A group-theoretic framework for signal processing exploits signal symmetry to reduce estimator variance and unifies DFT, DCT, and KLT as points on a transform manifold.
Compressed sensing
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Log-sum regularization with adaptive smoothing for the proximal operator yields state-evolution predictions that match AMP and ADMM performance, outperforming l1 regularization in low-density or high-measurement-rate regimes.
DU-PSISTA combines linear sketching with periodic ISTA and deep unfolding to achieve linear convergence to a neighborhood of the true sparse signal at lower computational cost when the period and sketch size are chosen appropriately.
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