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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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Lattice configuration for the demosaicing procedure.
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pone-0061846-g005: Lattice configuration for the demosaicing procedure.

Mentions: We now show the concept in two dimensions. Using the relationship (8), one can prove that (for the grid orientation of Figure 4) the following relations hold between the wavelet coefficients of and the wavelet coefficients , and of the target signals , and , where the subscript signifies the filter used and we drop the spatial index for notational simplicity:(10)with the subscript again denoting color differences as in (1). As explained in Section 1.2 and visible in Figure 2, more convenient bandwidth assumptions on the aliased signals can be made by rewriting the signals in a ‘luminance-chrominance’ interpretation. As the color difference signals and have very small bandwidth, it is reasonable to assume that only their scaling (low-pass) coefficients from a two stage wavelet decomposition will represent significant color difference energy:(11)Also in analogy to Section 1.2, the total signal bandwidth, the luminance/green bandwidth added to the chrominance bandwidth, should not exceed the total Nyquist bandwidth. Assuming perfect wavelet filters, this imposes the following assumption on the luminance/green wavelet coefficients:(12)Using (12), (11) and (8), the mosaic wavelet coefficients can be expressed as a linear system of equations in the wavelet coefficients of the luminance and chrominance signals , and ;(13)Note that, under the aforementioned assumptions, some coefficients contain the same information(14)in (13), we will exploit this in the proposed algorithm to perform locally adaptive demosaicing. Resolving this linear system for , , is now well-posed and this solves the hard part of the demosaicing problem: Demultiplexing the three low pass spectral energy components (as seen in Figure 1). This summarizes into the demosaicing rules of Table 1. Using a two level wavelet packet transform, more realistic bandwidth assumptions can be applied to the signal. When attributing of the bandwidth to green signal and to the color differences, the demosaicing rules in Table 2 are derived. The final demosaiced image can be recovered by using the inverse wavelet packet transform on the demosaiced wavelet subbands of the respective color bands. This demosaicing approach was first proposed in [14]. Note that the demosaicing rules in (2) are only valid for the lattice configuration of Figure 5. Other lattice configurations can easily be handled by using boundary extensions of the mosaic image, or by deriving the analogous demosaicing equations.


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)

Lattice configuration for the demosaicing procedure.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0061846-g005: Lattice configuration for the demosaicing procedure.
Mentions: We now show the concept in two dimensions. Using the relationship (8), one can prove that (for the grid orientation of Figure 4) the following relations hold between the wavelet coefficients of and the wavelet coefficients , and of the target signals , and , where the subscript signifies the filter used and we drop the spatial index for notational simplicity:(10)with the subscript again denoting color differences as in (1). As explained in Section 1.2 and visible in Figure 2, more convenient bandwidth assumptions on the aliased signals can be made by rewriting the signals in a ‘luminance-chrominance’ interpretation. As the color difference signals and have very small bandwidth, it is reasonable to assume that only their scaling (low-pass) coefficients from a two stage wavelet decomposition will represent significant color difference energy:(11)Also in analogy to Section 1.2, the total signal bandwidth, the luminance/green bandwidth added to the chrominance bandwidth, should not exceed the total Nyquist bandwidth. Assuming perfect wavelet filters, this imposes the following assumption on the luminance/green wavelet coefficients:(12)Using (12), (11) and (8), the mosaic wavelet coefficients can be expressed as a linear system of equations in the wavelet coefficients of the luminance and chrominance signals , and ;(13)Note that, under the aforementioned assumptions, some coefficients contain the same information(14)in (13), we will exploit this in the proposed algorithm to perform locally adaptive demosaicing. Resolving this linear system for , , is now well-posed and this solves the hard part of the demosaicing problem: Demultiplexing the three low pass spectral energy components (as seen in Figure 1). This summarizes into the demosaicing rules of Table 1. Using a two level wavelet packet transform, more realistic bandwidth assumptions can be applied to the signal. When attributing of the bandwidth to green signal and to the color differences, the demosaicing rules in Table 2 are derived. The final demosaiced image can be recovered by using the inverse wavelet packet transform on the demosaiced wavelet subbands of the respective color bands. This demosaicing approach was first proposed in [14]. Note that the demosaicing rules in (2) are only valid for the lattice configuration of Figure 5. Other lattice configurations can easily be handled by using boundary extensions of the mosaic image, or by deriving the analogous demosaicing equations.

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