Figure 1.
Interpretation of the mosaic image as the sum of three subsampled bands or as the sum of fully sampled green and two subsampled color difference bands (left) and the corresponding power spectral densities of the color difference interpretation (right).
The mixed cyan and magenta signifies a superposition of red and blue color difference spectral energy.
Figure 2.
Effects of mosaicing on the signal power spectral density: Three color bands (top row) are subsampled to form one interleaved mosaic image, which is a superposition of the three subsampled color bands (bottom row).
Figure 3.
Power spectra of the filters from a bilinear demosaicing filter implementation (black means high power spectral density).
Figure 4.
Demonstration of demosaicing artifacts due to local high bandwidth.
Bilinear Demosaicing (right) on the Barbara image (original version on the left). note how the local high bandwidth content of the stripes introduces discolorations in the black/white veil, indicated by the highlighted regions.
Figure 5.
Lattice configuration for the demosaicing procedure.
Table 1.
Single scale wavelet subband demosaicing: the three color bands ,
,
's wavelet subbands in terms of wavelet subbands of the mosaic data
.
Table 2.
Two scale wavelet packet subband demosaicing: the three color bands ,
,
's wavelet subbands in terms of wavelet subbands of the mosaic data
.
Figure 6.
Demosaicing artifacts examples.
Figure 7.
Color corruption can be caused either by excess luminance bandwidth in the vertical or horizontal direction.
Figure 8.
From the filtered wavelet coefficients , whose support is indicated by the colored area on the left, and two initial hypotheses: either high horizontal luminance bandwidth (
) or high vertical luminance bandwidth (
) is dominant, the costs of making an “incorrect” decision
or an “unsure” decision
is indicated.
The cost for a “correct” decision is not indicated.
Figure 9.
Demonstration of the suitability of a Laplacian model on the high pass band .
Original image (middle) and its high pass band (right) and its logarithmic histogram of these coefficients (left), along with a Laplacian distribution fit (green) and Gaussian fit (red).
Figure 10.
The detection framework choses one hypothesis, from left to right ,
or
, and uses a corresponding reconstruction rule (the checkered chrominance alias).
Only one hypothesis uses exclusively uncorrupted chrominance.
Figure 11.
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.
Table 3.
Alternatives for the low pass wavelet demosaicing rules when compared to Table 2.
Table 4.
Comparison between the errors accumulated in the low pass coefficient, due to either a “miss” decision and an “unsure” decision.
Figure 12.
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.
Table 5.
Locally adaptive complex wavelet subband demosaicing for the first tree: the three color bands ,
,
's wavelet subbands in terms of wavelet subbands of the mosaic data
.
Table 6.
Demosaicing rules for the extended luminance bandwidth coefficients beyond the ones in table 5, for the first tree.
Table 7.
Comparison between the errors accumulated in the high pass coefficient, due to either a “miss” decision and an “unsure” decision.
Figure 13.
Flowchart of the demosaicing algorithm.
The greyed area shows which part of the R,G,B spectrum is recovered in each step, for each tree. The relevant sections for each block are mentioned.
Figure 14.
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.
Figure 15.
Effect of postprocessing on the proposed demosaicing algorithm.
Note the negligible visual difference, but the large difference in PSNR due to the data fidelity property.
Figure 16.
Demonstration of the artifacts occuring with high chrominance bandwidths.
Top: Ground truth image, Middle: LPA-ICI (PSNR = 41 dB), Bottom: Proposed Algorithm (PSNR = 39 dB).
Figure 17.
Demonstration of the high luminance bandwidth reconstruction properties, note the blue and orange artifacts due to excess luminance bandwidth.
Table 8.
Quantitative demosaicing result (in dB PSNR) for the different demosaicing algorithms on the Kodak data set.
Table 9.
Local patch PSNR for some very difficult demosaicing problems, i.e. the images shown in figure 17.
Table 10.
Timing (in seconds) for different Matlab implementations of demosaicing algorithms on the 512×768 images of the Kodak data set.