Dictionary-Based Estimation of Spectra for Wide-Gamut Color Imaging

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1 Dictionary-Based Estimation of Spectra for Wide-Gamut Color Imaging Yuri Murakami, 1 * Masahiro Yamaguchi, 2 Nagaaki Ohyama 1 1 Imaging Science and Engineering Laboratory, Tokyo Institute of Technology, Yokohama, Japan 2 Global Scientific Information and Computing Center, Tokyo Institute of Technology, Yokohama, Japan Received 28 March 2011; revised 19 June 2011; accepted 20 June 2011 Abstract: With the widespread use of commercialized wide-gamut displays, the demand for wide-gamut image content is increasing. To acquire wide-gamut image content using camera systems, color information should be accurately reconstructed from recorded image signals for a wide range of colors. However, it is difficult to obtain color information accurately, especially for saturated colors, if conventional color cameras are used. Spectrumbased color image reproduction can solve this problem; however, bulky spectral imaging systems are required for this purpose. To acquire spectral images more conveniently, a new spectral imaging scheme has been proposed that uses two types of data: high spatial-resolution red, green, and blue (RGB) images and low spatial-resolution spectral data measured from the same scene. Although this method estimates spectral images with high overall accuracy, the error becomes relatively large when multiple different colors, especially those with high saturation, are arranged in a small region. The main reason for this error is that the spectral data are utilized as low-order spectral statistics of local spectra in this method. To solve this problem, in this study, a nonlinear estimation method based on sparse and redundant dictionaries was used for spectral image estimation where the dictionary contains a number of spectra without loss of information from the low spatial-resolution spectral data. The estimated spectra are represented by a mixture of a few spectra included in the dictionary. Therefore, the respective feature of every spectrum is expected to be preserved in the estimation, and the color saturation is also preserved for any region. Experiments performed using the simulated data showed that the dictionary-based estimation can be used VC *Correspondence to: Yuri Murakami ( yuri@isl.titech.ac.jp). Contract grant sponsor: KAKENHI; contract grant number: Wiley Periodicals, Inc. to obtain saturated colors accurately, even when multiple colors are arranged in a small region. Ó 2011 Wiley Periodicals, Inc. Col Res Appl, 00, , 2011; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI /col Key words: color reproduction; wide-gamut; spectral estimation; spectrum-based color reproduction; sparse and redundant dictionaries; nonlinear estimation INTRODUCTION Wide-gamut displays, such as liquid crystal displays with LED backlight 1 and laser displays 2 have become widely commercialized. However, the color spaces of conventional video signals that comply with standards such as BT.709 are not wide enough to utilize the extended color gamut. With this background in mind, several extended color spaces have recently been specified, such as xvycc (IEC ) and Adobe RGB. However, most conventional color cameras are yet to conform to the extended color spaces. Now we can only utilize artificial wide-gamut image content produced by expanding the color gamut of conventional narrow-gamut image content. 3,4 Therefore, it is desired to realize the acquisition of real wide-gamut image content through imaging systems. To acquire real wide-gamut image content, color information of the scene should be accurately reconstructed from recorded image signals, especially those for saturated colors. The accuracy of the recorded colors depends on the spectral sensitivity of the cameras. If the spectral sensitivity of a camera is identical to the spectral sensitivity of human vision or its linear transformation, every existing color can be obtained without error. However, there exist only a few actual fabricated examples at present, 5 because of their inherent low signal-to-noise ratio. On the other hand, when the spectral sensitivity of cameras is different from that of human vision, which is the common case, it is difficult to acquire the color information accurately for a Volume 00, Number 0, Month

