@article{zhu_baron_2018, title={Performance Limits With Additive Error Metrics in Noisy Multimeasurement Vector Problems}, volume={66}, ISSN={["1941-0476"]}, DOI={10.1109/TSP.2018.2866844}, abstractNote={Real-world applications such as magnetic resonance imaging with multiple coils, multiuser communication, and diffuse optical tomography often assume a linear model, where several sparse signals sharing common sparse supports are acquired by several measurement matrices and then contaminated by noise. Multimeasurement vector (MMV) problems consider the estimation or reconstruction of such signals. In different applications, the estimation error that we want to minimize could be the mean squared error or other metrics, such as the mean absolute error and the support set error. Seeing that minimizing different error metrics is useful in MMV problems, we study information-theoretic performance limits for MMV signal estimation with arbitrary additive error metrics. We also propose a message passing algorithmic framework that achieves the optimal performance, and rigorously prove the optimality of our algorithm for a special case. We further conjecture the optimality of our algorithm for some general cases and back it up through numerical examples. As an application of our MMV algorithm, we propose a novel setup for active user detection in multiuser communication and demonstrate the promise of our proposed setup.}, number={20}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={Zhu, Junan and Baron, Dror}, year={2018}, month={Oct}, pages={5338–5348} }
 @article{zhu_baron_krzakala_2017, title={Performance Limits for Noisy Multimeasurement Vector Problems}, volume={65}, ISSN={["1941-0476"]}, DOI={10.1109/tsp.2016.2646663}, abstractNote={Compressed sensing (CS) demonstrates that sparse signals can be estimated from underdetermined linear systems. Distributed CS (DCS) further reduces the number of measurements by considering joint sparsity within signal ensembles. DCS with jointly sparse signals has applications in multisensor acoustic sensing, magnetic resonance imaging with multiple coils, remote sensing, and array signal processing. Multimeasurement vector (MMV) problems consider the estimation of jointly sparse signals under the DCS framework. Two related MMV settings are studied. In the first setting, each signal vector is measured by a different independent and identically distributed (i.i.d.) measurement matrix, while in the second setting, all signal vectors are measured by the same i.i.d. matrix. Replica analysis is performed for these two MMV settings, and the minimum mean squared error (MMSE), which turns out to be identical for both settings, is obtained as a function of the noise variance and number of measurements. To showcase the application of MMV models, the MMSE's of complex CS problems with both real and complex measurement matrices are also analyzed. Multiple performance regions for MMV are identified where the MMSE behaves differently as a function of the noise variance and the number of measurements. Belief propagation (BP) is a CS signal estimation framework that often achieves the MMSE asymptotically. A phase transition for BP is identified. This phase transition, verified by numerical results, separates the regions where BP achieves the MMSE and where it is suboptimal. Numerical results also illustrate that more signal vectors in the jointly sparse signal ensemble lead to a better phase transition.}, number={9}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={Zhu, Junan and Baron, Dror and Krzakala, Florent}, year={2017}, month={May}, pages={2444–2454} }
 @inproceedings{han_zhu_niu_baron_2016, title={Multi-processor approximate message passing using lossy compression}, DOI={10.1109/icassp.2016.7472877}, abstractNote={In this paper, a communication-efficient multi-processor compressed sensing framework based on the approximate message passing algorithm is proposed. We perform lossy compression on the data being communicated between processors, resulting in a reduction in communication costs with a minor degradation in recovery quality. In the proposed framework, a new state evolution formulation takes the quantization error into account, and analytically determines the coding rate required in each iteration. Two approaches for allocating the coding rate, an online back-tracking heuristic and an optimal allocation scheme based on dynamic programming, provide significant reductions in communication costs.}, booktitle={International conference on acoustics speech and signal processing}, author={Han, P. X. and Zhu, J. N. and Niu, R. X. and Baron, Dror}, year={2016}, pages={6240–6244} }
