Jason T. Parker

TL;DR: The accessible framework provided by compressed sensing illuminates the impact of joining these themes and potential future directions are conjectured both for extension of theory motivated by practice and for modification of practice based on theoretical insights.

TL;DR: This paper derives the Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, where central-limit theorem arguments and Taylor-series approximations apply, and under the assumption of statistically independent matrix entries with known priors.

TL;DR: This paper derived the Bilinear G-AMP (BiG-AMP) algorithm as an approximation of the sum-product belief propagation algorithm in the high-dimensional limit, and proposed an adaptive damping mechanism that aids convergence under finite problem sizes, an expectation-maximization (EM)-based method to automatically tune the parameters of the assumed priors, and two rank-selection strategies.

TL;DR: This work extends the Approximate Message Passing approach to the case of probabilistic uncertainties in the elements of the measurement matrix, and shows that it can be applied in an alternating fashion to learn both the unknown measurement matrix and signal vector.

TL;DR: The proposed scheme generalizes previous instances of bilinear G-AMP, such as those that estimate matrices B and C from a noisy measurement of Z = BC, allowing the application of AMP methods to problems such as self-calibration, blind deconvolution, and matrix compressive sensing.