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Figure-3 16 subimages obtained after step 2 3) Define a threshold value y for the selection of subimages to be decomposed furtherly. If the relative energy of a subimage in a subband is more than y, then select it for step 4, otherwise eliminate it and modify its coefficients as zero for reconstruction.

Figure 3 -3 16 subimages obtained after step 2 3) Define a threshold value y for the selection of subimages to be decomposed furtherly. If the relative energy of a subimage in a subband is more than y, then select it for step 4, otherwise eliminate it and modify its coefficients as zero for reconstruction.

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Figure-1 Conventional pyramid structured wavelet decomposition Index Terms— Discrete Wavelet Transform, Entropy, Multiresolution Signal Analysis, Relative Energy.
Figure-1 Conventional pyramid structured wavelet decomposition Index Terms— Discrete Wavelet Transform, Entropy, Multiresolution Signal Analysis, Relative Energy.
We eliminate the subimages according to the step 3, by defining the threshold value as 20%. This means if the energy of a subimage is less than 20% then modify its coeffient values as zero. Selected subimages for further decomposition can be seen in Fig.6. Proceedings of The IRES 21“ International Conference, Amsterdam, Netherland, 25" December 2015, ISBN: 978-93-85832-79-
We eliminate the subimages according to the step 3, by defining the threshold value as 20%. This means if the energy of a subimage is less than 20% then modify its coeffient values as zero. Selected subimages for further decomposition can be seen in Fig.6. Proceedings of The IRES 21“ International Conference, Amsterdam, Netherland, 25" December 2015, ISBN: 978-93-85832-79-
Figure-7 Energy distribution of 16 subimages. From a) to d), distribution revealed when A, H, V and D decomposed. Numbers 1,2,3 and 4 represent A, H, V and D subimage respectively. For instance, in c), 2 represent the subimage VH. For step 4 and 5, to be analyzed, there are 6 subimages left out of 13. Let us illustrate the remaining steps on a subimage in Fig.6. Assume that we need to understand whether further decomposition of HH into subchannels is necessary to extract more details or not. We decompose it to subimages HHA, HHH, HHV, HHD. The energy distribution of these subimages is shown in Fig.8. At this point, subimages HH and HHH should be compared in terms of relevant energies they contain since they share the same positional edge detail (step 5). It is seen from Fig.7-b and Fig.8, subimages HHH and HH have almost the same relative energies. Moreover, entropies of energy distributions of Fig.7-b and Fig.8 are almost identical which is a fact that points to dominancy of approximation and horizontal detail coefficients in terms of relative energy in the subband they are located in. Since there is not a significant change between the relative energies of HH and HHH, we conclude that the further decomposition of HH is not required.Fig.9 shows the final decomposition structure of image in Fig.4 according to the proposed algorithm. Reconstructed image from the selected coefficients and its difference with the original image are shown in Fig.10 and Fig.11 respectively. As seen from Fig.10, reconstructed image is blurred, however it is still containing the intensity transition information between pixels.
Figure-7 Energy distribution of 16 subimages. From a) to d), distribution revealed when A, H, V and D decomposed. Numbers 1,2,3 and 4 represent A, H, V and D subimage respectively. For instance, in c), 2 represent the subimage VH. For step 4 and 5, to be analyzed, there are 6 subimages left out of 13. Let us illustrate the remaining steps on a subimage in Fig.6. Assume that we need to understand whether further decomposition of HH into subchannels is necessary to extract more details or not. We decompose it to subimages HHA, HHH, HHV, HHD. The energy distribution of these subimages is shown in Fig.8. At this point, subimages HH and HHH should be compared in terms of relevant energies they contain since they share the same positional edge detail (step 5). It is seen from Fig.7-b and Fig.8, subimages HHH and HH have almost the same relative energies. Moreover, entropies of energy distributions of Fig.7-b and Fig.8 are almost identical which is a fact that points to dominancy of approximation and horizontal detail coefficients in terms of relative energy in the subband they are located in. Since there is not a significant change between the relative energies of HH and HHH, we conclude that the further decomposition of HH is not required.Fig.9 shows the final decomposition structure of image in Fig.4 according to the proposed algorithm. Reconstructed image from the selected coefficients and its difference with the original image are shown in Fig.10 and Fig.11 respectively. As seen from Fig.10, reconstructed image is blurred, however it is still containing the intensity transition information between pixels.
Relative Energy and Entropy Based Wavelet Packet Decomposition of Images Figure-8 Relevant energies of subimages HHA, HHH, HHV and HHD or 1, 2, 3 and 4 respectively. IV. DISCUSSION The proposed algorithm differs from the conventional pyramid structured and tree structured wavelet decomposition algorithms by considering the relative energy change between the parentsubimageand its corresponding child subimage which contains the same positional edge detail with it. In addition to the relative energy, entropy also reflects the dominancy of a specific subchannel in terms of relative energy. This method can be used in image compression and image enhancement applications. For image compression applications elected subbands can be exploited for compression process, while on the other hand selected coefficients can be amplified for enhancing images. An application of enhancing medical images via proposed method is being studied by the authors of this paper.
Relative Energy and Entropy Based Wavelet Packet Decomposition of Images Figure-8 Relevant energies of subimages HHA, HHH, HHV and HHD or 1, 2, 3 and 4 respectively. IV. DISCUSSION The proposed algorithm differs from the conventional pyramid structured and tree structured wavelet decomposition algorithms by considering the relative energy change between the parentsubimageand its corresponding child subimage which contains the same positional edge detail with it. In addition to the relative energy, entropy also reflects the dominancy of a specific subchannel in terms of relative energy. This method can be used in image compression and image enhancement applications. For image compression applications elected subbands can be exploited for compression process, while on the other hand selected coefficients can be amplified for enhancing images. An application of enhancing medical images via proposed method is being studied by the authors of this paper.
Figure-9 Completed decomposition of the image in Fig.4
Figure-9 Completed decomposition of the image in Fig.4
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