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Computationally efficient locally adaptive demosaicing of color filter array images using the dual-tree complex wavelet packet transform.

Aelterman J, Goossens B, De Vylder J, Pižurica A, Philips W - PLoS ONE (2013)

Bottom Line: By using a novel locally adaptive approach for demosaicing (complex) wavelet coefficients, we show that many of the common demosaicing artifacts can be avoided in an efficient way.Results demonstrate that the proposed method is competitive with respect to the current state of the art, but incurs a lower computational cost.The wavelet approach also allows for computationally effective denoising or deblurring approaches.

View Article: PubMed Central - PubMed

Affiliation: IPI-TELIN-IMINDS, Ghent University, Ghent, Belgium. jaelterm@telin.ugent.be

ABSTRACT
Most digital cameras use an array of alternating color filters to capture the varied colors in a scene with a single sensor chip. Reconstruction of a full color image from such a color mosaic is what constitutes demosaicing. In this paper, a technique is proposed that performs this demosaicing in a way that incurs a very low computational cost. This is done through a (dual-tree complex) wavelet interpretation of the demosaicing problem. By using a novel locally adaptive approach for demosaicing (complex) wavelet coefficients, we show that many of the common demosaicing artifacts can be avoided in an efficient way. Results demonstrate that the proposed method is competitive with respect to the current state of the art, but incurs a lower computational cost. The wavelet approach also allows for computationally effective denoising or deblurring approaches.

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Comparison of reconstruction bandwidths when extended demosaicing rules are used.Reconstructed luminance bandwidth (indicated by the spectral support in green) of (a) the reconstruction rules in Table 5 and (b) the reconstruction rules in Table 5 combined with the rules in Table 6.
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pone-0061846-g012: Comparison of reconstruction bandwidths when extended demosaicing rules are used.Reconstructed luminance bandwidth (indicated by the spectral support in green) of (a) the reconstruction rules in Table 5 and (b) the reconstruction rules in Table 5 combined with the rules in Table 6.

Mentions: The reconstruction rules in Table 5 allow for a reconstruction of the luminance bandwidth that is limited to the regions indicated in green in Figure 12(a). We now investigate the possibility of extending the reconstruction bandwidth for the luminance to the one shown in Figure 12(b). We take a look at the wavelet coefficients and under hypothesis , which means a dominant horizontal local feature. In this scenario, we may write:(29)This opens the possibility of reconstructing the high frequency luminance as  = . Similarly, for hypothesis , it is possible to reconstruct  = . Reconstructing these high luminance frequency coefficients this way is undesirable, as requires compensating for the time inverted wavelet filter in the reconstruction, increasing the complexity, however we note that this can not be avoided: Consider filtering the mosaic with non time inverted first scale wavelet filters, then exploiting that (9) holds such that :In this case,  =  only holds wheni.e. when the lowpass filter is a perfectly symmetric filter, which is usually not the case. Still, symmetric filters can be implemented for the first complex wavelet tree, but it becomes problematic when looking at different trees of our dual-tree complex wavelet packet decomposition. This is because of the one sample shift requirement for complex wavelet filter trees (21), as now:i.e. in anything but the most trivial case (), is impossible for both the filters and to be perfectly symmetric. This makes it impossible to use the normal reconstruction filter bank when reconstructing these high frequency luminance coefficients. We therefore revert to the first idea, to use the reconstruction rules in Table 6, which in contrast with the rules in Table 5 make use of time reversed wavelet reconstruction filters, which increases the implementation complexity. Again, we take a look at the errors accumulating when the wrong hypothesis is chosen, these are shown in Table 7. Since the dual-tree complex wavelet transform is a Parseval frame, the influence of the coefficients in Table 4 and Table 7 can be directly related to mean square error (MSE) in the image domain. The MSE due to a “miss” decision is, which we will use as the cost in (28) is , while the cost for an “unsure” decision is . This leads to a ratio The significance of this result is that it pays off to include the “unsure” decision in our decision framework as it can be seen from (28) that the decision will only improve MSE and be used when , which is true in this case.


