Page 53 - ITU Journal, Future and evolving technologies - Volume 1 (2020), Issue 1, Inaugural issue
P. 53

ITU Journal on Future and Evolving Technologies, Volume 1 (2020), Issue 1




            0.8                      1                        1                         1
                                    0.5                       0.5                       0.5
            0.6
                                     0                        0                         0
            0.4
                                    -0.5                      -0.5                     -0.5
            0.2                      -1                       -1                        -1
           Amplitude  0              0   50  100  Approximation  200  250  300  0  50  100  Approximation  200  250  300  0  50  100  Approximation  200  250  300
                                                150
                                                                         150
                                                                                                   150
            -0.2                    0.2                       0.2                       0.1
                                                              0.1                      0.05
            -0.4                    0.1
                                                              0                         0
            -0.6                     0
                                                              -0.1                     -0.05
            -0.8                    -0.1                      -0.2                     -0.1
             0  100  200  300  400  500  600  0  50  100  150  200  250  300  0  50  100  150  200  250  300  0  50  100  150  200  250  300
                     Audio Signal               Detail                   Detail                   Detail
                      (a)                      (b)                       (c)                      (d)
            1                        1                         1                        1
           0.5                      0.5                       0.5                      0.5
            0                        0                         0                        0
           -0.5                     -0.5                      -0.5                     -0.5
            -1                       -1                       -1                        -1
            0   50  100  150  200  250  300  0  50  100  150  200  250  300  0  50  100  150  200  250  300  0  20  40  60  80  100  120  140  160  180  200
                     Approximation            Approximation             Approximation            Approximation
           0.1                      0.2                       0.1                      0.2
           0.05                     0.1                       0.05                     0.1
            0                        0                         0                        0
           -0.05                    -0.1                      -0.05                    -0.1
           -0.1                     -0.2                      -0.1                     -0.2
            0   50  100  150  200  250  300  0  50  100  150  200  250  300  0  50  100  150  200  250  300  0  20  40  60  80  100  120  140  160  180  200
                      Detail                    Detail                   Detail                   Detail
                      (e)                      (f)                       (g)                      (h)
          Fig. 11 – Approximation and detail coefficients obtained from an audio signal by some well-known wavelet transforms and MSICA.
          (a) Original audio Signal. Approximation and detail by (b) Daubechies 3; (c) Haar; (d) Biorthogonal 2.2; (e) Coiflets 4; (f) Fejer-Korovkin 4;
          (g) discrete Meyer; (h) MSICA.
          have examined its performance on the signal depicted     2011.
          in Fig. 11(a), which is an audio signal with a sampling  [2] Y. Kopsinis and S. McLaughlin, “Development of emd-
          frequency equal to 16 KHz. Fig. 11(b)-(g) show the       based denoising methods inspired by wavelet threshold-
          performance of the considered wavelet transforms in de-  ing,” IEEE Transactions on Signal Processing, vol. 57,
          composing this signal into approximation and detail. As  no. 4, pp. 1351–1362, 2009.
          it is clear from Fig. 11(h), like the other transforms,  [3] A. F. Laine, S. Schuler, J. Fan, and W. Huda, “Mam-
          MSICA is also able to decompose this audio signal into   mographic feature enhancement by multiscale analysis,”
          approximation and detail.                                IEEE Transactions on Medical Imaging, vol. 13, no. 4,
                                                                   pp. 725–740, 1994.
          5.  CONCLUSIONS                                       [4] F. M. Bayer, A. J. Kozakevicius, and R. J. Cintra, “An
                                                                   iterative wavelet threshold for signal denoising,” Signal
          We presented MSICA, a new method for Multi-Scale         Processing, vol. 162, pp. 10–20, 2019.
          decomposition based on Independent Component Anal-    [5] P. G. Bascoy, P. Quesada-Barriuso, D. B. Heras, and
          ysis (ICA), where the approximation and detail are sta-  F. Argüello, “Wavelet-based multicomponent denoising
          tistically independent. First, we extracted two corre-   profile for the classification of hyperspectral images,”
                                                                   IEEE Journal of Selected Topics in Applied Earth Ob-
          lated signals from the original digital signal by separat-  servations and Remote Sensing, vol. 12, no. 2, pp.
          ing their even and odd samples; then, we proved that ex-  722–733, 2019.
          tracting the independent components of the correlated  [6] A. Wong and A. K. Mishra, “Generalized probabilistic
          signals leads to the decomposition of the original sig-  scale space for image restoration,” IEEE Transactions
          nal into the approximation and detail. We showed that    on Image Processing, vol. 19, no. 10, pp. 2774–2780,
          MSICA outperforms well-known wavelet transforms in       2010.
          signal denoising when transmitting a signal over mul-  [7] G. Gilboa, “Nonlinear scale space with spatially varying
          tiple (noisy) channels as it exploits channel diversity.  stopping time,” IEEE Transactions on Pattern Analysis
          This property makes MSICA useful in many critical        and Machine Intelligence, vol. 30, no. 12, pp. 2175–2187,
          scenarios such as transmitting multimedia content reli-  2008.
          ably through underwater acoustic channels. Since these  [8] A. Mishra, A. Wong, D. A. Clausi, and P. W. Fieguth,
          channels may vary quickly over time, it is difficult to  “Quasi-random nonlinear scale space,” Pattern Recog-
          estimate them, which makes transmitting multimedia       nition Letters, vol. 31, no. 13, pp. 1850–1859, 2010.
          content underwater a very challenging task.           [9] T. Lindeberg, “Scale-space theory: A basic tool for ana-
                                                                   lyzing structures at different scales,” Journal of applied
          REFERENCES                                               statistics, vol. 21, no. 1-2, pp. 225–270, 1994.
                                                               [10] F. Jager, I. Koren, and L. Gyergyek, “Multiresolution
          [1] B. Ophir, M. Lustig, and M. Elad, “Multi-scale dictio-  representation and analysis of ecg waveforms,” in Pro-
             nary learning using wavelets,” IEEE Journal of Selected  ceedings Computers in Cardiology.  IEEE, 1990, pp.
             Topics in Signal Processing, vol. 5, no. 5, pp. 1014–1024,  547–550.





                                             © International Telecommunication Union, 2020                    33
   48   49   50   51   52   53   54   55   56   57   58