Universal Demosaicking of Colour Filter Arrays

 

Chao Zhang, Yan Li, Jue Wang, and Pengwei Hao

 

We recently have developed a universal demosaicking method, which can be used for all Colour Filter Arrays, periodic or aperiodic, regular or irregular, uniform or nonuniform. It is non-iterative, and can be linear (image-independent) or nonlinear (image-dependent), so it is good for CFA demosaicking, design and comparison.

 

You can download our MATLAB code here:

http://www.eecs.qmul.ac.uk/~phao/CFA/acude/acude.zip

which is only for demonstration of our Acude method for the Bayer CFA pattern, and are implemented naively, thus they may run slowly. If you wish us to test our method on your CFA patterns, we are also happy to do it. Please contact us.

 

Actually the algorithm can be implemented very fast, which can be faster than 1 second/image with MATLAB and can be even much faster with C or with the help of some hardware. Please contact Pengwei Hao for further information: p.hao@qmul.ac.uk.

 

If the code or the method is used for research, please cite:

Chao Zhang, Yan Li, Jue Wang, and Pengwei Hao, "Universal Demosaicking of Color Filter Arrays", IEEE Transactions on Image Processing, Vol. xx, No. xx, pp. xxxx-xxxx, 2016.

DOI: 10.1109/TIP.2016.2601266

Available on http://ieeexplore.ieee.org/document/7547314/

 

The comparison is highly favourable between our method and other universal demosaicking methods, i.e. Condat's variational method (Var) and Menon&Calvagno's regularization approach (Rad, adaptive) with the Bayer CFA, the Kodak's CFA2.0, Fuji X-Trans, Sony RGBW, our previously proposed CFAs (Hao40, Hao50, Hao60, Hao4x4), a random CFA proposed by Condat and two non-RGBWCMY color CFAs respectively by Hirakawa et al and Condat (See Figures 1&2 below). Note that our method is fast since it is non-iterative and can be implemented with small filters, while Condat's method (Var) is iterative thus is slow and its convergence is highly dependent on the initial estimate, and Menon&Calvagno's (Rad) actually only works for uniform and periodic CFAs thus we only used the first 36x36 sub-pattern of the random CFA for the experiments and it is much slower than our method.

 

Figure 1: The tested CFAs proposed by others

 

Figure 2: The tested CFAs proposed by us

 

The demosaicking results that we have obtained are listed in the tables (See Summary Tables 0 for the averages and the details in the Tables 1-12 below), for colour MSE (CMSE), the corresponding colour PSNR (CPSNR) and the mean CIE Lab error between the demosaicked images and the original images. These results were obtained using 24 test images of Kodak Lossless True Colour Image Suite (http://r0k.us/graphics/kodak/) and 18 test images of the IMAX dataset (http://www4.comp.polyu.edu.hk/~cslzhang/CDM_Dataset.htm). The experiments have been done without mixed noise and with additive noise of standard deviation 5.

 

Table 0: Averages of the demosaicking performance on Kodak and IMAX datasets with all 11 CFAs

Dataset

Kodak dataset

IMAX dataset

CFA pattern

Demosaicking method

Noise free

Additive Noise (std=5)

Noise free

Additive Noise (std=5)

