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We propose an efficient ADMM method with guarantees for high-dimensional problems. We provide explicit bounds for the sparse optimization problem and the noisy matrix decomposition problem. For sparse optimization, we establish that the…
We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and…
This letter proposes a novel message-passing algorithm for signal recovery in compressed sensing. The proposed algorithm solves the disadvantages of approximate message-passing (AMP) and orthogonal/vector AMP, and realizes their advantages.…
Motivated by the recent interest in approximate message passing (AMP) for matrix-valued linear observations with superposition of \emph{multiple statistically asymmetric signal sources}, we introduce a multi-source AMP framework in which…
A signal recovery scheme is developed for linear observation systems based on expectation consistent (EC) mean field approximation. Approximate message passing (AMP) is known to be consistent with the results obtained using the replica…
In this paper, we extend the bilinear generalized approximate message passing (BiG-AMP) approach, originally proposed for high-dimensional generalized bilinear regression, to the multi-layer case for the handling of cascaded problem such as…
In this paper, we address the problem of recovering complex-valued signals from a set of complex-valued linear measurements. Approximate message passing (AMP) is one state-of-the-art algorithm to recover real-valued sparse signals. However,…
Traditional machine learning methods usually minimize a simple loss function to learn a predictive model, and then use a complex performance measure to measure the prediction performance. However, minimizing a simple loss function cannot…
This paper proves the convergence of Bayes-optimal orthogonal/vector approximate message-passing (AMP) to a fixed point in the large system limit. The proof is based on Bayes-optimal long-memory (LM) message-passing (MP) that is guaranteed…
This paper proposes a fast approximate message-passing (AMP) algorithm for solving compressed sensing (CS) recovery problems with 1D-finite-difference sparsity in term of MMSE estimation. The proposed algorithm, named ssAMP-BGFD, is…
We consider a remote inference system with multiple modalities, where a multimodal machine learning (ML) model performs real-time inference using features collected from remote sensors. When sensor observations evolve dynamically over time,…
We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state…
The strength of multimodal learning lies in its ability to integrate information from various sources, providing rich and comprehensive insights. However, in real-world scenarios, multi-modal systems often face the challenge of dynamic…
We extend the generalized approximate message passing (G-AMP) approach, originally proposed for high-dimensional generalized-linear regression in the context of compressive sensing, to the generalized-bilinear case, which enables its…
We analyse the matrix factorization problem. Given a noisy measurement of a product of two matrices, the problem is to estimate back the original matrices. It arises in many applications such as dictionary learning, blind matrix…
In this paper, an efficient distributed approach for implementing the approximate message passing (AMP) algorithm, named distributed AMP (DAMP), is developed for compressed sensing (CS) recovery in sensor networks with the sparsity K…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under…
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…
We consider the problem of parameter estimation from a generalized linear model with a random design matrix that is orthogonally invariant in law. Such a model allows the design have an arbitrary distribution of singular values and only…