2 wide range of colors without limiting target subjects or scenes. In addition, it has been reported that large errors occur for saturated colors, and these colors are shifted into the direction of lower saturation 6,7 when the colors are estimated on the basis of a simple matrix-based estimation aiming for reducing mean error. To acquire images with accurate color information for a wide range of colors, spectrum-based color imaging is a promising technique, which has been investigated extensively The spectrum-based approach uses multispectral/spectral cameras. In general, 4 30 color channels are used for color image reproduction applications. By acquiring multispectral images, spectral reflectance functions of the scene can be accurately estimated. In this manner, the calculation of accurate colors for the scene can be realized. Some experiments have shown that saturated colors are accurately obtained by spectrum-based color image reproduction. 7,13 Although high color reproducibility can be obtained by spectral image acquisition, the method requires bulky imaging systems or a time-consuming process that involves scanning data along the wavelength or the spatial axis. To overcome this problem, we propose to estimate a spectral image from two types of data: high spatial-resolution RGB images and low spatial-resolution spectral data, measured from the corresponding scenes. In this method, spectra are measured at multiple points in a scene by using a spectral scanning sensor or low spatial-resolution spectral imaging system. These spectra are then used to derive the statistical characteristics of the spectra for a given target scene. Although these methods improve the estimation accuracy of spectral images, relatively large errors tend to occur in specific regions. In particular, if many different colors especially those with high saturation are arranged in a relatively small region, 16 color saturation and color contrast reduce. As a result, the original vivid impression of wide-gamut images is lost. The main reason for this error is that in the previously proposed methods, spectral data were used to derive the low-order statistical characteristics of local spectra. Because features characterized by low-order statistics are not sufficient to represent a set of various spectra of saturated colors, this type of error occurs. Therefore, to improve the estimation accuracy for the abovementioned regions, spectral data should not be used as low-order statistical information. Recently, a signal reconstruction theory called compressed sensing or compressive sampling has attracted attention, 18,19 and a number of applications have been proposed based on this theory. 20,21 In this approach, a signal is reconstructed from a few linear observations by a nonlinear estimation based on the assumption that the signal is sparse (i.e., most are zero). In addition, extended methods have been proposed based on sparse and redundant representations of prespecified dictionaries, 22,23 where signals are represented by a linear combination of atom signals in the dictionaries with sparse linear coefficients. The sparse coefficients are then reconstructed on the basis of the compressed sensing theory. This dictionary-based scheme can be used for spectral estimation, where the low spatial-resolution spectral data are used to design a dictionary matrix. Because dictionaries can contain a number of various spectra while maintaining the dimensionality of the data, the information contained in the spectral data can be effectively utilized without any loss in the spectral estimation. Although dictionary-based estimation has been applied to the reconstruction of spectral signals 24 and spectral images, 25 it has not been evaluated in terms of the accuracy of saturated colors. In addition, designing dictionaries on the basis of the spectral data measured from a scene is a promising approach. In this study, dictionary-based estimation was applied to the spectral estimation of an RGB image with low spatial-resolution spectra data, and the estimation accuracy was examined, especially for saturated colors. The results showed that the estimation accuracy was improved, especially for the regions with intricate arrangements of saturated colors. The present article is structured as follows: first, we introduce the approach of estimating spectral images from two types of data, and the issues concerning the conventional method are discussed. Then, we describe the application of dictionary-based estimation to our problem. The next section presents the simulation results, in which the dictionarybased estimation method is compared to several conventional methods. The final section presents the conclusions. SPECTRAL IMAGE ESTIMATION BASED ON LOW-RESOLUTION SPECTRAL DATA Overview In this section, we introduce the imaging scheme used in the proposed method. The system captures a high spatial-resolution B-band image (B ¼ 3 for an RGB image) without spatial degradation and a low spatial-resolution spectral image from the same original image of spectral reflectance. Below, we use the term low-resolution to mean low spatial-resolution. Let f(i 1, i 2 )beanl-dimensional column vector representing the spectral reflectance function of the original spectral reflectance image at pixel (i 1, i 2 ), where L is the number of spectral samplings and 1 i 1 N 1,1 i 2 N 2. Instead of f(i 1, i 2 ), we use f(i) by setting (i 1, i 2 ) ) i, i.e., 1 i N 1 3 N 2 ¼ N. Digital imaging devices can be modeled as linear systems, if the nonlinearity of the system is adequately corrected. The B-band image signal corresponding to f(i) is then represented by gðþ¼hf i ðþþe i G ðþ; i (1) where H is a B 3 L system matrix comprising the spectral characteristics of the camera and illumination spectrum and e G (i) isab-dimensional noise vector. In Eq. (1), it is assumed that there is no spatial deterioration. Let s(j) beanl-dimensional column vector representing a spectrum of low-resolution spectral data indexed by 1 j M. Let O j be an area in the original spectral image corresponding to the j-th spectrum of the low-resolution spectral 2 COLOR research and application

