通信学报 ›› 2018, Vol. 39 ›› Issue (7): 26-38.doi: 10.11959/j.issn.1000-436x.2018111
修回日期:
2018-06-01
出版日期:
2018-07-01
发布日期:
2018-08-08
作者简介:
王金铭(1978-),男,浙江富阳人,浙江树人大学副教授,主要研究方向为非线性信息处理、图像处理、压缩感知等。|叶时平(1967-),男,浙江丽水人,浙江树人大学教授,主要研究方向为图像处理、智能系统、地理信息系统等。|尉理哲(1983-),女,内蒙古呼伦贝尔人,浙江树人大学讲师,主要研究方向为车联网、WSN、深度学习等。|许森(1982-),男,湖北荆门人,浙江树人大学讲师,主要研究方向为人工智能、智能控制、物联网等。|蒋燕君(1973-),男,浙江诸暨人,博士,浙江树人大学教授,主要研究方向为智能电网、图像处理等。
基金资助:
Jinming WANG,Shiping YE,Lizhe YU(),Sen XU,Yanjun JIANG
Revised:
2018-06-01
Online:
2018-07-01
Published:
2018-08-08
Supported by:
摘要:
为降低随机观测矩阵在压缩感知应用中所需的存储空间,提升大尺寸图像重构的实时性,提出一种半张量积压缩感知方法。利用该方法构建低阶随机观测矩阵,对原始信号进行全局采样,随后将测量值进行分组处理并采用lq-范数(0时,仍可得到与传统方法一致的重构质量),同时极大地提升重构的实时性,对于1024像素×1024像素大小的图像,其重构时间可提升近260倍。
中图分类号:
王金铭,叶时平,尉理哲,许森,蒋燕君. 半张量积压缩感知模型的快速重构方法[J]. 通信学报, 2018, 39(7): 26-38.
Jinming WANG,Shiping YE,Lizhe YU,Sen XU,Yanjun JIANG. Fast reconstruction method for compressed sensing model with semi-tensor product[J]. Journal on Communications, 2018, 39(7): 26-38.
表2
不同大小的高斯随机观测矩阵重构2维图像峰值信噪比"
原始图像 | t | 峰值信噪比/dB | |||||||
0.125 0 | 0.250 0 | 0.375 0 | 0.437 5 | 0.500 0 | 0.562 5 | 0.625 0 | 0.750 0 | ||
1 | 19.282 8 | 26.610 5 | 31.165 7 | 33.838 1 | 35.586 5 | 37.423 6 | 39.932 3 | 44.381 2 | |
2 | 19.636 6 | 27.603 6 | 31.338 3 | 33.487 7 | 35.333 0 | 37.411 2 | 39.699 2 | 44.702 1 | |
Peppers | 4 | 20.766 3 | 26.917 3 | 31.237 3 | 32.932 1 | 35.265 6 | 37.270 5 | 38.834 2 | 43.545 1 |
(256像素×256像素) | 8 | 19.018 9 | 27.232 3 | 31.271 6 | 32.749 9 | 34.830 6 | 36.700 4 | 38.845 1 | 43.592 9 |
16 | 18.756 4 | 25.921 4 | 30.783 0 | 32.554 3 | 34.467 2 | 36.488 1 | 38.073 3 | 43.514 8 | |
32 | 18.075 7 | 25.373 5 | 29.429 6 | 31.795 2 | 32.997 5 | 34.157 8 | 36.986 4 | 41.876 1 | |
1 | 25.526 1 | 29.850 9 | 34.288 7 | 35.074 8 | 36.053 6 | 37.651 6 | 39.035 0 | 41.885 5 | |
2 | 25.458 2 | 30.192 0 | 34.216 3 | 35.767 9 | 36.506 8 | 37.436 6 | 39.727 8 | 42.287 9 | |
Lena | 4 | 25.412 3 | 29.578 1 | 34.124 7 | 35.086 4 | 36.342 2 | 37.493 0 | 39.270 5 | 42.433 7 |
(512像素×512像素) | 8 | 25.751 4 | 29.734 7 | 33.225 8 | 35.286 4 | 36.226 6 | 37.530 1 | 38.591 0 | 41.950 1 |
16 | 25.369 5 | 30.683 7 | 33.117 5 | 35.002 9 | 36.594 2 | 37.237 4 | 38.991 9 | 42.083 8 | |
32 | 24.926 4 | 29.219 5 | 33.015 7 | 34.907 1 | 36.035 9 | 37.795 8 | 38.317 1 | 41.254 6 | |
1 | 19.974 2 | 22.428 7 | 25.103 1 | 26.572 4 | 28.694 6 | 30.274 1 | 32.895 9 | 37.861 0 | |
2 | 20.084 6 | 22.364 1 | 25.067 4 | 26.581 1 | 28.903 9 | 30.315 6 | 32.529 6 | 37.656 2 | |
Mandrill | 4 | 19.842 0 | 22.266 0 | 25.025 6 | 26.710 0 | 29.230 6 | 29.942 1 | 32.008 4 | 37.959 1 |
(1 024像素×1 024像素) | 8 | 20.179 6 | 22.372 4 | 24.948 5 | 25.943 3 | 28.804 9 | 30.318 6 | 32.255 4 | 37.249 4 |
16 | 20.185 0 | 22.668 0 | 24.889 7 | 25.877 1 | 28.825 3 | 30.312 6 | 31.957 1 | 37.262 6 | |
32 | 19.298 5 | 22.049 6 | 24.892 6 | 26.090 4 | 28.392 9 | 31.465 6 | 31.833 9 | 37.049 6 |
表3
不同大小的高斯随机观测矩阵重构2维图像重构时间"
原始图像 | t | 重构时间/s | ||||||
