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. 2018 Jun 14;8:9108. doi: 10.1038/s41598-018-27490-2

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© The Author(s) 2018

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Phantom 3-D focused image slices for (a) resolution and (b) contrast evaluation comparison between the random array (rand256 on the right-hand column), the optimal sparse array opti256 central columns), and the reference array (ref1024 on the left-hand column). The best performance between the two sparse arrays is highlighted in green. The dynamic range is 60 dB. XZ and YZ refer to the central image planes in the azimuth and elevation direction, respectively.