3 FIG. 1. Overall flow of experiments. Original is described by pixels, spectral reflectance function of each pixel being represented by a spectral function of 65 components at 5-nm intervals. Upper one of measurements is given by pixels and each pixel is described by its RGB-values and a white noise value added, the lower one is composed from spectral reflection functions of 65 components averaged within pixels of the original, and regions of such functions are measured. Spectral reflectance image is estimated by three methods: Wiener means the standard Wiener estimation, PW-Wiener is the method of peace-wise Wiener estimation, and Dictionary is the new method applied in this article. data. Then, the spectral reflectance functions included in O j are assumed to be spatially averaged and observed; i.e., s(j) is given by sðþ¼ j 1 X fðþþe i S ðþ; j (2) x j i2x j where x j is the area of O j and e S (j) isanl-dimensional noise vector. The SS-MAP (spatio-spectral maximum a posteriori) estimation method 14 and PW-Wiener (piecewise Wiener) estimation method 17 have been proposed for the reconstruction of spectral images from the two types of data mentioned above. In addition, conventional spectral estimation methods such as the Wiener estimation 26 method and GMD-based (Gaussian-mixture-distribution-based) estimation method 27 have been applied. 16 Although these methods are based on different concepts, each of them are eventually used to estimate the spectral reflectance by means of the B 3 L estimation matrix A; i.e., the estimated spectral reflectance is given by ^f ðþ¼ag i ðþ; i (3) where A is generated on the basis of the spectral characteristics of the camera and the illumination spectrum (i.e., the matrix H), and low-resolution spectral data. Depending on the methods, the matrix is designed for the whole image (Wiener), the spectral class (GMD-based), the local area (PW-Wiener), or per pixel (SS-MAP). In this study, PW-Wiener was experimentally compared with the dictionary-based approach. The former is one the most effective methods in terms of both accuracy and computational cost. We briefly review the PW-Wiener estimation method below. Piecewise Wiener Estimation Method In the PW-Wiener estimation method, 17 RGB images are divided into Q blocks, where each block is indexed by q(1 q Q). The estimation is performed by using Eq. (3) based on the estimation matrix defined for every block. The estimation matrix assigned to block q, i.e., A q, is calculated using the Wiener estimation theory: A q ¼ R q H T HR q H T þ R Noise Þ 1 ; (4) where R Noise is the correlation matrix of noise vectors e G (i) and R q corresponds to the correlation matrix of spectral reflectance for block q. Matrix R q is calculated using the low-resolution spectral data s(j) that are weighted according to the Euclidean distance d(q, j) between the center position of block q and the center position of low-resolution spectral data s(j): 1 X M n R q ¼ wq; ð jþ 2 sðþs j ðþ j T g; (5) P M wq; ð jþ 2 j¼1 j¼1 wq; ð jþ ¼ q dq;j ð Þ ; (6) where 0 \ q \ 1 is a constant. In the implementation, to avoid discontinuities at the block boundary, the estimation of a pixel is performed using the matrix assigned to its Volume 00, Number 0, Month

4 FIG. 2. Original spectral reflectance images presented in srgb images: (a) Toys and (b) Scarf. Squares in images are ROIs used for evaluation. Each ROI of image Toys and Scarf consists of and pixels, respectively. neighboring blocks as well as its own block. These are summed by using smooth window functions such as a two-dimensional Hamming window. In PW-Wiener estimation, estimation of all the pixels in a block is performed using a single matrix. In addition, the estimation matrix is derived mainly from the spectral data measured spatially near the block. Therefore, when similar spectra are spatially localized, which occurs often in natural images, the method works effectively. On the other hand, when several different spectra are present in a single block, the advantage of this method is not significant. In addition, because the matrix is designed to reduce the estimation error in the sense of an ensemble average, errors for minor spectra tend to be larger as compared to those for dominant spectra. It should be noted that such problems not only arise in the PW-Wiener estimation method but also in the other estimation methods (Wiener, GMD-based, and SS-MAP), because they use low-resolution spectral data to derive low-order statistical features of spectra. In this study, this problem was solved by introducing dictionary-based estimation, which is presented in the next section. Spectral sensitivity of RGB camera used in simu- FIG. 3. lation. DICTIONARY-BASED SPECTRAL IMAGE ESTIMATION Dictionary-Based Signal Reconstruction We first review the dictionary-based signal reconstruction method. 