0.125 0 | 0.250 0 | 0.375 0 | 0.437 5 | 0.500 0 | 0.562 5 | 0.625 00.750 0 | ||
1 | 15.43 | 29.92 | 44.58 | 67.86 | 68.74 | 79.81 | 87.54101.1 | |
2 | 6.63 | 11.36 | 17.22 | 19.92 | 20.88 | 22.46 | 23.8025.55 | |
Peppers | 4 | 4.18 | 6.70 | 8.36 | 9.12 | 9.22 | 10.04 | 10.8911.15 |
(256像素×256像素) | 8 | 4.16 | 5.08 | 5.79 | 6.04 | 6.11 | 6.63 | 6.086.21 |
16 | 5.13 | 6.27 | 6.56 | 6.56 | 6.30 | 6.59 | 6.295.90 | |
32 | 6.34 | 8.13 | 8.73 | 8.86 | 8.89 | 8.96 | 8.568.00 | |
1 | 343.27 | 799.88 | 1 148.72 | 1 502.25 | 1 981.27 | 2 089.41 | 2 149.902 622.18 | |
2 | 73.29 | 145.95 | 241.79 | 283.20 | 299.61 | 327.55 | 357.10421.12 | |
Lena | 4 | 27.33 | 45.22 | 70.33 | 86.18 | 86.93 | 99.41 | 97.01102.31 |
(512像素×512像素) | 8 | 15.52 | 24.40 | 31.65 | 37.24 | 41.09 | 41.33 | 44.2044.87 |
16 | 17.72 | 19.00 | 25.18 | 27.15 | 27.78 | 27.74 | 27.6727.58 | |
32 | 16.77 | 16.56 | 22.34 | 23.95 | 24.50 | 25.33 | 25.4826.15 | |
1 | 7 290.30 | 17 256.07 | 21 678.50 | 30 188.10 | 35 471.23 | 39 676.34 | 42 527.23 43 109.70 | |
2 | 1 372.94 | 3 196.25 | 4 426.00 | 6 423.35 | 7 239.75 | 8 097.23 | 8 306.439 055.33 | |
Mandrill | 4 | 287.38 | 596.67 | 926.51 | 1 217.80 | 1 270.33 | 1 581.75 | 1 688.31692.5 |
(1 024像素×1 024像素) | 8 | 99.87 | 210.04 | 327.23 | 369.90 | 368.14 | 418.80 | 442.65482.11 |
16 | 85.83 | 123.42 | 149.09 | 167.18 | 171.70 | 177.75 | 199.72204.44 | |
32 | 73.28 | 83.17 | 92.48 | 104.28 | 112.36 | 112.39 | 113.02113.65 |
表5
与其他低存储压缩感知方法比较的峰值信噪比(Lena 512像素×512像素)"
压缩感知方法 | 峰值信噪比/dB | |||||||
0.125 0 | 0.250 0 | 0.375 0 | 0.437 5 | 0.500 0 | 0.562 5 | 0.625 0 | 0.750 0 | |
本文t=2 | 25.458 2 | 30.192 0 | 34.216 3 | 35.767 9 | 36.506 8 | 37.436 6 | 39.727 8 | 42.287 9 |
本文t=4 | 25.412 3 | 29.578 1 | 34.124 7 | 35.086 4 | 36.342 2 | 37.493 0 | 39.270 5 | 42.433 7 |
本文t=8 | 25.751 4 | 29.734 7 | 33.225 8 | 35.286 4 | 36.226 6 | 37.530 1 | 38.591 0 | 41.950 1 |
本文t=16 | 25.369 5 | 30.683 7 | 33.117 5 | 35.002 9 | 36.594 2 | 37.237 4 | 38.991 9 | 42.083 8 |
本文t=32 | 24.926 4 | 29.219 5 | 33.015 7 | 34.907 1 | 36.035 9 | 37.795 8 | 38.317 1 | 41.254 6 |
文献[ | 24.331 4 | 29.633 3 | 32.984 7 | 34.657 5 | 36.334 9 | 37.436 7 | 38.628 1 | 41.490 3 |
文献[ | 25.060 9 | 28.349 7 | 29.528 1 | 31.121 5 | 33.785 3 | 34.981 0 | 35.296 1 | 37.237 2 |
表6
与其他低存储压缩感知方法比较的重构时间(Lena 512像素×512像素)"
压缩感知方法 | 重构时间/s | |||||||
0.125 0 | 0.250 0 | 0.375 0 | 0.437 5 | 0.500 0 | 0.562 5 | 0.625 0 | 0.750 0 | |
本文t=2 | 73.29 | 145.95 | 241.79 | 283.20 | 299.61 | 327.55 | 357.10 | 421.12 |
本文t=4 | 27.33 | 45.22 | 70.33 | 86.18 | 86.93 | 99.41 | 97.01 | 102.31 |
本文t=8 | 15.52 | 24.40 | 31.65 | 37.24 | 41.09 | 41.313 | 44.20 | 44.87 |
本文t=16 | 17.72 | 19.00 | 25.18 | 27.15 | 22.78 | 25.748 | 25.67 | 26.58 |
本文t=32 | 24.77 | 26.56 | 28.34 | 28.95 | 26.50 | 26.633 | 26.48 | 26.15 |
文献[ | 24.149 3 | 26.918 8 | 35.43 | 55.60 | 71.31 | 94.93 | 122.27 | 196.38 |
文献[ | 230.79 | 542.66 | 989.49 | 1 212.8 | 1 649.6 | 1879.1 | 2 132.2 | 2 448.3 |
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