 @inproceedings{zhu_beirami_baron_2016, title={Performance trade-offs in multi-processor approximate message passing}, DOI={10.1109/isit.2016.7541385}, abstractNote={We consider large-scale linear inverse problems in Bayesian settings. Our general approach follows a recent line of work that applies the approximate message passing (AMP) framework in multi-processor (MP) computational systems by storing and processing a subset of rows of the measurement matrix along with corresponding measurements at each MP node. In each MP-AMP iteration, nodes of the MP system and its fusion center exchange lossily compressed messages pertaining to their estimates of the input. There is a trade-off between the physical costs of the reconstruction process including computation time, communication loads, and the reconstruction quality, and it is impossible to simultaneously minimize all the costs. We pose this minimization as a multi-objective optimization problem (MOP), and study the properties of the best trade-offs (Pareto optimality) in this MOP. We prove that the achievable region of this MOP is convex, and conjecture how the combined cost of computation and communication scales with the desired mean squared error. These properties are verified numerically.}, booktitle={2016 ieee international symposium on information theory}, author={Zhu, J. and Beirami, A. and Baron, Dror}, year={2016}, pages={680–684} }
 @article{zhu_baron_duarte_2015, title={Recovery From Linear Measurements With Complexity-Matching Universal Signal Estimation}, volume={63}, ISSN={["1941-0476"]}, DOI={10.1109/tsp.2015.2393845}, abstractNote={We study the compressed sensing (CS) signal estimation problem where an input signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the input signal during recovery, the signal structure that can be leveraged is often not known a priori. In this paper, we consider universal CS recovery, where the statistics of a stationary ergodic signal source are estimated simultaneously with the signal itself. Inspired by Kolmogorov complexity and minimum description length, we focus on a maximum a posteriori (MAP) estimation framework that leverages universal priors to match the complexity of the source. Our framework can also be applied to general linear inverse problems where more measurements than in CS might be needed. We provide theoretical results that support the algorithmic feasibility of universal MAP estimation using a Markov chain Monte Carlo implementation, which is computationally challenging. We incorporate some techniques to accelerate the algorithm while providing comparable and in many cases better reconstruction quality than existing algorithms. Experimental results show the promise of universality in CS, particularly for low-complexity sources that do not exhibit standard sparsity or compressibility.}, number={6}, journal={IEEE TRANSACTIONS ON SIGNAL PROCESSING}, author={Zhu, Junan and Baron, Dror and Duarte, Marco F.}, year={2015}, month={Mar}, pages={1512–1527} }
 @inproceedings{zhu_baron_duarte_2014, title={Complexity-adaptive universal signal estimation for compressed sensing}, DOI={10.1109/ssp.2014.6884657}, abstractNote={We study the compressed sensing (CS) signal estimation problem where a signal is measured via a linear matrix multiplication under additive noise. While this setup usually assumes sparsity or compressibility in the signal during estimation, additional signal structure that can be leveraged is often not known a priori. For signals with independent and identically distributed (i.i.d.) entries, existing CS algorithms achieve optimal or near optimal estimation error without knowing the statistics of the signal. This paper addresses estimating stationary ergodic non-i.i.d. signals with unknown statistics. We have previously proposed a universal CS approach to simultaneously estimate the statistics of a stationary ergodic signal as well as the signal itself. This paper significantly improves on our previous work, especially for continuous-valued signals, by offering a four-stage algorithm called Complexity-Adaptive Universal Signal Estimation (CAUSE), where the alphabet size of the estimate adaptively matches the coding complexity of the signal. Numerical results show that the new approach offers comparable and in some cases, especially for non-i.i.d. signals, lower mean square error than the prior art, despite not knowing the signal statistics.}, booktitle={2014 IEEE Workshop on Statistical Signal Processing (SSP)}, author={Zhu, J. N. and Baron, Dror and Duarte, M. F.}, year={2014}, pages={388–391} }
 @inproceedings{zhu_baron_2013, title={Performance regions in compressed sensing from noisy measurements}, DOI={10.1109/ciss.2013.6552256}, abstractNote={In this paper, compressed sensing with noisy measurements is addressed. The theoretically optimal reconstruction error is studied by evaluating Tanaka's equation. The main contribution is to show that in several regions, which have different measurement rates and noise levels, the reconstruction error behaves differently. This paper also evaluates the performance of the belief propagation (BP) signal reconstruction method in the regions discovered. When the measurement rate and the noise level lie in a certain region, BP is suboptimal with respect to Tanaka's equation, and it may be possible to develop reconstruction algorithms with lower error in that region.}, booktitle={2013 47th Annual Conference on Information Sciences and Systems (CISS)}, author={Zhu, J. A. and Baron, Dror}, year={2013} }