In low-rank matrix recovery, many kinds of measurements fail to meet the standard restricted isometry property (RIP), such as rank-one measurements, that is, [A(X)](i) = with rank (A(i)) = 1, i = 1, ..., m. Historical iterative hard thresholding sequence for low-rank matrix recovery and rank-one measurements was taken as Xn+1 = P-s(X-n - mu P-n(t)(A*sign(A(X-n) - y))), which introduced the "tail" and "head" approximations P-s and P-t, respectively. In this paper, we remove the term P-t and provide a new iterative hard thresholding algorithm with adaptive step size (abbreviated as AIHT). The linear convergence analysis and stability results on AIHT are established under the l(1)/l(2)-RIP. Particularly, we discuss the rank-one Gaussian measurements under the tight upper and lower bounds on E parallel to A(X)parallel to(1), and provide better convergence rate and sampling complexity. Besides, several empirical experiments are provided to show that AIHT performs better than the historical rank-one iterative hard thresholding method. (c) 2023 Elsevier Inc. All rights reserved.
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