Mina Karzand

Demosaicking by Alternating Projections: Theory and Fast One-Step Implementation

Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we study a well-known and influential demosaicking algorithm based upon alternating projections (AP), proposed by Gunturk, Altunbasak and Mersereau in 2002. Since its publication, the AP algorithm has been widely cited and compared against in a series of more recent papers in the demosaicking literature. Despite good performances, a limitation of the AP algorithm is its high computational complexity. We provide three main contributions in this paper. First, we present a rigorous analysis of the convergence property of the AP demosaicking algorithm, showing that it is a contraction mapping, with a unique fixed point. Second, we show that this fixed point is in fact the solution to a constrained quadratic minimization problem, thus, establishing the optimality of the AP algorithm. Finally, using the tool of polyphase representation, we show how to obtain the results of the AP algorithm in a single step, implemented as linear filtering in the polyphase domain. Replacing the original iterative procedure by the proposed one-step solution leads to substantial computational savings, by about an order of magnitude in our experiments.

Achievability of nonlinear degrees of freedom in correlatively changing fading channels

A new approach toward the noncoherent communications over the time varying fading channels is presented. In this approach, the relationship between the input signal space and the output signal space of a correlatively changing fading channel is shown to be a nonlinear mapping between manifolds of different dimensions. Studying this mapping, it is shown that using nonlinear decoding algorithms for single input-multiple output (SIMO) and multiple input multiple output (MIMO) systems, extra numbers of degrees of freedom (DOF) are available. We call them the nonlinear degrees of freedom.

Iterative demosaicking accelerated: Theory and fast noniterative implementations

Color image demosaicking is a key process in the digital imaging pipeline. In this paper, we present a rigorous treatment of a classical demosaicking algorithm based on alternating projections (AP). Since its publication, the AP algorithm has been wildly cited and served as a benchmark in a flurry of papers in the demosaicking literature. Despite its impressive performances, a relative weakness of the AP algorithm is its high computational complexity. In our work, we provide a rigorous analysis of the convergence of the AP algorithm based on the concept of contraction mapping. Furthermore, we propose an efficient noniterative implementation of the AP algorithm in the polyphase domain. Numerical experiments show that the proposed noniterative implementation achieves the same results obtained by the original AP algorithm at convergence, but is about an order of magnitude faster than the latter.

Communication strategies for low-latency trading

The possibility of latency arbitrage in financial markets has led to the deployment of high-speed communication links between distant financial centers. These links are noisy and so there is a need for coding. In this paper, we develop a game-theoretic model of trading behavior where two traders compete to capture latency arbitrage opportunities using binary signalling. Different coding schemes are strategies that trade off between reliability and latency. When one trader has a better channel, the second trader should not compete. With statistically identical channels, we find there are two different regimes of channel noise for which: there is a unique Nash equilibrium yielding ties; and there are two Nash equilibria with different winners.

Degrees of freedom in fading channels with memory: Achievability through nonlinear decoding

In noncoherent communication systems, neither the transmitter nor the receiver knows the realization of channel fading coefficients. To overcome this limitation and facilitate reliable communication, the transmitter sends fixed values on some predetermined training symbols. The maximum number of symbols that can be used for communication in a block of time is the degrees of freedom (DOF) of the system. Given DOF equals to D, reliable communication (in high SNR regime) implies existence of a D dimensional subspace of the input signal space which is recoverable by the receiver with probability one. The training symbols specify this D dimensional subspace. Thus the minimum number of necessary training symbols determines the DOF of the system. We formalize this rationale and name it Dimension Counting Argument. We then use this argument to prove a lower bound on the DOF of fading channels with memory. We study the Multiple-Input Multiple-Output (MIMO) systems with nt transmit antennas and nr receive antennas where fading coefficients in blocks of length T have a temporal correlation matrix with rank Q. We prove that in these systems, nt* transmit antennas (nt* = min[nt, ⌊T/Q⌋]) should be used to achieve min [nr(T - nt*Q), nt*(T - nt*)] DOF per block of time. We show that the geometric interpretation of the fading channel with memory is equivalent to a nonlinear mapping over manifolds of different dimensions. The inherent nonlinearity of the model manifests itself in the necessary nonlinearity of the proposed decoding algorithms.