Multi-dimensional Systems Design and Implementation

多维(MD)系统用于处理具有多于一个自变量的信号。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微分方程组、偏差分方程组和微分-差分方程组的动力学系统。MD系统的一些最重要的应用包括图像、视频、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。在光场图像处理领域，将开发新的深度过滤、重聚焦遮挡抑制和基于图像的绘制技术。处理光场视频的工作将涉及深度速度滤波和去噪。这里使用的方法将基于分析4D和5D频域中的光场图像和视频。这将允许通过扩展为2D和3D系统开发的设计方法来进行设计。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。另一个新兴的应用是光领域的编辑。这里将用一种新的方法来解决这一问题，该方法基于在梯度域而不是强度域中进行编辑。这项工作将侧重于从梯度域处理获得的梯度数据重建光场图像/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迭代泊松求解器来提高平滑度。在宽带波束形成领域，MD滤波器的新技术和高效实现将被开发用于通信、射电天文等应用。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现。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，光场图像和视频处理的工作将提供新的方法来处理重要的新兴应用。宽带波束形成的工作将为在各种应用中实现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 dynamic systems based on partial differential, partial difference and differential-difference equations. Some of the most important applications of MD systems include image, video, 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 image processing, new techniques for depth filtering, refocusing occlusion suppression and image based rendering will be developed. The work on processing of light field videos will deal with depth-velocity filtering and denoising. The approach used here will be based on analyzing the light field images and video in the 4D and 5D frequency domain. This will allow carrying out the design by extending 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. Another emerging application is light field is editing. This will be addressed here with a new method which is based on editing in the gradient domain instead of the intensity domain. The work will focus on the reconstruction of light field images/video from gradient data obtained from processing in the gradient domain. The approach will be wavelet based, multiresolution which will further allow the use of iterative Poisson solvers at each resolution to improve smoothness. In the area of broadband beamforming, new techniques and efficient implementations of MD filters will be developed for applications such as communications, radio astronomy etc. 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 light field image and video processing will have provide new methods to deal with important emerging applications. The work on broadband beamforming, will open new possibilities for fast and computationally efficient methods of implementations in various applications.