Designing Gabor windows using convex optimization

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found

BM3D Frames and Variational Image Deblurring

A family of the Block Matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patch-wise image modeling [1], [2]. In this paper we construct analysis and synthesis frames, formalizing the BM3D image modeling and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem: one given by minimization of the single objective function and another based on the Nash equilibrium balance of two objective functions. The latter results in an algorithm where the denoising and deblurring operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the Nash equilibrium formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.Comment: Submitted to IEEE Transactions on Image Processing on May 18, 2011. implementation of the proposed algorithm is available as part of the BM3D package at http://www.cs.tut.fi/~foi/GCF-BM3

Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy

We present an efficient algorithm for calculating spectral properties of large sparse Hamiltonian matrices such as densities of states and spectral functions. The combination of Chebyshev recursion and maximum entropy achieves high energy resolution without significant roundoff error, machine precision or numerical instability limitations. If controlled statistical or systematic errors are acceptable, cpu and memory requirements scale linearly in the number of states. The inference of spectral properties from moments is much better conditioned for Chebyshev moments than for power moments. We adapt concepts from the kernel polynomial approximation, a linear Chebyshev approximation with optimized Gibbs damping, to control the accuracy of Fourier integrals of positive non-analytic functions. We compare the performance of kernel polynomial and maximum entropy algorithms for an electronic structure example.Comment: 8 pages RevTex, 3 postscript figure

Concepts for on-board satellite image registration. Volume 3: Impact of VLSI/VHSIC on satellite on-board signal processing

Anticipated major advances in integrated circuit technology in the near future are described as well as their impact on satellite onboard signal processing systems. Dramatic improvements in chip density, speed, power consumption, and system reliability are expected from very large scale integration. Improvements are expected from very large scale integration enable more intelligence to be placed on remote sensing platforms in space, meeting the goals of NASA's information adaptive system concept, a major component of the NASA End-to-End Data System program. A forecast of VLSI technological advances is presented, including a description of the Defense Department's very high speed integrated circuit program, a seven-year research and development effort

Cyclic LTI systems in digital signal processing

Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. In such cases, the frequency domain is defined as a uniform discrete grid (as in L-point DFT). This offers more freedom in theoretical as well as design aspects. While circular convolution has been the centerpiece of many algorithms in signal processing for decades, such freedom, especially from the viewpoint of linear system theory, has not been studied in the past. In this paper, we introduce the fundamentals of cyclic multirate systems and filter banks, presenting several important differences between the cyclic and noncyclic cases. Cyclic systems with allpass and paraunitary properties are studied. The paraunitary interpolation problem is introduced, and it is shown that the interpolation does not always succeed. State-space descriptions of cyclic LTI systems are introduced, and the notions of reachability and observability of state equations are revisited. It is shown that unlike in traditional linear systems, these two notions are not related to the system minimality in a simple way. Throughout the paper, a number of open problems are pointed out from the perspective of the signal processor as well as the system theorist