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，也可以是空间的，可以是连续的，也可以是离散的。因此，多维系统包含了大量基于偏差分方程组、偏差分方程组和微分-差分方程组的动力系统。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。 这项研究方案涉及开发MD系统的新设计和实现技术，以解决上述应用领域的问题。 在光场处理领域，将使用光场的4D表示来开发用于深度过滤、重新聚焦和基于图像的绘制的新技术。这种方法将允许在4D频域中进行设计，并使用为2D和3D系统开发的设计方法。预计这将导致比当前技术水平的光场处理方法在计算上显著更有效的技术。 在图像和视频处理领域，工作重点将是从梯度域处理或从Shack-Hartmann波前传感器等测量获得的梯度数据重建图像/视频。该方法将是基于小波的多分辨率，这将进一步允许在每个分辨率使用泊松解算器来提高精度。视频编辑、视觉逼真渲染将是需要考虑的一些应用程序。 在宽带波束形成领域，将为通信和射电天文学等应用开发MD滤波器的新技术和有效实现。这一领域的挑战是开发在广泛的时间频率范围内具有高角度选择性的系统的设计技术，同时又可以有效地实施。 由于具有多个自变量的信号是许多应用的核心，拟议的研究有望在几个应用领域产生重要的和新颖的结果。特别是在宽带波束形成、视频处理和光场处理方面的工作将为这些快速发展的研究领域中的快速和计算高效的方法开辟新的可能性。

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.