Arian Maleki
Columbia University
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Featured researches published by Arian Maleki.
IEEE Transactions on Information Theory | 2013
Arian Maleki; Laura Anitori; Zai Yang; Richard G. Baraniuk
Recovering a sparse signal from an undersampled set of random linear measurements is the main problem of interest in compressed sensing. In this paper, we consider the case where both the signal and the measurements are complex-valued. We study the popular recovery method of l1-regularized least squares or LASSO. While several studies have shown that LASSO provides desirable solutions under certain conditions, the precise asymptotic performance of this algorithm in the complex setting is not yet known. In this paper, we extend the approximate message passing (AMP) algorithm to solve the complex-valued LASSO problem and obtain the complex approximate message passing algorithm (CAMP). We then generalize the state evolution framework recently introduced for the analysis of AMP to the complex setting. Using the state evolution, we derive accurate formulas for the phase transition and noise sensitivity of both LASSO and CAMP. Our theoretical results are concerned with the case of i.i.d. Gaussian sensing matrices. Simulations confirm that our results hold for a larger class of random matrices.
IEEE Transactions on Information Theory | 2016
Christopher A. Metzler; Arian Maleki; Richard G. Baraniuk
A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, todays denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high-performance denoiser for natural images, D-AMP offers the state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.
IEEE Transactions on Information Theory | 2014
Shirin Jalali; Arian Maleki; Richard G. Baraniuk
The nascent field of compressed sensing is founded on the fact that high-dimensional signals with simple structure can be recovered accurately from just a small number of randomized samples. Several specific kinds of structures have been explored in the literature, from sparsity and group sparsity to low-rankness. However, two fundamental questions have been left unanswered. What are the general abstract meanings of structure and simplicity? Do there exist universal algorithms for recovering such simple structured objects from fewer samples than their ambient dimension? In this paper, we address these two questions. Using algorithmic information theory tools such as the Kolmogorov complexity, we provide a unified definition of structure and simplicity. Leveraging this new definition, we develop and analyze an abstract algorithm for signal recovery motivated by Occams Razor. Minimum complexity pursuit (MCP) requires approximately 2κ randomized samples to recover a signal of complexity κ and ambient dimension n. We also discuss the performance of the MCP in the presence of measurement noise and with approximately simple signals.
international symposium on information theory | 2015
Charles Jeon; Ramina Ghods; Arian Maleki; Christoph Studer
Optimal data detection in multiple-input multiple-output (MIMO) communication systems with a large number of antennas at both ends of the wireless link entails prohibitive computational complexity. In order to reduce the computational complexity, a variety of sub-optimal detection algorithms have been proposed in the literature. In this paper, we analyze the optimality of a novel data-detection method for large MIMO systems that relies on approximate message passing (AMP). We show that our algorithm, referred to as individually-optimal (IO) large-MIMO AMP (short IO-LAMA), is able to perform IO data detection given certain conditions on the MIMO system and the constellation set (e.g., QAM or PSK) are met.
international symposium on information theory | 2016
Charles Jeon; Arian Maleki; Christoph Studer
We investigate the performance of mismatched data detection in large multiple-input multiple-output (MIMO) systems, where the prior distribution of the transmit signal used in the data detector differs from the true prior. To minimize the performance loss caused by this prior mismatch, we include a tuning stage into our recently-proposed large MIMO approximate message passing (LAMA) algorithm, which allows us to develop mismatched LAMA algorithms with optimal as well as sub-optimal tuning. We show that carefully-selected priors often enable simpler and computationally more efficient algorithms compared to LAMA with the true prior while achieving near-optimal performance. A performance analysis of our algorithms for a Gaussian prior and a uniform prior within a hypercube covering the QAM constellation recovers classical and recent results on linear and non-linear MIMO data detection, respectively.
Annals of Statistics | 2017
Ali Mousavi; Arian Maleki; Richard G. Baraniuk
We consider the problem of recovering a vector
international conference on image processing | 2015
Christopher A. Metzler; Arian Maleki; Richard G. Baraniuk
beta_o in mathbb{R}^p
Annals of Statistics | 2018
Haolei Weng; Arian Maleki; Le Zheng
from
international symposium on information theory | 2017
Ramina Ghods; Charles Jeon; Gulnar Mirza; Arian Maleki; Christoph Studer
n
international symposium on information theory | 2013
Shirin Jalali; Arian Maleki
random and noisy linear observations