{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:41:08Z","timestamp":1760240468562,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,6,26]],"date-time":"2019-06-26T00:00:00Z","timestamp":1561507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003787","name":"Natural Science Foundation of Hebei Province","doi-asserted-by":"publisher","award":["F2018501051"],"award-info":[{"award-number":["F2018501051"]}],"id":[{"id":"10.13039\/501100003787","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/a12070126","type":"journal-article","created":{"date-parts":[[2019,6,26]],"date-time":"2019-06-26T07:24:17Z","timestamp":1561533857000},"page":"126","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Regularized Reconstruction Algorithm Based on Compressed Sensing for the Sparse Underdetermined Problem and Applications of One-Dimensional and Two-Dimensional Signal Recovery"],"prefix":"10.3390","volume":"12","author":[{"given":"Bin","family":"Wang","sequence":"first","affiliation":[{"name":"School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Li","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hao","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Northeastern University, Shenyang 110819, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fengming","family":"Xin","sequence":"additional","affiliation":[{"name":"School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,6,26]]},"reference":[{"key":"ref_1","unstructured":"Cand\u00e9s, E. (2006, January 22\u201330). Compressive sampling. Proceedings of the international congress of mathematicians, Madrid, Spain."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"118","DOI":"10.1109\/MSP.2007.4286571","article-title":"Compressive sensing","volume":"24","author":"Baraniuk","year":"2007","journal-title":"IEEE Signal Process. Mag."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1207","DOI":"10.1002\/cpa.20124","article-title":"Stable signal recovery from incomplete and inaccurate measurements","volume":"59","author":"Romberg","year":"2006","journal-title":"Commun. Pure Appl. Math."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"953","DOI":"10.1109\/LCOMM.2015.2416711","article-title":"Thresholded smoothed \u2113\u00b0 norm for accelerated Sparse recovery","volume":"19","author":"Wang","year":"2015","journal-title":"IEEE Commun, Lett."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.sigpro.2015.11.024","article-title":"Regularized smoothed \u2113\u00b0 norm algorithm and its application to CS-based radar imaging","volume":"122","author":"Bu","year":"2016","journal-title":"Signal Process."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1016\/j.procs.2017.12.031","article-title":"Subspace pursuit for sparse signal reconstruction in wireless sensor networks","volume":"125","author":"Goyal","year":"2018","journal-title":"Procedia. Comput. Sci."},{"key":"ref_7","first-page":"619","article-title":"Underdetermined blind separation based on potential function with estimated parameter\u2019s decreasing sequence","volume":"36","author":"Huang","year":"2014","journal-title":"Syst. Eng. Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"3397","DOI":"10.1109\/78.258082","article-title":"Matching pursuit in time\u2013frequency dictionary","volume":"41","author":"Mallat","year":"1993","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","unstructured":"Pati, Y.C., Rezaiifar, R., and Krishnaprasad, P.S. (1993, January 1\u20133). Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition. Proceedings of the 27th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2230","DOI":"10.1109\/TIT.2009.2016006","article-title":"Subspace pursuit for compressive sensing signal reconstruction","volume":"5","author":"Dai","year":"2009","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1145\/1859204.1859229","article-title":"CoSaMP: Iterative signal recovery from incomplete and inaccurate samples","volume":"12","author":"Needell","year":"2010","journal-title":"Commun. ACM"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Do, T.T., Lu, G., Nguyen, N., and Tran, T.D. (2008, January 26\u201329). Sparsity adaptive matching pursuit algorithm for practical compressed sensing. Proceedings of the 2008 42nd Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA.","DOI":"10.1109\/ACSSC.2008.5074472"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2049","DOI":"10.1109\/TSP.2016.2639467","article-title":"Recovery of Sparse Signals Using Multiple Orthogonal Least Squares","volume":"65","author":"Wang","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4735","DOI":"10.1109\/TSP.2011.2160058","article-title":"Recovery of Sparse Translation-Invariant Signals with Continuous Basis Pursuit","volume":"10","author":"Ekanadham","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_15","first-page":"198","article-title":"New Improved Algorithms for Compressive Sensing Based on lp Norm","volume":"61","author":"Pant","year":"2014","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1109\/JSTSP.2007.910281","article-title":"Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems","volume":"1","author":"Figueiredo","year":"2008","journal-title":"IEEE J. Sel. Top. Signal Process"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1137\/16M108940X","article-title":"Another look at the fast iterative shrinkage\/thresholding algorithm (FISTA)","volume":"28","author":"Kim","year":"2018","journal-title":"Siam J. Optim"},{"key":"ref_18","unstructured":"Mohimani, G.H., Babaie-Zadeh, M., and Jutten, C. (2007, January 9\u201312). Fast sparse representation based on smoothed \u21130 norm, in: Independent Component Analysis and Signal Separation. Proceedings of the International Conference on Latent Variable Analysis and Signal Separation, London, UK."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, L., Yin, X., Yue, H., and Xiang, J. (2018). A regularized weighted smoothed L0 norm minimization method for underdetermined blind source separation. Sensors, 18.","DOI":"10.3390\/s18124260"}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/7\/126\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:01:22Z","timestamp":1760187682000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/12\/7\/126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,6,26]]},"references-count":19,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["a12070126"],"URL":"https:\/\/doi.org\/10.3390\/a12070126","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2019,6,26]]}}}