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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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Flowchart for the two scale dual-tree complex wavelet transform as used in this paper.Note that the analyticity recombination, see text, is not performed for in this paper.
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pone-0061846-g014: Flowchart for the two scale dual-tree complex wavelet transform as used in this paper.Note that the analyticity recombination, see text, is not performed for in this paper.

Mentions: A complete flowchart of the algorithm is shown in Figure 13. Without loss of generality, the assumed top left of the input Bayer mosaic is oriented as in Figure 5. Conceptually, there two concurrent dual-tree complex wavelet packet transformations needed for a basic implementation, such as the one implemented for this paper. However, computational complexity can be reduced due to the large number of zero, unused wavelet bands. Memory complexity can be halved as the non-zero complex wavelet bands in both transforms are mutually exclusive (compare the bands set to zero in Table 5 with Table 6). The first scale filters need to be designed according to requirement (9), i.e.The first scale filter for the second complex wavelet tree should then be chosen according to requirement (21) and (20):For the second scale of the complex wavelet filters there are no further special requirements concerning this demosaicing application. The need for a different demosaicing procedure for every complex wavelet tree has its origin in the sign change which is introduced into the demosaicing equation by the Hilbert transform first scale filter (22). The flowchart for the DT-CWT transforms is shown in Figure 14. For a 2D DT-CWT, it is necessary to perform a linear transformation of the output of the four separate filter trees, because only then the coefficients have an interpretation as coefficients of a complex 2D wavelet (see section “2-D dual-tree CWT” in [23]) and only then (diagonal) directional analysis is possible. We call this a recombination step. For example, from [23] we get that the real part of a 2D complex wavelet can be obtained as:For this work, this means subtracting wavelet bands such that:We forgo this recombination step in this paper, as this step complicates derivation of the demosaicing rules and in the proposed method no diagonal analysis is used. However for future work, we remark that diagonal directional analysis could open up the possibility of reconstructing even more of the original luminance bandwidth in the diagonal direction, at the cost of added implementation complexity.


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)

Flowchart for the two scale dual-tree complex wavelet transform as used in this paper.Note that the analyticity recombination, see text, is not performed for in this paper.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3643977&req=5

pone-0061846-g014: Flowchart for the two scale dual-tree complex wavelet transform as used in this paper.Note that the analyticity recombination, see text, is not performed for in this paper.
Mentions: A complete flowchart of the algorithm is shown in Figure 13. Without loss of generality, the assumed top left of the input Bayer mosaic is oriented as in Figure 5. Conceptually, there two concurrent dual-tree complex wavelet packet transformations needed for a basic implementation, such as the one implemented for this paper. However, computational complexity can be reduced due to the large number of zero, unused wavelet bands. Memory complexity can be halved as the non-zero complex wavelet bands in both transforms are mutually exclusive (compare the bands set to zero in Table 5 with Table 6). The first scale filters need to be designed according to requirement (9), i.e.The first scale filter for the second complex wavelet tree should then be chosen according to requirement (21) and (20):For the second scale of the complex wavelet filters there are no further special requirements concerning this demosaicing application. The need for a different demosaicing procedure for every complex wavelet tree has its origin in the sign change which is introduced into the demosaicing equation by the Hilbert transform first scale filter (22). The flowchart for the DT-CWT transforms is shown in Figure 14. For a 2D DT-CWT, it is necessary to perform a linear transformation of the output of the four separate filter trees, because only then the coefficients have an interpretation as coefficients of a complex 2D wavelet (see section “2-D dual-tree CWT” in [23]) and only then (diagonal) directional analysis is possible. We call this a recombination step. For example, from [23] we get that the real part of a 2D complex wavelet can be obtained as:For this work, this means subtracting wavelet bands such that:We forgo this recombination step in this paper, as this step complicates derivation of the demosaicing rules and in the proposed method no diagonal analysis is used. However for future work, we remark that diagonal directional analysis could open up the possibility of reconstructing even more of the original luminance bandwidth in the diagonal direction, at the cost of added implementation complexity.

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