Multi-dimensional Systems Design and Implementation

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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.