In the sublinear sparsity limit the ML estimator achieves vanishing squared error below a noise threshold that coincides with the converse bound for constant-amplitude signals, proving asymptotic optimality of separable Bayesian estimators.
Mutual i nformation and optimality of approximate message-passing in random linea r estimation,
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GOAMP achieves error-free reconstruction of sublinearly sparse signals from linear measurements when the measurement dimension exceeds a threshold matching that of Gaussian AMP, provided the non-zero support avoids a neighborhood of the origin.
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Direct and Converse Theorems in Estimating Signals with Sublinear Sparsity
In the sublinear sparsity limit the ML estimator achieves vanishing squared error below a noise threshold that coincides with the converse bound for constant-amplitude signals, proving asymptotic optimality of separable Bayesian estimators.
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Generalized Orthogonal Approximate Message-Passing for Sublinear Sparsity
GOAMP achieves error-free reconstruction of sublinearly sparse signals from linear measurements when the measurement dimension exceeds a threshold matching that of Gaussian AMP, provided the non-zero support avoids a neighborhood of the origin.