22 The sparse and redundant representation of an L-dimensional signal x is defined as x ¼ Dh; (7) where D is a L 3 K(K [ L) redundant dictionary matrix and h is a K-dimensional sparse coefficient (i.e., most are zero). Each column of the dictionary matrix is called an atom, which corresponds to the typical samples of signal x. Considering the sparsity of h, x is represented by a linear combination of a few atoms of D. By setting D to be overcomplete or redundant (i.e., K [ L), any signals can be represented using a sparse and redundant expression such as Eq. (7). Because of its sparsity, h can be estimated on the basis of the compressed sensing theory from its small number of observations, 18,19 which is eventually used to estimate x using Eq. (7). Application to Spectral Image Estimation We now apply the dictionary-based estimation method to our problem: estimation of a spectral reflectance image. A straightforward way is to directly use low-resolution spectral data as the dictionary matrix, i.e., D ¼ ½ sð1þ; sðþ; 2 ; sðmþš. Then, the spectral reflectance function is considered as signal x, whereas a set of RGB image signals is considered as the small number of observations. Considering the extreme case of one-sparsity for h (i.e., except one, all coefficients of h are zero), the estimated spectrum is in proportion to one of the atoms in the dictionary, i.e., one of the spectra of low-resolution spectral data. This means that each spectrum of the low-resolution spectral data is directly used for the estimation, and there is no dimensionality reduction of the data. In addition, each atom spectrum plays the same role, whether it is a dominant 4 COLOR research and application

5 FIG. 4. Example data related to dictionary-learning process and dictionary-based estimation process for image Scarf. (a) Randomly selected 50 spectra from 1024 training spectra for K-SVD, (b) 40 atom spectra of learned dictionary, (c) two samples of original and estimated spectra by dictionary-based estimation, (d) five atom spectra with nonzero coefficients for the two samples, and (e) corresponding two sparse coefficient vectors. or minor spectrum. As a result, the feature of every spectrum should be preserved in the estimation, even if various spectra are arranged together in a local area. As a result, the saturation of colors is preserved. Because there is redundancy in low-resolution spectral data, the K-SVD method, 22 which is a dictionary learning algorithm, was adopted. The K-SVD method designs a dictionary matrix D consisting of K atom spectra for representing sparse signals. The derived atom spectra are not orthogonal to each other but normalized to have unit norm. All M ([ K) spectra of low-resolution spectral data are used as the training data for K-SVD. The software of K-SVD is available at elad/software/. Using the learned dictionary D KSVD, the spectral reflectance is approximately represented as fðþd i KSVD hðþ: i (8) h(i) is estimated as the solution of the next optimization problem kðgðþ HD i Minimize jhðþ i j 1 subject to KSVD hðþ i Þk 2 Br 2 ; D KSVD hðþ0 i (9) Volume 00, Number 0, Month

6 Conditions Two spectral reflectance images referred to here as Toys and Flower were obtained; these were estimated from 16-band images captured using a filter-wheel multispectral camera. 28 The image size was N ¼ pixels, and 65 spectral samples were estimated from 16 samples per pixel for nm with 5-nm intervals (L ¼ 65). Figure 2 shows the images in color; because some colors in the green, red, yellow, and blue regions of the Toys image are outside of srgb gamut, they are clipped to the gamut surface only for presentation of Fig. 2. Although both images include saturated colors, similar colors are spatially localized in the Toys image whereas different colors are laid out in small regions of the Scarf image. Thus, the PW-Wiener method is effective for Toys, but not for Scarf. From these spectral reflectance images, both RGB images and low-resolution spectral data were calculated as follows. RGB images are calculated on the basis of the spectral sensitivity of a typical HDTV video camera, shown in Fig. 3, and the spectrum of CIE D65. Gaussian random white noise is added to the image data where the peak signal-tonoise ratio is 50 db. The low-resolution spectral data are calculated as average spectral reflectance functions over 4 FIG. 5. Comparison of estimation accuracy among three methods for Toys: (a) NRMSE of spectral reflectance and (b) average color difference under D65 illuminant in CIE L*a*b* color space. where jhðþ i j 1 is the L1 norm of h(i) and r 2 is the variance of noise in RGB images. By minimizing the L1 norm of h(i), sparse h(i) is estimated. 