# An Effective Directional Residual Interpolation Algorithm for Color Image Demosaicking
## 1 Introduction
Then they used different weighted interpolation to effectively reduce the color artifacts at the edge of the image and enhance the image quality. [PERSON] and [PERSON] [13] exploited an orientation-free edge strength filter to estimate edge information, and applied it to reconstruction process. However, the demosaicking algorithm failed in utilizing spectral correlation. To solve this problem, [PERSON] and [PERSON] [14] proposed a novel edge-adaptive demosaicking algorithm, which reduces the aliasing error in R and B channels by exploiting high-frequency information of the G channel. [PERSON] and [PERSON] [15] exploited chrominance and luminance with \(5\times 5\) neighborhoods interpolation equation. The advantage of method is computationally efficient in both execution time and memory storage requirements. On the basis of this interpolation method, several demosaicking algorithms [16; 17; 18] have been proposed. [PERSON] and [PERSON] [16] designed a gradient-based threshold free color filter. It combined the estimations of color difference from each direction into a gradient without setting the thresholds. To estimate different directions, in [17], the color differences were combined by using multiscale color gradients adaptively. This algorithm does not  
Figure 1: Bayer pattern CFA. need any threshold because it makes no hard decision. [PERSON] et al. [18] proposed an algorithm by combining voting-based edge direction detection with weighting-based interpolation, because some other algorithms may use false edge information in irregular edges. The residual interpolation (RI) method has been widely used recently [19; 20; 21; 22; 23; 24; 25]. The RI algorithm exploited the characteristics of the guided filter [26] and showed outstanding performance [19]. [PERSON] et al. [20] incorporated the RI into the gradient-based threshold free algorithm. The better the interpolation results of images are, the smaller the Laplacian energies of images will have. In this way, the RI algorithm combined with minimizing the Laplacian energies of the residuals, which is termed as minimized Laplacian RI (MLRI) [21]. [PERSON] and [PERSON] [22] exploited iterative RI process and reconstructed a highly accurate G channel to reduce reconstruction error for the first time. [PERSON] and [PERSON] [23] reconstructed only R and B channels by using RI algorithm, while the missing color components of G channel were estimated by eight-direction weighted color difference interpolation. The demosaicking algorithm effectively combined the advantages of color difference interpolation and residual interpolation. [PERSON] and [PERSON] [24] proposed a four-directional RI algorithm to reduce severe demosaicking artifacts. The adaptive residual interpolation (ARI) algorithm [25] adaptively combined two RI-based algorithms and selected the appropriate number of iterations at each pixel to improve the existing RI-based algorithm. However, the weakness of this algorithm is that the algorithm has high computational complexity. Furthermore, a demosaicking algorithm was proposed for the multispectral filter array about RI in [27]. There are some demosaicking algorithms based on other patterns such as RGB-white color filter arrays [28]. The image reconstructed in [28] contains much important information that cannot be perceived in the color image reconstructed by conventional CFA. However, they still have other artifacts, and further improvements are needed. RI can be used as an alternative to the widely used color different interpolation and it performs better in some image datasets. MLRI has better interpolation results because the images have smaller Laplacian energies. Furthermore, MLRI also produces other artifacts in some complex edge areas. However, we find that the directional color difference estimations are not completely the same as the actual values sometimes. With the process of research, we think the problem can be solved by reducing the weights of directional color difference estimations.