CMSE

CPSNR

CIE LAB

CMSE

CPSNR

CIE LAB

CMSE

CPSNR

CIE LAB

CMSE

CPSNR

CIE LAB

Bayer CFA

Var

10.74

38.60

1.515

32.56

33.09

2.767

24.57

35.28

3.621

42.66

32.18

6.720

Rad

7.96

39.95

1.320

29.89

33.44

2.695

20.89

36.05

3.269

39.92

32.43

6.072

Ours

6.46

40.84

1.186

29.44

33.49

2.513

19.36

36.38

3.150

39.80

32.41

5.811

Kodak CFA2.0

Var

14.38

37.29

2.146

39.77

32.23

3.364

31.82

34.19

4.764

61.27

30.55

8.859

Rad

12.42

37.88

1.949

39.81

32.20

3.552

28.99

34.61

4.404

58.46

30.73

7.733

Ours

10.50

38.70

1.764

37.01

32.52

3.093

25.52

35.15

3.868

54.29

31.04

6.971

Fuji X-Trans

Var

11.58

38.25

1.714

34.34

32.86

2.894

27.23

34.85

3.869

46.41

31.83

6.891

Rad

10.23

38.83

1.569

32.22

33.14

2.807

24.12

35.39

3.558

43.61

32.07

6.247

Ours

8.69

39.54

1.437

32.28

33.11

2.628

21.02

35.99

3.276

41.42

32.26

5.729

Sony RGBW

Var

16.82

36.59

2.279

41.41

32.08

3.365

33.96

33.90

4.827

61.07

30.59

8.663

Rad

14.90

37.19

2.056

40.72

32.14

3.479

29.98

34.46

4.427

57.89

30.79

7.661

Ours

12.10

38.10

1.861

37.45

32.49

3.007

27.05

34.87

3.976

53.42

31.14

6.688

Random CFA

Var

9.41

39.19

1.527

31.74

33.19

2.766

28.74

34.36

4.036

46.92

31.73

6.926

Rad

8.34

39.72

1.413

29.95

33.43

2.696

21.19

35.99

3.373

39.68

32.47

6.125

Ours

7.70

40.10

1.341

30.25

33.38

2.571

19.86

36.25

3.198

38.36

32.60

5.654

Hirakawa 4 color

Var

7.57

39.34

1.606

33.32

32.90

3.135

25.37

34.09

4.261

52.59

30.92

7.452

Rad

7.68

39.28

1.618

33.14

32.93

3.140

24.87

34.17

4.261

54.71

30.75

7.841

Ours

6.83

39.79

1.501

33.56

32.87

3.036

24.75

34.20

4.083

54.14

30.80

7.215

Condat 6 color

Var

7.46

39.40

1.569

32.37

33.03

3.089

21.74

34.76

3.987

47.68

31.35

7.322

Rad

7.52

39.37

1.575

32.10

33.07

3.102

21.28

34.85

4.003

48.40

31.28

7.507

Ours

6.64

39.91

1.467

31.94

33.09

2.924

18.66

35.42

3.647

44.69

31.63

6.856

Hao4x4

Var

7.94

39.89

1.713

33.59

32.91

3.179

25.27

35.29

4.636

53.79

31.09

8.581

Rad

7.34

40.22

1.623

32.18

33.10

3.122

23.17

35.64

4.267

52.22

31.19

7.646

Ours

6.52

40.73

1.524

32.20

33.09

3.013

23.27

35.64

4.049

50.40

31.38

7.115

Hao40

Var

12.48

37.88

1.925

36.08

32.65

3.066

26.34

35.02

4.222

50.26

31.42

7.722

Rad

11.08

38.44

1.780

33.80

32.93

3.012

23.50

35.53

3.935

48.10

31.58

7.004

Ours

9.90

38.93

1.652

34.18

32.86

2.849

20.08

36.21

3.467

42.94

32.06

6.115

Hao50

Var

10.96

38.47

1.889

37.49

32.46

3.524

25.27

35.26

4.466

57.73

30.74

9.766

Rad

8.72

39.55

1.682

35.27

32.71

3.488

21.65

35.96

4.081

54.85

30.94

8.274

Ours

6.79

40.61

1.496

35.13

32.71

3.415

18.15

36.71

3.841

53.59

31.00

8.186

Hao60

Var

15.79

36.82

2.496

41.34

32.07

3.713

33.47

34.02

5.543

65.55

30.26

10.166

Rad

15.15

37.02

2.342

40.26

32.19

3.644

29.43

34.59

4.889

62.77

30.41

8.654

Ours

13.57

37.51

2.119

40.36

32.16

3.461

24.72

35.31

4.338

54.81

30.98

7.687

 

 

The tables show that our new universal demosaicking method gives the best performance in average. The performance with Bayer CFA is even better than most of the published methods that were specially designed for the Bayer pattern.

 

For the demosaicked images, we show in the figure tables (See Figure Table F1-4 below) for the crops of the image 19 of Kodak dataset and image 3 of IMAX dataset.

All the demosaicked images with Kodak and IMAX datasets without and with noise (std=5) are available to download on web:

Demosaicking with Condat's generic variational method (var) :

Kodak (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/var-images/

Kodak (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/var-n5-images/

IMAX (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/var-images/

IMAX (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/var-n5-images/

Demosaicking with Menon&Calvagno's regularization approach (rad) :

Kodak (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/rad-images/

Kodak (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/rad-n5-images/

IMAX (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/rad-images/

IMAX (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/rad-n5-images/

Demosaicking with our adaptive universal demosaicking method (acude) :

Kodak (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/acude-images/

Kodak (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/Kodak/acude-n5-images/

IMAX (noise free): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/acude-images/

IMAX (noise std=5): http://www.eecs.qmul.ac.uk/~phao/CFA/acude/IMAX/acude-n5-images/

 

In our view, the big advantages of our new universal demosaicking method are as follows:

1)       The demosaicking performance of our method is very good, in terms of the image quality. Based on our experiments, for all the tested CFAs, our method does the best, and Menon&Calvagno's does better than Condat's.

2)       Our method can be used for all CFAs, periodic or aperiodic, regular or irregular, uniform or nonuniform.

3)       Our method can be fast for its non-iterative characteristic and can be implemented with small filters.

4)       Our method can be further optimised easily for a specific given CFA.

5)       Our method can be linear or nonlinear, and can be adaptive or non-adaptive to images.

 

References:

 

CFA patterns:

[Bayer] B. E. Bayer, "Color imaging array", US Patent 3 971 065, 1976.

[Kodak CFA2.0] T. Kijima, H. Nakamura, J. Compton, and J. Hamilton, "Image sensor with improved light sensitivity", US Patent 20070268533, 22 Nov 2007.

