In this paper, we propose a novel GPU-based method for highly parallel compressed sensing of n-dimensional (nD) signals based on the smoothed l(0) (SL0) algorithm. We demonstrate the efficiency of our approach by showing several examples of nD tensor reconstructions. Moreover, we also consider the traditional 1D compressed sensing, and compare the results. We show that the multidimensional SL0 algorithm is computationally superior compared to the 1D variant due to the small dictionary sizes per dimension. This allows us to fully utilize the GPU and perform massive batch-wise computations, which is not possible for the 1D compressed sensing using SL0. For our evaluations, we use light field and light field video data sets. We show that we gain more than an order of magnitude speedup for both one-dimensional as well as multidimensional data points compared to a parallel CPU implementation. Finally, we present a theoretical analysis of the SL0 algorithm for nD signals, which generalizes previous work for 1D signals.

Wireless devices have been used to investigate the environment and to understand our physical world. In this work, we undertake the challenging problem of identifying location of obstacles and objects by WiFi signals. Gathering wireless sensory data to form an image is difficult since wireless signals are susceptible to multipath. Moreover, reconstructing an image of unknown objects based on the measurements of sparse signals is an ill-posed problem. To tackle these problems, we first present a linear model using received signal strength indicator (RSSI) measurements. We define the sparse beamforming problem as an l(0)-norm optimization problem, then use the iterative reweighted l(1) heuristic algorithm to obtain an optimal solution as a multipath. Finally, the multipath fading is removed by using Machine Learning. More specifically, we use Support Vector Regression (SVR) to identify a clear image of the unknown object. Our results show that the proposed method can reconstruct signals as a 3D image with a satisfactory visual appearance, i.e. the generated data mesh is well defined and smooth compared to previous work.

Photorealistic rendering is an essential tool for immersive virtual reality. In this regard, the data structure of choice is typically light fields since they contain multidimensional information about the captured environment that can provide motion parallax and view-dependent information such as highlights. There are various ways to acquire light fields depending on the nature of the scene, limitations on the capturing setup, and the application at hand. Our focus in this paper is on full-parallax imaging of large-scale static objects for photorealistic real-time rendering. To this end, we introduce and simulate a new design for capturing inward-looking spherical light fields, and propose a system for efficient compression and real-time rendering of such data using consumer-level hardware suitable for virtual reality applications.

Use of wireless signal for identification of unknown object, or technology to see-through a wall to form an image, is gaining growing interest from various fields including law enforcement and military sectors, disaster management, or even in civilian sectors such as construction sites. The great challenge in the implementation of such technology is the stochastic disturbances on wireless signal which will result in a signal with missing samples. Compressive Sensing (CS) is a powerful tool for estimating the missing samples since it can find accurate solution to largely underdetermined linear wireless signals. However, sparse models like CS can also suffer from information loss dues to stochastic lossy nature of wireless, making CS not to have accurate information for reconstruction of a signal. In this paper, we developed a theoretical and experimental framework for the mapping of obstacles by reconstructing the wireless signal based on a sparse signal. We apply tensor format to perform the computations along each mode by relaxing the tensor constraints to obtain accurate results. The proposed framework demonstrates how to take 2D signals, formulate estimate signals and produce a 3D image location in a completely unknown area inside of the obstacle (wall).

We present a method for GPU accelerated compression of light fields. The approach is by using a dictionary learning framework for compression of light field images. The large amount of data storage by capturing light fields is a challenge to compress and we seek to accelerate the encoding routine by GPGPU computations. We compress the data by projecting each data point onto a set of trained multi-dimensional dictionaries and seek the most sparse representation with the least error. This is done by a parallelization of the tensor-matrix product computed on the GPU. An optimized greedy algorithm to suit computations on the GPU is also presented. The encoding of the data is done segmentally in parallel for a faster computation speed while maintaining the quality. The results shows an order of magnitude faster encoding time compared to the results in the same research field. We conclude that there are further improvements to increase the speed, and thus it is not too far from an interacti ve compression speed.