Abstract
We propose a new iterative greedy algorithm to reconstruct sparse signals in Compressed Sensing. The algorithm, called Conjugate Gradient Hard Thresholding Pursuit (CGHTP), is a simple combination of Hard Thresholding Pursuit (HTP) and Conjugate Gradient Iterative Hard Thresholding (CGIHT). The conjugate gradient method with a fast asymptotic convergence rate is integrated into the HTP scheme that only uses simple line search, which accelerates the convergence of the iterative process. Moreover, an adaptive step size selection strategy, which constantly shrinks the step size until a convergence criterion is met, ensures that the algorithm has a stable and fast convergence rate without choosing step size. Finally, experiments on both Gaussian-signal and real-world images demonstrate the advantages of the proposed algorithm in convergence rate and reconstruction performance.
Highlights
As a new sampling method, Compressed Sensing (CS) has received broad research interest in signal processing, image processing, biomedical engineering, electronic engineering and other fields [1,2,3,4,5,6]
We investigated the performance of Conjugate Gradient Hard Thresholding Pursuit (CGHTP) to reconstruct natural images
In the case of low sampling rate (T = 0.2), the reconstructed PSNR value of the four tested images obtained by CGHTP algorithm is about 2 dB higher than that obtained by Hard Thresholding Pursuit (HTP) algorithm with the best step size
Summary
As a new sampling method, Compressed Sensing (CS) has received broad research interest in signal processing, image processing, biomedical engineering, electronic engineering and other fields [1,2,3,4,5,6]. This means f = ψx, and x has at most s(s N ) nonzero entries This system can be measured by a sampling matrix Φ ∈ R M× N ( M < N ):. If Φ is incoherent with ψ, the coefficient vector x can be reconstructed exactly from a few measurements by solving the undetermined linear system y = Ax with constraint k xk0 ≤ s, i.e., solving the following0 norm minimization problem: min k xk0 s.t. As a combinatorial optimization problem, the above0 norm optimization is NP-hard [8]. Sparse signals can be quickly recovered by these algorithms while the measurement matrix satisfying the so-called restricted isometry property (RIP) with a constant parameter. The core ideas of this paper include: (1) by combining the steps of HTP and CGIHT in each iteration, a new algorithm called Conjugate Gradient Hard Thresholding Pursuit (CGHTP) is presented;.
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