In this paper, we revisit the forward, backward and bidirectional Bahl-Cocke-Jelinek-Raviv (BCJR) soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 convolutional codes. From this we establish some interesting duality properties between encoding and decoding of rate-1 convolutional codes. We observe that the forward and backward BCJR SISO MAP decoder...

Recently, the stereo imaging-based image enhancement approach has attracted increasing attention in the field of video analysis. This paper presents a dual camera-based stereo image defogging algorithm. Optical flow is first estimated from the stereo foggy image pair, and the initial disparity map is generated from the estimated optical flow. Next, an initial transmission map is generated using...

Introduction:  The  advent  of  dual-modality  PET/CT  scanners  has  revolutionized  clinical  oncology  by  improving lesion localization and facilitating treatment planning for radiotherapy. In addition, the use of  CT images for CT-based attenuation correction (CTAC) decreases the overall scanning time and creates  a noise-free  attenuation  map  (6map).  CTAC  methods  include  scaling,  s...

Abstract. A rectangular cartogram is a type of map where every region is a rectangle. The size of the rectangles is chosen such that their areas represent a geographic variable such as population or GDP. In recent years several algorithms for the automated construction of rectangular cartograms have been proposed, some of which are based on rectangular duals of the dual graph of the input map. ...

We show that every uniformly asymptotically affine circle endomorphism has a uniformly asymptotically conformal (UAC) extension to the complex plane. Then we use the UAC extension to construct the dual dynamical system, the dual annulus, and the dual circle expanding map.

We show how to map the Belavin-Polyakov instantons of the O(3)-nonlinear sigma model to a dual theory where they then appear as nontopological solitons. They are stationary points of the Euclidean action in the dual theory, and moreover, the dual action and the O(3)-nonlinear sigma model action agree on shell.

This paper is a brief survey of momentum maps, dual pairs and reduction in deformation quantization. We recall the classical theory of momentum maps in Poisson geometry and present its quantum counterpart. We also discuss quantization of momentum maps and applications of quantum momentum maps to quantum versions of Marsden-Weinstein reduction. This paper is organized as follows. We recall the c...

Let $f\colon (\mathbb {R}^{3},0)\to {R}^{4},0)$ be an analytic map germ with isolated instability. Its link is a stable which obtained by taking the intersection of image $f$ small enough sphere $S^{3}_\epsilon$ centred at origin in $\mathbb {R}^{4}$ . If fold type, we define tree, that call dual contains all topological information and prove this case it complete invariant. As application give...