18 The first constraint means that the difference between the actual RGB image signals and the RGB image signals calculated from the estimated spectral reflectance is less than the noise variance. The second constraint is the nonnegativity of the estimated spectral reflectance. By substituting the estimated h(i) in Eq. (8), f(i) is estimated. Eq. (9) can be optimized to solve linear programming problems by methods such as simplex methods or convex programming problems by methods such as interior point methods. Either method requires iterative procedures to reach the solution. In addition, the optimization of Eq. (9) should be performed for every pixel. Therefore, the computation cost is much higher than that for the PW-Wiener estimation method, which mainly requires predefined matrix multiplications only. EXPERIMENTS We examined the dictionary-based estimation method using the simulated data. The flow of the overall experiment is shown in Fig. 1. FIG. 6. Comparison of estimation accuracy among three methods for Scarf: (a) NRMSE of spectral reflectance and (b) average color difference under D65 illuminant in CIE L*a*b* color space. 6 COLOR research and application

7 divided into blocks (Q ¼ ) for PW-Wiener estimation, each block size then becomes pixels. Note that the low-resolution spectral data used for PW-Wiener is identical to the data for the dictionarybased method. The results of PW-Wiener are referred to as PW-Wiener(RGBþS). Several ROIs (region of interests) were set for the evaluation (see Fig. 2); these were selected to include saturated colors. Each of the five pixel ROIs (red, green, orange, blue, and yellow) from the Toys image consists of approximately a single color. On the other hand, two pixel ROIs from the image Scarf consist of multiple FIG. 7. Scatter plots of original (open circle) and estimated (filled circle) colors from ROI#1 of Scarf on L* a* plane for three estimation methods. Arrows indicate the direction of color shift of estimated colors. 3 4 pixel square regions. The number of spectra is M ¼ ¼ 1024 ; these are located at equal intervals in the horizontal and vertical directions. In the dictionary-based estimation, the dimension of the dictionary K is determined to be 40 after several trials. This condition is not the optimum, but it gives stable and highly accurate estimations. The L1 norm minimization is performed using CVX, 29 which is a package for specifying and solving convex programs. Later, the results of the dictionary-based estimation are referred to as Dictionary(RGBþS), where RGBþS implies the use of low-resolution spectral data in addition to the RGB image. We compare the dictionary-based estimation method with two methods. The first is Wiener estimation from RGB images without the information about low-resolution spectral data, where the correlation matrix is formulated based on the Markov process of q 0 ¼ The Markov process can approximate a spectral correlation matrix fairly well, 26 if the correlation coefficient q 0 ¼ The results of this estimation are referred to as Wiener(RGB). The second method is PW-Wiener estimation, which utilizes both RGB images and low-resolution spectral data. The parameter q in Eq. (6) is set to 0.7 to obtain approximately optimal results. The image is FIG. 8. Scatter plots of original (open circle) and estimated (filled circle) colors from ROI#2 of Scarf on L* a* plane for three estimation methods. Arrows indicate the direction of color shift of estimated colors. Volume 00, Number 0, Month

8 FIG. 9. Visualized color difference images for two ROIs of Scarf. DEab ¼ 0 20 is allocated to eight-bit grayscale. colors. The evaluation measures were the normalized root mean squared error (NRMSE) of the spectral reflectance image and average color difference under D65 illuminant in CIE L*a*b* color space. They were calculated for the whole image and respective ROI. In addition, the distribution of the colors in the ROIs was examined. Results Before evaluating the estimation results of three methods, some example data related to the dictionary-learning process and dictionary-based estimation process are presented in Fig. 4. All data presented in Fig. 4 are originated from the image Scarf. Figure 4(a) shows randomly selected 50 spectra from all 1024 training spectra for K- SVD, where each spectrum is normalized to have unit norm for comparison with the normalized atom spectra. These training spectra are the low-resolution spectral data themselves, as mentioned before. Figure 4(b) shows 40 atom spectra of the learned dictionary, which are derived on the basis of K-SVD method and the data of Fig. 4(a). It can be found that various spectra are relatively included in the atom spectra evenly, whereas spectra are localized in the training spectra. However, the set of atom spectra have still a fair amount of redundancy. Figure 4(c) shows two samples of original and estimated spectra by dictionary-based estimation. Figure 4(d) shows five atom spectra with nonzero coefficients for these two samples. The corresponding sparse coefficient vectors are presented in Fig. 4(e). It is found that each spectrum is reconstructed using only three atom spectra; which atom spectra used is automatically selected in the optimization of Eq. (9). Figure 5 