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Register a new userApproximate Message Passing with Nearest Neighbor Sparsity Pattern Learning
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Xiangming Meng
Publication date
2016
fields
Informatics Engineering
and research's language is
English
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We consider the problem of recovering clustered sparse signals with no prior knowledge of the sparsity pattern. Beyond simple sparsity, signals of interest often exhibits an underlying sparsity pattern which, if leveraged, can improve the reconstruction performance. However, the sparsity pattern is usually unknown a priori. Inspired by the idea of k-nearest neighbor (k-NN) algorithm, we propose an efficient algorithm termed approximate message passing with nearest neighbor sparsity pattern learning (AMP-NNSPL), which learns the sparsity pattern adaptively. AMP-NNSPL specifies a flexible spike and slab prior on the unknown signal and, after each AMP iteration, sets the sparse ratios as the average of the nearest neighbor estimates via expectation maximization (EM). Experimental results on both synthetic and real data demonstrate the superiority of our proposed algorithm both in terms of reconstruction performance and computational complexity.
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Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machine (RBM) trained on the signal support to push reconstruction performance beyond that of simple iid priors for signals whose support can be well represented by a trained binary RBM. We present and analyze two methods of RBM factorization and demonstrate how these affect signal reconstruction performance within our proposed algorithm. Finally, using the MNIST handwritten digit dataset, we show experimentally that using an RBM allows AMP to approach oracle-support performance.
Approximate message passing (AMP) is a low-cost iterative parameter-estimation technique for certain high-dimensional linear systems with non-Gaussian distributions. However, AMP only applies to independent identically distributed (IID) transform matrices, but may become unreliable for other matrix ensembles, especially for ill-conditioned ones. To handle this difficulty, orthogonal/vector AMP (OAMP/VAMP) was proposed for general right-unitarily-invariant matrices. However, the Bayes-optimal OAMP/VAMP requires high-complexity linear minimum mean square error estimator. To solve the disadvantages of AMP and OAMP/VAMP, this paper proposes a memory AMP (MAMP), in which a long-memory matched filter is proposed for interference suppression. The complexity of MAMP is comparable to AMP. The asymptotic Gaussianity of estimation errors in MAMP is guaranteed by the orthogonality principle. A state evolution is derived to asymptotically characterize the performance of MAMP. Based on the state evolution, the relaxation parameters and damping vector in MAMP are optimized. For all right-unitarily-invariant matrices, the optimized MAMP converges to OAMP/VAMP, and thus is Bayes-optimal if it has a unique fixed point. Finally, simulations are provided to verify the validity and accuracy of the theoretical results.
The orthogonal-time-frequency-space (OTFS) modulation has emerged as a promising modulation scheme for high mobility wireless communications. To harvest the time and frequency diversity promised by OTFS, some promising detectors, especially message passing based ones, have been developed by taking advantage of the sparsity of the channel in the delay-Doppler domain. However, when the number of channel paths is relatively large or fractional Doppler {shifts have} to be considered, the complexity of existing detectors is a concern, and the message passing based detectors may suffer from performance loss due to the short loops involved in message passing. In this work, we investigate the design of OTFS detectors based on the approximate message passing (AMP). In particular, {leveraging the unitary AMP (UAMP), we design new detectors that enjoy} the structure of the channel matrix and allow efficient implementation. In addition, the estimation of noise variance is incorporated into the UAMP-based detectors. Thanks to the robustness of UAMP relative to AMP, the UAMP-based detectors deliver superior performance, and outperform state-of-the-art detectors significantly. We also investigate iterative joint detection and decoding in a coded OTFS system, where the OTFS detectors are integrated into a powerful turbo receiver, leading to considerable performance gains.
1-bit compressive sensing aims to recover sparse signals from quantized 1-bit measurements. Designing efficient approaches that could handle noisy 1-bit measurements is important in a variety of applications. In this paper we use the approximate message passing (AMP) to achieve this goal due to its high computational efficiency and state-of-the-art performance. In AMP the signal of interest is assumed to follow some prior distribution, and its posterior distribution can be computed and used to recover the signal. In practice, the parameters of the prior distributions are often unknown and need to be estimated. Previous works tried to find the parameters that maximize either the measurement likelihood or the Bethe free entropy, which becomes increasingly difficult to solve in the case of complicated probability models. Here we propose to treat the parameters as unknown variables and compute their posteriors via AMP as well, so that the parameters and the signal can be recovered jointly. This leads to a much simpler way to perform parameter estimation compared to previous methods and enables us to work with noisy 1-bit measurements. We further extend the proposed approach to the general quantization noise model that outputs multi-bit measurements. Experimental results show that the proposed approach generally perform much better than the other state-of-the-art methods in the zero-noise and moderate-noise regimes, and outperforms them in most of the cases in the high-noise regime.
Reconfigurable intelligent surfaces (RISs) have been recently considered as a promising candidate for energy-efficient solutions in future wireless networks. Their dynamic and lowpower configuration enables coverage extension, massive connectivity, and low-latency communications. Due to a large number of unknown variables referring to the RIS unit elements and the transmitted signals, channel estimation and signal recovery in RIS-based systems are the ones of the most critical technical challenges. To address this problem, we focus on the RIS-assisted multi-user wireless communication system and present a joint channel estimation and signal recovery algorithm in this paper. Specifically, we propose a bidirectional approximate message passing algorithm that applies the Taylor series expansion and Gaussian approximation to simplify the sum-product algorithm in the formulated problem. Our simulation results show that the proposed algorithm shows the superiority over a state-of-art benchmark method. We also provide insights on the impact of different RIS parameter settings on the proposed algorithms.
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