Abstract
The compressed sensing theory has been widely used in solving undetermined equations in various fields and has made remarkable achievements. The regularized smooth L0 (ReSL0) reconstruction algorithm adds an error regularization term to the smooth L0(SL0) algorithm, achieving the reconstruction of the signal well in the presence of noise. However, the ReSL0 reconstruction algorithm still has some flaws. It still chooses the original optimization method of SL0 and the Gauss approximation function, but this method has the problem of a sawtooth effect in the later optimization stage, and the convergence effect is not ideal. Therefore, we make two adjustments to the basis of the ReSL0 reconstruction algorithm: firstly, we introduce another CIPF function which has a better approximation effect than Gauss function; secondly, we combine the steepest descent method and Newton method in terms of the algorithm optimization. Then, a novel regularized recovery algorithm named combined regularized smooth L0 (CReSL0) is proposed. Under the same experimental conditions, the CReSL0 algorithm is compared with other popular reconstruction algorithms. Overall, the CReSL0 algorithm achieves excellent reconstruction performance in terms of the peak signal-to-noise ratio (PSNR) and run-time for both a one-dimensional Gauss signal and two-dimensional image reconstruction tasks.
Highlights
Compressed sensing, known as compressive sampling or sparse sampling, is a technique for finding sparse solutions of underdetermined linear systems
According to compressed sensing theory, if the signal is sparse on a dictionary basis, it can be sampled and compressed simultaneously with an observation matrix that is not related to the sparse dictionary to project the high-dimensional signal in the low-dimensional space
Through our research and investigation, we find that many approximation functions are better than the Gauss function, such as the approximation function in [19]; on the other hand, the steepest descent optimization method adopted by regularized smooth L0 (ReSL0) does not require the accurate initial value, the optimization algorithm itself has drawbacks
Summary
Compressed sensing, known as compressive sampling or sparse sampling, is a technique for finding sparse solutions of underdetermined linear systems. Compared with the previous convex optimization method, in this algorithm, the discrete l0 norm is replaced by the continuous Gaussian function with parameters to construct a new objective function, the steepest descent method is used to minimize the approximate continuous function, and the minimal solution is projected into the solution space to satisfy the constraints. The well-known Newton method has second-order convergence, but the Newton method requires a more accurate initial value, and it is not easy to get a perfect initial value For this reason, we add the combined optimization method of the steepest descent method and Newton method to the ReSL0 algorithm and select the approximation function as used in [19]. The combined-optimization ReSL0 algorithm is proposed in this paper, which is called the CReSL0 algorithm
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