Denoising and interpolation of noisy Bayer data with adaptive cross-color filters

Abstract

We propose a novel approach for joint denoising and interpolation of noisy Bayer-patterned data acquired from a digital imaging sensor (e.g., CMOS, CCD). The aim is to obtain a full-resolution RGB noiseless image. The proposed technique is speciÞcally targeted to Þlter signal-dependant, e.g. Poissonian, or heteroscedastic noise, and effectively exploits the correlation between the different color channels. The joint technique for denoising and interpolation is based on the concept of local polynomial approximation (LPA) and intersection of conÞdence intervals (ICI). These directional Þlters utilize simultaneously the green, red, and blue color channels. This is achieved by a linear combination of complementary-supported smoothing and derivative kernels designed for the Bayer data grid. With these Þlters, the denoised and the interpolated estimates are obtained by convolutions over the Bayer data. The ICI rule is used for data-adaptive selection of the length of the designed cross-color directional Þlter. Fusing estimates from multiple directions provides the Þnal anisotropic denoised and interpolated values. The full-size RGB image is obtained by placing these values into the corresponding positions in the image grid. The efficiency of the proposed approach is demonstrated by experimental results with simulated and real camera data.

Cross-color BM3D filtering of noisy raw data

“…Design of efÞcient joint algorithms is not an easy task because of the antagonistic nature of the denoising and interpolation procedures: denoising mainly performing some sort of data smoothing, while interpolation aims at reconstructing missing high-frequency details. The third approach, denoise and then demosaick, while apparently simple and straightforward, was long time considered to be inefÞcient [10], [9]. Direct application of conventional grayscale denoising Þlters to CFA is problematic due to the underlying mosaic structure of the CFA, which violates the basic assumptions about local smoothness in natural images which these Þlters rely upon.…”

“…In the presence of noise, the performance of the such algorithms degrades drastically. Three main strategies to deal with noisy data are possible: denoising after demosaicking, joint demosaicking-denoising (e.g., [5], [9], [10], [11]), and denoising before demosaicking (e.g., [7]). Denoising after demosaicking is very challenging, because sophisticated adaptive interpolation procedures change the statistical model of the noise in a complex and hardly computable form.…”

Realistic camera noise modeling with application to improved HDR synthesis

“…One of our main issues at this stage is that the approximations (20) and (21) only hold for differentiable CRFs, hence clipping of the dynamic range is not incorporated in our model. To resolve this issue, in Appendix 2, we derive bounds for t j E i √ α j for which the approximations (20) and (21) are accurate (up to an arbitrary precision).…”

“…To resolve this issue, in Appendix 2, we derive bounds for t j E i √ α j for which the approximations (20) and (21) are accurate (up to an arbitrary precision). If we denote the minimal and maximal intensity values (after applying the clipping function) as, respectively y min and y max , we have shown that the results hold (up to an arbitrary precision) in a "clipping-free" region y min ≤ t j E i √ α j ≤ y max , where typically y min < y min + y max /2 < y max (with y min and y max as in Appendix 2).…”

“…Next to this, many researchers address individual aspects of the noise in digital camera images (such as dealing with clipping [18], Poisson/multiplicative noise [19,20], signal-dependent/non-stationary noise [21][22][23]). Compared to these efforts, relatively little attention has gone to the joint modeling of the many involved factors that contribute to the noise characteristics in a digital camera.…”