shows the NRMSE of the spectral reflectance and average color difference under D65 for Toys. First, a comparison of the errors for the whole image (leftmost plots) shows that the NRMSE of Wiener(RGB) was reduced by almost half by PW-Wiener(RGBþS) and Dictionary(RGBþS). The average color difference of Wiener(RGB) was reduced by almost two-thirds. Moreover, we can see that extremely large errors as compared to the whole-image error occurred in some ROIs (red, green, and blue) for Wiener(RGB), and they were reduced by PW- Wiener(RGBþS) and Dictionary(RGBþS). PW-Wiener(RGBþS) performed better than Dictionary(RGBþS), because the localized color arrangement of Toys was suitable for the former method. Figure 6 shows the same results for the image Scarf. As in the case of the image Toys, the error of Wiener(RGB) was effectively reduced by the two methods using lowresolution spectral data. However, there were some differences from the results for Toys; Dictionary(RGBþS) produced a lower error for two ROIs than PW-Wiener(RGBþS). The ROIs of the image Scarf includes various colors with strong variations that cannot be handled by PW-Wiener. In contrast, the dictionary-based estimation effectively reduced the error in such regions. Although maximum error is not examined in detail here, it should be noted that any singular behaviors of the maximum error were not observed in the above results for dictionary-based estimation. For more details on the estimation results in the ROIs of Scarf, Figs. 7 and 8 show the scatter plots of the original and estimated colors on the L* a* plane, where 512 pixels were randomly selected from each ROI. For PW- Wiener(RGBþS) and Wiener(RGB), the estimated colors shifted to the direction of lower color saturation. In contrast, the distribution of the estimated colors by Dictionary(RGBþS) almost overlapped the distribution of the original colors, although the green colors in ROI#2 were slightly shifted inversely. The saturation of the estimated colors was well preserved by Dictionary(RGBþS). It seems that the differences among three methods are slight for reddish colors in the area of positive a* compared to greenish colors in the area of negative a*. 8 COLOR research and application

9 The reason is that the reddish colors constitute a far greater portion of the original image than the greenish colors, i.e., the spectra of reddish colors are dominant in the low-resolution spectral data. Because the spectral characteristics of dominant colors are utilized preferentially in the spectral estimation when using Wiener and PW-Wiener methods, the estimation error is small for these colors and the improvement by the dictionary-based method is small. Finally, the visualized color difference is shown in Fig. 9 for two ROIs of image Scarf. The range of 0 20 DE ab was allocated to eight-bit grayscale. For ROI#1, a large error occurred in the narrow regions of green and dark orange when the region was estimated by Wiener(RGB) and PW-Wiener(RGBþS). These errors were reduced by Dictionary(RGBþS). For ROI#2, large errors occurred in the overall results of Wiener(RGB). Only the dark pink region (right side) was improved by PW-Wiener(RGBþS), whereas most regions were improved by Dictionary(RGBþS). These results confirmed that dictionary-based estimation can obtain saturated colors even when various different spectra are intricately arranged in a small region. CONCLUSIONS In this study, we examined various methods to obtain widegamut image content from RGB images with low spatial-resolution spectral data measured from a given target scene. The PW-Wiener estimation method could estimate saturated colors accurately when similar colors were spatially localized. However, when different colors were present in a small region e.g., about the same size of the blocks assigned to a single estimation matrix the effectiveness was not significant. In contrast, the dictionary-based estimation method was effective for such regions. Saturated colors were estimated with high accuracy even when various colors were arranged in small regions. This was because the atom spectra appeared in the estimated spectra almost without mixing with each other for dictionary-based estimation. Considering the high computational cost of dictionary-based estimation, which is caused by the iterative procedure required to minimize the L1 norm, both methods are required, depending on the spatial color arrangements of scenes. On the basis of the experimental results presented in this article, we conclude that color image estimation from high spatial-resolution RGB images and low spatial-resolution spectral data is an effective approach for obtaining wide-gamut image content. One of the two methods, PW-Wiener and dictionary-based estimation, should be selected depending on the scene and requirements. 1. Sugiura H, Kagawa S, Kaneko H, Ozawa M, Tanizoe H, Kimura T, Ueno H. Wide color gamut displays using LED backlight: Signal processing, circuits, color calibration system and multi-primaries. 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