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Optimality of Approximate Message Passing Algorithms for Spiked Matrix Models with Rotationally Invariant Noise
At each iteration, these algorithms exploit prior knowledge about the noise structure by applying a non-linear matrix denoiser to the eigenvalues of the observed matrix and prior information regarding the signal structure by applying a non-linear iterate denoiser to the previous iterates generated by the algorithm.
Towards Designing Optimal Sensing Matrices for Generalized Linear Inverse Problems
We consider an inverse problem $\mathbf{y}= f(\mathbf{Ax})$, where $\mathbf{x}\in\mathbb{R}^n$ is the signal of interest, $\mathbf{A}$ is the sensing matrix, $f$ is a nonlinear function and $\mathbf{y} \in \mathbb{R}^m$ is the measurement vector.
Analysis of Sensing Spectral for Signal Recovery under a Generalized Linear Model
We define a notion for the spikiness of the spectrum of $\mathbf{A}$ and show the importance of this measure in the performance of the EP.
Approximate message passing for amplitude based optimization
We consider an $\ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations.
