Query: "Sangjun Park"

title: An Information Theoretic Study for Joint Sparsity Pattern Recovery With Different Sensing Matrices
abstract: In this paper, we study a support set reconstruction problem for multiple measurement vectors (MMV) with different sensing matrices, where the signals of interest are assumed to be jointly sparse and each signal is sampled by its own sensing matrix in the presence of noise. Using mathematical tools, we develop upper and lower bounds of the failure probability of the support set reconstruction in terms of the sparsity, the ambient dimension, the minimum signal to noise ratio, the number of measurement vectors, and the number of measurements. These bounds can be used to provide guidelines for determining the system parameters for various compressed sensing applications with noisy MMV with different sensing matrices. Based on the bounds, we develop necessary and sufficient conditions for reliable support set reconstruction. We interpret these conditions to provide theoretical explanations regarding the benefits of taking more measurement vectors. We then compare our sufficient condition with the existing results for noisy MMV with the same sensing matrix. As a result, we show that noisy MMV with different sensing matrices may require fewer measurements for reliable support set reconstruction, under a sublinear sparsity regime in a low noise level scenario.

title: Fast Mixed Integer Quadratic Programming for Sparse Signal Estimation
abstract: It has been recently shown that the $l_{0} norm problem can be reformulated into a mixed integer quadratic programming (MIQP) problem. CPLEX, a commercial optimization software package that can solve integer programming problems, is used to find the global solution to this MIQP problem for sparse signal estimation. However, CPLEX uses an exhaustive approach to search a feasible space to this MIQP problem. Thus, its running time grows exponentially as the problem dimension grows. This means that CPLEX quickly becomes computationally intractable for higher dimension problems. In this paper, we aim to propose a fast first order type method for solving this MIQP problem based on the alternating direction method. We conduct extensive simulations to demonstrate that: 1) our method is used to estimate a sparse signal by solving this problem and 2) our method is computationally tractable for problem dimensions up to the order of 1 million.

title: COMPU EYE: a high resolution computational compound eye.
abstract: In nature, the compound eyes of arthropods have evolved towards a wide field of view (FOV) infinite depth of field and fast motion detection. However, compound eyes have inferior resolution when compared with the camera type eyes of vertebrates, owing to inherent structural constraints such as the optical performance and the number of ommatidia. For resolution improvements, in this paper, we propose COMPUtational compound EYE (COMPU EYE) a new design that increases acceptance angles and uses a modern digital signal processing (DSP) technique. We demonstrate that the proposed COMPU EYE provides at least a four fold improvement in resolution.

title: Evolutionary Channel Sharing Algorithm for Heterogeneous Unlicensed Networks
abstract: Channel sharing in TV whitespace (TVWS) is challenging because of signal propagation characteristics and diversity in network technologies employed by secondary networks coexisting in TVWS. In this paper, the TVWS sharing problem is modeled as a multiobjective optimization problem, where each objective function tackles an important coexisting requirement, such as interference and disparity in network technologies. We propose an evolutionary algorithm that shares the TVWS among coexisting networks taking care of their channel occupancy requirements. In this paper, the channel occupancy is defined as the time duration; a network desires to radiate on a channel to achieve its desired duty cycle. Simulation results show that the proposed algorithm outperforms existing TVWS sharing algorithms regarding allocation fairness and a fraction of channel occupancy requirements of the coexisting networks.

title: Improving resolution of miniature spectrometers by exploiting sparse nature of signals.
abstract: In this paper, we present a signal processing approach to improve the resolution of a spectrometer with a fixed number of low cost, non ideal filters. We aim to show that the resolution can be improved beyond the limit set by the number of filters by exploiting the sparse nature of a signal spectrum. We consider an underdetermined system of linear equations as a model for signal spectrum estimation. We design a non negative L1 norm minimization algorithm for solving the system of equations. We demonstrate that the resolution can be improved multiple times by using the proposed algorithm.

title: An Information Theoretic Study for Noisy Compressed Sensing With Joint Sparsity Model 2
abstract: In this paper, we study a support set reconstruction problem in which the signals of interest are jointly sparse with a common support set, and sampled by joint sparsity model 2 (JSM 2) in the presence of noise. Using mathematical tools, we develop upper and lower bounds on the failure probability of support set reconstruction in terms of the sparsity, the ambient dimension, the minimum signal to noise ratio, the number of measurement vectors and the number of measurements. These bounds can be used to provide a guideline to determine the system parameters in various applications of compressed sensing with noisy JSM 2. Based on the bounds, we develop necessary and sufficient conditions for reliable support set reconstruction. We interpret these conditions to give theoretical explanations about the benefits enabled by joint sparsity structure in noisy JSM 2. We compare our sufficient condition with the existing result of noisy multiple measurement vectors model (MMV) As a result, we show that noisy JSM 2 may require less number of measurements than noisy MMV for reliable support set reconstruction.

title: On the derivation of RIP for random Gaussian matrices and binary sparse signals
abstract: The number of measurements, M, sufficient for successful recovery via the L1 minimization is well known to be M O[Klog(N/K) M [7] with Gaussian measurement matrices used for sensing K sparse signals of ambient dimension N. We aim to shed a light on the source of the log(N) factor, and see if the bound can be improved by considering it for simplest possible K sparse signals 0/1 binary K sparse signals. Previous work exists with which it is reasonable to expect reduction in the number of measurements when the signal has smaller degrees of freedom. We derive an upper bound on the probability that any set of K randomly selected Gaussian column vectors are mutually independent; we use this to find an upper bound on the probability that a Gaussian sensing matrix satisfies the restricted isometry condition. Using this result, a sufficient condition for good signal recovery is found. Surprisingly, the result remains the same, i.e. M O\Klog(N/K) which may suggest the log(N) factor is generic for Gaussian measurements.

title: Number of compressed measurements needed for noisy distributed compressed sensing
abstract: In this paper, we consider a data collection network (DCN) system where sensors take samples and transmit them to a Fusion Center (FC) Signal correlation is modeled with signal sparseness. The number of compressed measurements which allows correct signal recovery at FC is investigated. This is done by studying the probability of signal recovery failure. The joint typical decoder (JT decoder) similar to the one proposed by Akcakaya and Tarokh is used to avoid dependence on particular choice of recovery routines. The following interesting results have been obtained: 1) The detection failure probability linearly converges to zero as the number of sensors increases. 2) The number of compressed measurements per sensor (PSM) needed for successful recovery converges to sparsity as the number of sensors increases.

title: Study on performance behavior of compressive sensing measurements for multiple sensor system
abstract: In this paper, we will analyze the performance limit for a multiple sensor system (MSS) based on compressive sensing. In our MSS, all of the sensors measure signals from a common source. There exists the redundancy in the measured signal because the measured signal comes from the common source. To reduce communication costs, this redundancy must be removed. For this purpose, we use compressive sensing at each sensor to obtain compressed measurements. After all of the sensors obtain compressed measurements, they transmit them to a central unit. A decoder at the central unit receives all of the transmitted signals and attempts to jointly estimate the correct support set, which is the set of indices corresponding to the locations of the non zero coefficients of the measured signals. In order to analyze our MSS, we present a jointly typical decoder inspired by recent work  We first obtain the upper bound probability that the jointly typical decoder fails to estimate the correct support set. Next, we prove that as the number of sensors increases, the compressed measurements per sensor (per sensor measurements) can be reduced to sparsity, which is the number of non zero coefficients in the measured signal. We present the sufficient number of sensors required with the increase in the noise variance.

title: High Resolution Image Reconstruction from Old Video Recordings via Sparse Representation