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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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Demosaicing of Barbara image for the three demosaicing rules in figure 10.The incorrect rules (left and right), which use corrupted aliases to reconstruct chrominance, lead to local discolorations near high frequency regions, whereas the correct rule (center) results in no discolorations.
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pone-0061846-g011: Demosaicing of Barbara image for the three demosaicing rules in figure 10.The incorrect rules (left and right), which use corrupted aliases to reconstruct chrominance, lead to local discolorations near high frequency regions, whereas the correct rule (center) results in no discolorations.

Mentions: Now that we now know how to detect demosaicing hazards, artifact-free reconstruction is easy. Locally, it is now possible to detect which of the chrominance coefficients or are uncorrupted by luminance and then subsequently use these in the reconstruction, as in Figure 10. Using the (complex dual-tree) wavelet packet transform, this local demosaicing can be implemented, precisely because of the aforementioned ambiguity in the demosaicing rules presented in Section 2: under the assumptions of small chrominance bandwidth (12) and small luminance bandwidth (11), it follows from (10) that . Realizing this, the first line in 2 can be rewritten as in Table 3. Note that these equations are only valid for the first complex wavelet filter tree, as the sign change (22) results in switched signs for some coefficients in these equations, the derivation of these formulas for the other complex wavelet trees is not mentioned here to conserve space, but is completely analogous. Alternatively, the signs could be changed as a preprocessing step. From Figure 10, it is seen that there is only one situation where only uncorrupted bands are used, i.e. only one demosaicing rule will lead to correct colours in the demosaicing result. The consequence of using the different demosaicing rules is depicted by the comparison in Figure 11. Figure 11(left) suffers from the worst colour distortions, which is explained through the use of only corrupted chrominance aliases (Figure 10(left)). Conversely, Figure 11(middle) suffers from the least colour distortions. Figure 11(right) represents a kind of middle ground. Here the corrupted chrominance information of the subband is mixed with the uncorrupted information of the band. The global wavelet-based demosaicing approach, the one originally used in [14], corresponds to the middle ground concerning demosaicing artifacts (Figure 11c) by averaging the uncorrupted with the corrupted coefficient. In our proposed locally adaptive complex wavelet-based demosaicing, we switch locally between the demosaicing rules in Table 2 and Table 3, depending on the detection result explained in Section 2.2. On top of that, this approach maintains the translation invariance so far as possible, as the detection result (28) is constant across the different complex wavelet trees. Using (28), the cost of making a “miss” decision can be weighed against the cost of making an “unsure” decision . Let be the erroneous contribution due to luminance in one of the chrominance coefficients. The accumulated errors in the reconstructed coefficients can easily be calculated using (5), they are shown in Table 4.


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)

Demosaicing of Barbara image for the three demosaicing rules in figure 10.The incorrect rules (left and right), which use corrupted aliases to reconstruct chrominance, lead to local discolorations near high frequency regions, whereas the correct rule (center) results in no discolorations.
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC3643977&req=5

pone-0061846-g011: Demosaicing of Barbara image for the three demosaicing rules in figure 10.The incorrect rules (left and right), which use corrupted aliases to reconstruct chrominance, lead to local discolorations near high frequency regions, whereas the correct rule (center) results in no discolorations.
Mentions: Now that we now know how to detect demosaicing hazards, artifact-free reconstruction is easy. Locally, it is now possible to detect which of the chrominance coefficients or are uncorrupted by luminance and then subsequently use these in the reconstruction, as in Figure 10. Using the (complex dual-tree) wavelet packet transform, this local demosaicing can be implemented, precisely because of the aforementioned ambiguity in the demosaicing rules presented in Section 2: under the assumptions of small chrominance bandwidth (12) and small luminance bandwidth (11), it follows from (10) that . Realizing this, the first line in 2 can be rewritten as in Table 3. Note that these equations are only valid for the first complex wavelet filter tree, as the sign change (22) results in switched signs for some coefficients in these equations, the derivation of these formulas for the other complex wavelet trees is not mentioned here to conserve space, but is completely analogous. Alternatively, the signs could be changed as a preprocessing step. From Figure 10, it is seen that there is only one situation where only uncorrupted bands are used, i.e. only one demosaicing rule will lead to correct colours in the demosaicing result. The consequence of using the different demosaicing rules is depicted by the comparison in Figure 11. Figure 11(left) suffers from the worst colour distortions, which is explained through the use of only corrupted chrominance aliases (Figure 10(left)). Conversely, Figure 11(middle) suffers from the least colour distortions. Figure 11(right) represents a kind of middle ground. Here the corrupted chrominance information of the subband is mixed with the uncorrupted information of the band. The global wavelet-based demosaicing approach, the one originally used in [14], corresponds to the middle ground concerning demosaicing artifacts (Figure 11c) by averaging the uncorrupted with the corrupted coefficient. In our proposed locally adaptive complex wavelet-based demosaicing, we switch locally between the demosaicing rules in Table 2 and Table 3, depending on the detection result explained in Section 2.2. On top of that, this approach maintains the translation invariance so far as possible, as the detection result (28) is constant across the different complex wavelet trees. Using (28), the cost of making a “miss” decision can be weighed against the cost of making an “unsure” decision . Let be the erroneous contribution due to luminance in one of the chrominance coefficients. The accumulated errors in the reconstructed coefficients can easily be calculated using (5), they are shown in Table 4.

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