra...

This paper describes improved piecewise cubic convolution for two-dimensional image reconstruction. Piecewise cubic convolution is one of the most popular methods for image reconstruction, but the traditional approach uses a separable two-dimensional convolution kernel that is based on a onedimensional derivation. The traditional approach is suboptimal for the usual case of non-separable scenes...