基于自适应分块和联合优化光滑<i>l</i><sub>0</sub>范数的二维压缩感知算法

张小贝; 唐辰; 涂喜梅; 陆晓刚; 张琦

doi:10.11999/JEIT221097

基于自适应分块和联合优化光滑l₀范数的二维压缩感知算法

doi: 10.11999/JEIT221097

1.
上海大学通信与信息工程学院上海 200444
2.
上海飞机设计研究院上海 201210

基金项目: 工信部民用飞机专项科研项目(MJZ-2018-S-30)

详细信息

作者简介:
张小贝：男，教授，研究方向为光电信息技术

唐辰：男，硕士生，研究方向为航空图像压缩加密

涂喜梅：女，研究员，研究方向为航空无线通信系统

陆晓刚：男，高级工程师，研究方向为航空数据链通信系统

张琦：男，讲师，研究方向为光电信息技术

通讯作者:
张小贝　xbzhang@shu.edu.com

中图分类号: TN911.73
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- 被引次数: 0
出版历程
- 收稿日期: 2022-08-22
- 修回日期: 2023-03-31
- 网络出版日期: 2023-04-04
- 刊出日期: 2023-12-26

2D Compressed Sensing Algorithm Based on Adaptive Blocking and Joint Optimization Smooth l₀ Norm

1.
School of Communication and Information Engineering, Shanghai University, Shanghai 200444, China
2.
Shanghai Aircraft Design and Research Institute, Shanghai 201210, China

Funds: The Ministry of Industry and Information Technology Civil Aircraft Special Research Project (MJZ-2018-S-30)

摘要

摘要: 传统的压缩感知模型和重构方法，虽能有效减少数据量，但压缩和重构性能不佳，故该文提出一种基于自适应分块和联合优化光滑l₀范数(SL0)的2维压缩感知算法。压缩过程利用灰度熵和四叉树算法进行自适应分块和采样率分配，同时对压缩模型改进，使用混沌循环矩阵作为测量矩阵，提升了压缩性能。重构过程基于SL0算法，采用陡峭性更高的拟合函数，结合拟牛顿法和动态迭代的方案提高重构质量和效率。该算法峰值信噪比和结构相似性指数相比现有算法平均提升了5.44 dB和21.08%，平均计算时间仅需1.59 s，表明该算法能稳定、快速地实现图像的压缩感知和精确重构，为压缩感知和图像重构提供了新方法。
- 2维压缩感知 /
- 自适应分块 /
- 图像重构 /
- 光滑l₀范数算法 /
- 拟牛顿法
Abstract: A 2-dimension compressed sensing algorithm based on adaptive blocking and joint optimization Smooth l₀ (SL0) norm is proposed to solve the problem of poor compression and reconstruction performance of the traditional compressed sensing model and reconstruction method. In the compression process, gray entropy and quadtree algorithm are used for adaptive blocking and sample rate allocation. At the same time, the compressed sensing model is optimized and the chaotic cyclic matrix is used as the measure matrix, which improves the compression performance. In the reconstruction process based on SL0 algorithm, a fitting function with higher steepness and a scheme combined with Quasi-Newton method and dynamic iteration are adopted to improve the reconstruction quality and efficiency. Compared with other algorithms, the peak signal to noise ratio and structural similarity index of the proposed algorithm are improved by 5.44 dB and 21.08% on average respectively. The average calculation time is only 1.59 s. Based on realizing image compression and accurate reconstruction stably and quickly, the proposed algorithm provides a new method for compressed sensing and image reconstruction.
- 2-Dimensional compressed sensing /
- Adaptive blocking /
- Image reconstruction /
- Smooth l₀ algorithm /
- Quasi-Newton method

