densel
2009-09-05, 16:10
我们知道 f 和c 的卷积结果是fc ，现在是想通过实际的测量值s 来表示fc 再恢复出f 出来，c 是知道的，最大的麻烦就是fc的维数跟f 的维数不一样，现在的话就是如何来通过测的值s来模拟恢复出 f ？望高手指导！
下面是假设 f 知道的情况下算出卷积 fc 的。
f =
0.4018 9.2796 1.6633 5.1098 7.4174 0.2971 9.3169 1.8860 4.6156
9.2796 1.6716 5.1611 7.5295 0.3031 9.5528 1.9434 4.7800 7.5081
1.6633 5.1611 7.5672 0.3061 9.6972 1.9827 4.9010 7.7368 0.1954
5.1098 7.5295 0.3061 9.7458 2.0026 4.9751 7.8931 0.2003 9.2868
7.4174 0.3031 9.6972 2.0026 5.0000 7.9724 0.2033 9.4744 2.1905
0.2971 9.5528 1.9827 4.9751 7.9724 0.2044 9.5696 2.2236 4.4741
9.3169 1.9434 4.9010 7.8931 0.2033 9.5696 2.2347 4.5191 7.8490
1.8860 4.7800 7.7368 0.2003 9.4744 2.2236 4.5191 7.8884 0.1145
4.6156 7.5081 0.1954 9.2868 2.1905 4.4741 7.8490 0.1145 8.8294
fc =
0.4018 9.6815 11.3447 16.4545 23.8719 24.1690 33.4859 5.3719 39.9875 39.5857 30.3061 28.6428 23.5330 16.1156
15.8185 6.5016 4.6156
9.6815 20.6327 27.4571 40.0964 47.8169 57.6668 68.9271 75.5931 87.7168 78.0354 67.0841 60.2597 47.6205 39.9000 30.0501 18.7897 12.1237
11.3447 27.4571 41.8488 54.7942 72.2118 84.0444 100.2058 114.6086 126.9276 115.5829 99.4705 85.0789 72.1335 54.7158 42.8832 26.7218 12.3191
16.4545 40.0964 54.7942 77.4853 96.9056 113.7133 137.7677 152.3708 173.9767 157.5222 133.8803 119.1825 96.4913 77.0711 60.2634 36.2090 21.6059
23.8719 47.8169 72.2118 96.9056 121.3259 146.1060 170.3638 194.4412 218.2376 194.3657 170.4207 146.0258 121.3320 96.9117 72.1316 47.8739 23.7964
24.1690 57.6668 84.0444 113.7133 146.1060 171.0904 204.9178 231.2189 259.4894 235.3204 201.8226 175.4450 145.7761 113.3834 88.3990 54.5716 28.2705
33.4859 68.9271 100.2058 137.7677 170.3638 204.9178 240.9800 271.8002 307.9197 274.4338 238.9925 207.7139 170.1520 137.5559 103.0019 66.9397 36.1195
35.3719 75.5931 114.6086 152.3708 194.4412 231.2189 271.8002 310.5087 346.7427 311.3708 271.1496 232.1342 194.3719 152.3015 115.5238 74.9426 36.2340
39.9875 87.7168 126.9276 173.9767 218.2376 259.4894 307.9197 346.7427 391.8061 351.8186 304.0893 264.8785 217.8294 173.5685 132.3167 83.8864 45.0634
39.5857 78.0354 115.5829 157.5222 194.3657 235.3204 274.4338 311.3708 351.8186 312.2329 273.7832 236.2357 194.2964 157.4529 116.4982 77.3848 40.4478
30.3061 67.0841 99.4705 133.8803 170.4207 201.8226 238.9925 271.1496 304.0893 273.7832 237.0051 204.6187 170.2089 133.6685 102.2666 65.0967 32.9397
28.6428 60.2597 85.0789 119.1825 146.0258 175.4450 207.7139 232.1342 264.8785 236.2357 204.6187 179.7996 145.6959 118.8527 89.4335 57.1646 32.7443
23.5330 47.6205 72.1335 96.4913 121.3320 145.7761 170.1520 194.3719 217.8294 194.2964 170.2089 145.6959 121.3381 96.4974 72.0533 47.6775 23.4575
16.1156 39.9000 54.7158 77.0711 96.9117 113.3834 137.5559 152.3015 173.5685 157.4529 133.6685 118.8527 96.4974 76.6568 60.1850 36.0125 21.2670
15.8185 30.0501 42.8832 60.2634 72.1316 88.3990 103.0019 115.5238 132.3167 116.4982 102.2666 89.4335 72.0533 60.1850 43.9177 29.3148 16.7929
6.5016 18.7897 26.7218 36.2090 47.8739 54.5716 66.9397 74.9426 83.8864 77.3848 65.0967 57.1646 47.6775 36.0125 29.3148 16.9467 8.9438
4.6156 12.1237 12.3191 21.6059 23.7964 28.2705 36.1195 36.2340 45.0634 40.4478 32.9397 32.7443 23.4575 21.2670 16.7929 8.9438 8.8294
