Gil Shabat

Superresolution in turbulent videos: making profit from damage

It is shown that one can make use of local instabilities in turbulent video frames to enhance image resolution beyond the limit defined by the image sampling rate. We outline the processing algorithm, present its experimental verification on simulated and real-life videos, and discuss its potentials and limitations.

Accelerating Particle Filter Using Randomized Multiscale and Fast Multipole Type Methods

Particle filter is a powerful tool for state tracking using non-linear observations. We present a multiscale based method that accelerates the tracking computation by particle filters. Unlike the conventional way, which calculates weights over all particles in each cycle of the algorithm, we sample a small subset from the source particles using matrix decomposition methods. Then, we apply a function extension algorithm that uses a particle subset to recover the density function for all the rest of the particles not included in the chosen subset. The computational effort is substantial especially when multiple objects are tracked concurrently. The proposed algorithm significantly reduces the computational load. By using the Fast Gaussian Transform, the complexity of the particle selection step is reduced to a linear time in n and k, where n is the number of particles and k is the number of particles in the selected subset. We demonstrate our method on both simulated and on real data such as object tracking in video sequences.

Superresolution in color videos acquired through turbulent media

Color videos acquired with a single CCD through turbulent media can be enhanced in their resolution beyond the limit defined by the image sampling rate. We provide a mathematical justification for this claim, present an efficient superresolution algorithm and its experimental verification on a real-life video, and finally, discuss its potentials and limitations.

Randomized LU decomposition using sparse projections

A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation error of the algorithm is analyzed and a theoretical error bound is presented. Finally, numerical examples illustrate that for a similar approximation error, the sparse LU algorithm is faster than recent state-of-the-art methods. The algorithm is completely parallelizable that enables to run on a GPU. The performance is tested on a GPU card, showing a significant improvement in the running time in comparison to sequential execution.

INTEREST ZONE MATRIX APPROXIMATION

An algorithm for matrix approximation, when only some of its entries are taken into consideration, is described. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank approximations, this type of algorithms appears recently in the literature under different names, where it usually uses the Expectation-Maximization algorithm that maximizes the likelihood for the missing entries. In this paper, the algorithm is extended to different cases other than low rank approximations under Frobenius norm, such as minimizing the Frobenius norm under nuclear norm constraint, spectral norm constraint, orthogonality constraint and more. The geometric interpretation of the proposed approximation process along with its op- timality for convex constraints is also discussed. In addition, it is shown how the approximation algorithm can be used for matrix completion as well, under a variety of spectral regularizations. Its applications to physics, electrical engineering and data interpolation problems are also described.

Super-resolution of turbulent video: potentials and limitations

A common distortion in videos acquired in long range observation systems is image instability in form of chaotic local displacements of image frames caused by fluctuations in the refraction index of the atmosphere turbulence. At the same time, such videos, which are designed to present moving objects on a stable background, contain tremendous redundancy that potentially can be used for image stabilization and perfecting provided reliable separation of stable background from true moving objects. Recently, it was proposed to use this redundancy for resolution enhancement of turbulent video through elastic registration, with sub-pixel accuracy, of segments of video frames that represent stable scenes. This paper presents results of investigation, by means of computer simulation, into how parameters of such a resolution enhancement process affect its performance and its potentials and limitations.

Direct Inversion of the Three-Dimensional Pseudo-polar Fourier Transform

The pseudo-polar Fourier transform is a specialized nonequally spaced Fourier transform, which evaluates the Fourier transform on a near-polar grid known as the pseudo-polar grid. The advantage of the pseudo-polar grid over other nonuniform sampling geometries is that the transformation, which samples the Fourier transform on the pseudo-polar grid, can be inverted using a fast and stable algorithm. For other sampling geometries, even if the nonequally spaced Fourier transform can be inverted, the only known algorithms are iterative. The convergence speed of these algorithms and their accuracy are difficult to control, as they depend both on the sampling geometry and on the unknown reconstructed object. In this paper, a direct inversion algorithm for the three-dimensional pseudo-polar Fourier transform is presented. The algorithm is based only on one-dimensional resampling operations and is shown to be significantly faster than existing iterative inversion algorithms.

Accelerating Particle filter using multiscale methods

We present a method that accelerates the Particle Filter computation. Particle Filter is a powerful method for tracking the state of a target based on non-linear observations. Unlike the conventional way of calculating weights over all particles in each run, we sample a small subset of the particles using matrix decomposition methods, followed by a novel function extension algorithm to recover the density function of all particles. This significantly reduces the computational load where the measurement computation is substantial, as often happens, for example, when tracking targets in videos. We demonstrate our method on both simulated data and real data (videos).

Similarity search over graphs using localized spectral analysis

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points1 and an additional reference data point for similarity finding, the algorithm uses kernel method that embeds the data points into a low dimensional manifold. Unlike other kernel methods, which considers the entire data for the embedding, our method selects a specific set of kernel eigenvectors. The eigenvectors are chosen to separate between the data points and the reference data point so that similar data points can be easily identified as being distinct from most of the members in the dataset.