HTML全文

图 1 2D-ABCS-JOSL0算法流程图

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图 2 图像自适应分块流程

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图 3 l₀近似函数对比图

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图 4 6幅测试图像

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图 5 图像自适应分块后结果

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图 6 图像单一优化算法PSNR对比

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图 7 图像单一优化算法SSIM对比

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图 8 30%压缩采样率下不同算法Lena图像结果对比

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图 9 30%压缩采样率下不同算法Barbara图像重构结果对比

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图 10 不同算法计算时间对比

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表 1 不同图像不同算法PSNR(dB)/SSIM(%))对比

压缩采样率(%)	算法	Peppers	Lena	Goldhill	Barbara	Boat	Mandrill	平均值
10	BCS-SPL	23.79/64.86	23.58/64.57	26.71/54.98	23.12/55.12	23.64/55.1	22.54/37.15	23.65/55.30
	ABCSDI-SPL	24.79/72.09	24.05/73.87	27.57/57.26	23.97/55.52	24.28/56.54	20.81/36.02	24.24/58.55
	2DPL	27.79/86.81	27.13/83.99	27.05/74.42	24.34/72.96	23.54/73.43	21.89/50.84	25.29/73.74
	TV-MS-BCS-SPL	28.21/87.03	27.33/80.43	28.21/75.89	28.01/74.04	24.27/74.33	22.97/52.32	26.50/74.01
	2D-ABCS-JOSL0	28.75/87.13	29.50/85.89	28.79/78.76	28.67/80.33	26.57/77.84	24.38/59.73	27.77/78.28
30	BCS-SPL	28.54/77.08	29.04/81.35	30.13/73.02	26.20/68.25	26.65/73.42	26.03/52.47	27.35/70.93
	ABCSDI-SPL	29.93/82.50	29.92/87.12	32.09/72.25	30.39/70.01	27.65/73.43	24.54/52.59	29.09/72.98
	2DPL	34.24/94.34	34.33/93.16	30.48/87.91	28.46/85.76	30.48/87.98	26.36/69.88	30.73/86.50
	TV-MS-BCS-SPL	34.32/93.13	30.99/88.94	33.12/83.95	29.76/82.46	28.87/83.32	27.04/73.56	30.68/84.23
	2D-ABCS-JOSL0	34.94/94.49	35.74/94.27	33.51/90.36	32.58/88.11	31.13/89.71	27.47/79.50	32.56/89.41
50	BCS-SPL	31.53/84.90	32.43/87.04	32.85/80.08	30.05/79.54	28.93/82.51	29.38/68.72	30.20/80.47
	ABCSDI-SPL	33.02/88.45	33.72/92.65	33.84/81.54	33.12/81.11	30.02/82.50	26.85/70.32	31.76/82.76
	2DPL	36.75/95.03	37.56/95.29	34.01/91.22	32.64/91.04	34.01/93.72	29.01/86.25	34.00/92.26
	TV-MS-BCS-SPL	36.95/96.00	33.20/92.00	34.84/88.47	33.96/88.91	32.72/90.13	28.04/81.23	33.29/89.46
	2D-ABCS-JOSL0	37.85/96.04	38.61/96.00	35.87/93.67	35.12/92.03	34.58/93.73	29.94/86.95	35.33/93.07
70	BCS-SPL	33.81/90.75	34.87/94.02	34.28/91.19	33.52/87.89	31.89/90.42	32.01/81.02	32.90/89.22
	ABCSDI-SPL	36.71/94.34	38.12/96.14	34.95/89.26	36.01/88.14	33.38/90.99	28.55/82.34	34.62/90.20
	2DPL	38.63/96.55	39.55/96.88	36.98/94.56	36.25/94.65	36.22/95.13	31.83/90.75	36.58/94.75
	TV-MS-BCS-SPL	38.10/96.09	34.92/93.91	36.52/93.87	36.32/93.43	35.93/94.81	31.75/90.12	35.59/93.70
	2D-ABCS-JOSL0	39.64/96.74	40.05/96.88	37.28/95.08	37.21/94.80	36.66/95.54	32.56/91.97	37.23/95.17

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