Computationally efficient locally adaptive demosaicing of color filter array images using the dual-tree complex wavelet packet transform.

Aelterman J, Goossens B, De Vylder J, Pižurica A, Philips W - PLoS ONE (2013)

Comparison of reconstruction bandwidths when extended demosaicing rules are used.Reconstructed luminance bandwidth (indicated by the spectral support in green) of (a) the reconstruction rules in Table 5 and (b) the reconstruction rules in Table 5 combined with the rules in Table 6.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3643977&req=5

pone-0061846-g012: Comparison of reconstruction bandwidths when extended demosaicing rules are used.Reconstructed luminance bandwidth (indicated by the spectral support in green) of (a) the reconstruction rules in Table 5 and (b) the reconstruction rules in Table 5 combined with the rules in Table 6.
Mentions: The reconstruction rules in Table 5 allow for a reconstruction of the luminance bandwidth that is limited to the regions indicated in green in Figure 12(a). We now investigate the possibility of extending the reconstruction bandwidth for the luminance to the one shown in Figure 12(b). We take a look at the wavelet coefficients and under hypothesis , which means a dominant horizontal local feature. In this scenario, we may write:(29)This opens the possibility of reconstructing the high frequency luminance as  = . Similarly, for hypothesis , it is possible to reconstruct  = . Reconstructing these high luminance frequency coefficients this way is undesirable, as requires compensating for the time inverted wavelet filter in the reconstruction, increasing the complexity, however we note that this can not be avoided: Consider filtering the mosaic with non time inverted first scale wavelet filters, then exploiting that (9) holds such that :In this case,  =  only holds wheni.e. when the lowpass filter is a perfectly symmetric filter, which is usually not the case. Still, symmetric filters can be implemented for the first complex wavelet tree, but it becomes problematic when looking at different trees of our dual-tree complex wavelet packet decomposition. This is because of the one sample shift requirement for complex wavelet filter trees (21), as now:i.e. in anything but the most trivial case (), is impossible for both the filters and to be perfectly symmetric. This makes it impossible to use the normal reconstruction filter bank when reconstructing these high frequency luminance coefficients. We therefore revert to the first idea, to use the reconstruction rules in Table 6, which in contrast with the rules in Table 5 make use of time reversed wavelet reconstruction filters, which increases the implementation complexity. Again, we take a look at the errors accumulating when the wrong hypothesis is chosen, these are shown in Table 7. Since the dual-tree complex wavelet transform is a Parseval frame, the influence of the coefficients in Table 4 and Table 7 can be directly related to mean square error (MSE) in the image domain. The MSE due to a “miss” decision is, which we will use as the cost in (28) is , while the cost for an “unsure” decision is . This leads to a ratio The significance of this result is that it pays off to include the “unsure” decision in our decision framework as it can be seen from (28) that the decision will only improve MSE and be used when , which is true in this case.

Bottom Line: By using a novel locally adaptive approach for demosaicing (complex) wavelet coefficients, we show that many of the common demosaicing artifacts can be avoided in an efficient way.Results demonstrate that the proposed method is competitive with respect to the current state of the art, but incurs a lower computational cost.The wavelet approach also allows for computationally effective denoising or deblurring approaches.

View Article: PubMed Central - PubMed

Affiliation: IPI-TELIN-IMINDS, Ghent University, Ghent, Belgium. jaelterm@telin.ugent.be

ABSTRACT
Most digital cameras use an array of alternating color filters to capture the varied colors in a scene with a single sensor chip. Reconstruction of a full color image from such a color mosaic is what constitutes demosaicing. In this paper, a technique is proposed that performs this demosaicing in a way that incurs a very low computational cost. This is done through a (dual-tree complex) wavelet interpretation of the demosaicing problem. By using a novel locally adaptive approach for demosaicing (complex) wavelet coefficients, we show that many of the common demosaicing artifacts can be avoided in an efficient way. Results demonstrate that the proposed method is competitive with respect to the current state of the art, but incurs a lower computational cost. The wavelet approach also allows for computationally effective denoising or deblurring approaches.

Show MeSH