Multidimensional System Design and Implementation

多维（MD）系统用于处理具有多个自变量的信号。这些变量可以是时间的或空间的，连续的或离散的。因此，多维系统包含了基于偏差分、偏差分和微分-差分方程的多种动力系统。MD系统的一些最重要的应用包括图像、视频和光场处理以及平面波携带的宽带信号的处理。

Multi-dimensional (MD) Systems are used to process signals which have more than one independent variable. These variables can be temporal or spatial, continuous or discrete. As such multidimensional systems encompass a large variety of dynamical systems based on partial difference, partial difference and differential-difference equations. Some of the most important applications of MD systems include image, video and light field processing as well as processing of broadband signals carried by plane waves. This research proposal deals with the development of new design and implementation techniques of MD systems to address problems in the above application areas. In the area of light field processing, new techniques for depth filtering, refocusing and image based rendering will be developed using a 4D representation of light fields. This approach will allow carrying out the design in the 4D frequency domain and using design methods developed for 2D and 3D systems. This is expected to lead to techniques which will be considerably more computationally efficient than current state of the art light field processing methods. In the area of image and video processing, the work will focus on the reconstruction of images/video from gradient data obtained either from processing in the gradient domain or from measurements like the Shack-Hartmann wavefront sensor. The approach will be wavelet based, multiresolution which will further allow the use of Poisson solvers at each resolution to improve accuracy. Video editing, vision-realistic rendering will be some of the applications to be considered. In the area of broadband beamforming, new techniques and efficient implementations of MD filters will be developed for applications such as communications and radio astronomy. The challenge in this area is to develop design techniques for systems with high angular selectivity over a wide range of temporal frequencies and which at the same time can be implemented efficiently. Since signals which have more than one independent variable are central to many applications, the proposed research is expected to lead to important and novel results for several applications areas. In particular the work on broadband beamforming, video processing and light field processing will open new possibilities for fast and computationally efficient methods in these fast evolving research areas.