显然：f 是9行9列，而卷积的结果 fc是17行17列。现在我们可以探测出s的值也就是等价于fc，麻烦是如何将s的值转化为准确的 fc 的值，后面再恢复出 f 的值就容易啦！
下面是假设 f 知道的情况下算出卷积 fc 的。
f =
0.4018 9.2796 1.6633 5.1098 7.4174 0.2971 9.3169 1.8860 4.6156
9.2796 1.6716 5.1611 7.5295 0.3031 9.5528 1.9434 4.7800 7.5081
1.6633 5.1611 7.5672 0.3061 9.6972 1.9827 4.9010 7.7368 0.1954
5.1098 7.5295 0.3061 9.7458 2.0026 4.9751 7.8931 0.2003 9.2868
7.4174 0.3031 9.6972 2.0026 5.0000 7.9724 0.2033 9.4744 2.1905
0.2971 9.5528 1.9827 4.9751 7.9724 0.2044 9.5696 2.2236 4.4741
9.3169 1.9434 4.9010 7.8931 0.2033 9.5696 2.2347 4.5191 7.8490
1.8860 4.7800 7.7368 0.2003 9.4744 2.2236 4.5191 7.8884 0.1145
4.6156 7.5081 0.1954 9.2868 2.1905 4.4741 7.8490 0.1145 8.8294
fc =
0.4018 9.6815 11.3447 16.4545 23.8719 24.1690 33.4859 5.3719 39.9875 39.5857 30.3061 28.6428 23.5330 16.1156
15.8185 6.5016 4.6156
9.6815 20.6327 27.4571 40.0964 47.8169 57.6668 68.9271 75.5931 87.7168 78.0354 67.0841 60.2597 47.6205 39.9000 30.0501 18.7897 12.1237
11.3447 27.4571 41.8488 54.7942 72.2118 84.0444 100.2058 114.6086 126.9276 115.5829 99.4705 85.0789 72.1335 54.7158 42.8832 26.7218 12.3191
16.4545 40.0964 54.7942 77.4853 96.9056 113.7133 137.7677 152.3708 173.9767 157.5222 133.8803 119.1825 96.4913 77.0711 60.2634 36.2090 21.6059
23.8719 47.8169 72.2118 96.9056 121.3259 146.1060 170.3638 194.4412 218.2376 194.3657 170.4207 146.0258 121.3320 96.9117 72.1316 47.8739 23.7964
24.1690 57.6668 84.0444 113.7133 146.1060 171.0904 204.9178 231.2189 259.4894 235.3204 201.8226 175.4450 145.7761 113.3834 88.3990 54.5716 28.2705
33.4859 68.9271 100.2058 137.7677 170.3638 204.9178 240.9800 271.8002 307.9197 274.4338 238.9925 207.7139 170.1520 137.5559 103.0019 66.9397 36.1195
35.3719 75.5931 114.6086 152.3708 194.4412 231.2189 271.8002 310.5087 346.7427 311.3708 271.1496 232.1342 194.3719 152.3015 115.5238 74.9426 36.2340
39.9875 87.7168 126.9276 173.9767 218.2376 259.4894 307.9197 346.7427 391.8061 351.8186 304.0893 264.8785 217.8294 173.5685 132.3167 83.8864 45.0634
39.5857 78.0354 115.5829 157.5222 194.3657 235.3204 274.4338 311.3708 351.8186 312.2329 273.7832 236.2357 194.2964 157.4529 116.4982 77.3848 40.4478
30.3061 67.0841 99.4705 133.8803 170.4207 201.8226 238.9925 271.1496 304.0893 273.7832 237.0051 204.6187 170.2089 133.6685 102.2666 65.0967 32.9397
28.6428 60.2597 85.0789 119.1825 146.0258 175.4450 207.7139 232.1342 264.8785 236.2357 204.6187 179.7996 145.6959 118.8527 89.4335 57.1646 32.7443
23.5330 47.6205 72.1335 96.4913 121.3320 145.7761 170.1520 194.3719 217.8294 194.2964 170.2089 145.6959 121.3381 96.4974 72.0533 47.6775 23.4575
16.1156 39.9000 54.7158 77.0711 96.9117 113.3834 137.5559 152.3015 173.5685 157.4529 133.6685 118.8527 96.4974 76.6568 60.1850 36.0125 21.2670
15.8185 30.0501 42.8832 60.2634 72.1316 88.3990 103.0019 115.5238 132.3167 116.4982 102.2666 89.4335 72.0533 60.1850 43.9177 29.3148 16.7929
6.5016 18.7897 26.7218 36.2090 47.8739 54.5716 66.9397 74.9426 83.8864 77.3848 65.0967 57.1646 47.6775 36.0125 29.3148 16.9467 8.9438
4.6156 12.1237 12.3191 21.6059 23.7964 28.2705 36.1195 36.2340 45.0634 40.4478 32.9397 32.7443 23.4575 21.2670 16.7929 8.9438 8.8294
显然：f 是9行9列，而卷积的结果 fc是17行17列。现在我们可以探测出s的值也就是等价于fc，麻烦是如何将s的值转化为准确的 fc 的值，后面再恢复出 f 的值就容易啦！