[Fuji X-Trans] http://fujifilm-x.com/x-pro1/en/about/sensor/index.html

[Sony RGBW] I. Hirota, "Solid-state imaging device, method for processing signal of solid-state imaging device, and imaging apparatus", Dec. 4 2009, US Patent App. 12/630,988.

[Random] L. Condat, "Color filter array design using random patterns with blue noise chromatic spectra", Image and Vision Computing, vol. 28, no. 8, pp. 1196-1202, Aug. 2010.

[Hao4x4] P. Hao, Y. Li, Z. Lin, and E. Dubois, "A geometric method for optimal design of color filter arrays", IEEE Transactions on Image Processing, Vol. 20, No. 3, pp. 709-722, March 2011.

[Hao40] J. Wang, C. Zhang, and P. Hao, "New Color Filter Arrays of High Light Sensitivity and High Demosaicking Performance", IEEE International Conference on Image Processing (ICIP), Brussels, Belgium, Sept 11-14, 2011.

[Hao50, Hao60] P. Hao, "Colour Filter", UK Patent Application 1101288.7.

[Hirakawa 4 color] K. Hirakawa, and P.J. Wolfe, "Spatio-spectral color filter array design for optimal image recovery", IEEE Transactions on Image Processing, vol. 17, no. 10, pp. 1876-1890, October 2008.

[Condat 6 color] L. Condat, "A new color filter array with optimal properties for noiseless and noisy color image acquisition", IEEE Transactions on Image Processing, vol. 20, no. 8, pp. 2200-2210, August 2011.

 

Universal demosaicking methods:

[Var] L. Condat, "A generic variational approach for demosaicking from an arbitrary color filter array", IEEE International Conference on Image Processing, pp. 1625-8, Nov 7-10 2009, Cairo, Egypt.

[Rad] D. Menon, and G. Calvagno, "Regularization approaches to demosaicking", IEEE Transactions on Image Processing, vol. 18, no. 10, pp. 2209-2210, October 2009.

[Ours Acude] Our newly proposed universal demosaicking method: C. Zhang, Y. Li, J. Wang and P. Hao, "Universal demosaicking of Color Filter Arrays", submitted to IEEE Transactions on Image Processing, .

 

 

 

Figure Table F1. Demosaicked image region 1 of Lighthouse (Kodak image 19)

Noise

Noise Free

Noise std=5

Demosaicking Method

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Original image

19-parts2-web.png

19-parts2-web.png

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

(Our RGBW)

Hao50

Hao60

 

Figure Table F2. Demosaicked image region 2 of Lighthouse (Kodak image 19)

Noise

Noise Free

Noise std=5

Demosaicking Method

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Original image

19-parts1-web.png

19-parts1-web.png

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

(Our RGBW)

Hao50

Hao60

 

Figure Table F3. Demosaicked image region 1 of IMAX image 3

Noise

Noise Free

Noise std=5

Demosaicking Method

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Original image

03-parts2-web.png

03-parts2-web.png

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

(Our RGBW)

Hao50

Hao60

 

Figure Table F4. Demosaicked image region 2 of IMAX image 3

Noise

Noise Free

Noise std=5

Demosaicking Method

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Condat's generic variational approach (Var)

Menon&Calvagno's regularization approach (Rad)

Our adaptive universal demosaicking (acude)

Original image

03-parts3-web.png

03-parts3-web.png

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

(Our RGBW)

Hao50

Hao60

 

Tables 1-12: Details of demosaicking performance- CMSE, CPSNR & CIE LAB error

 

Table 1: Demosaicking performance (CMSE) on Kodak dataset (noise free) with all 11 CFAs

CMSE

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random CFA

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

Hao50

Hao60

Image

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

1

12.91

9.57

7.20

13.82

12.99

10.10

11.56

12.38

9.35

18.05

20.80

13.02

8.66

9.07

7.59

6.90

7.46

6.08

7.03

7.58

5.26

6.84

7.74

6.11

12.46

13.16

10.41

13.27

10.67

7.10

15.60

17.01

15.17

2

8.11

6.52

4.62

9.99

9.51

7.22

8.52

7.71

6.15

12.26

10.43

8.56

7.03

6.64

5.54

6.29

6.89

5.56

6.12

6.74

5.34

6.26

6.18

5.59

9.00

8.24

6.98

8.34

6.56

5.19

10.45

9.20

10.08

3

5.44

3.55

3.27

7.82

6.77

5.05

6.67

4.91

4.45

10.03

6.33

6.35

5.51

4.24

3.89

4.21

4.21

3.56

3.95

3.84

3.57

4.96

3.92

3.47

8.86

6.41

6.02

5.77

3.85

3.25

12.34

10.46

9.66

4

6.29

5.00

4.89

10.14

8.95

8.75

7.70

6.51

6.73

12.33

9.40

10.74

6.21

5.44

5.69

5.67

5.80

6.05

5.43

5.49

5.68

5.36

4.88

5.05

8.75

7.26

7.82

7.10

5.13

5.74

10.18

8.95

12.48

5

13.14

9.32

8.39

27.68

21.43

19.45

18.95

14.82

13.75

33.34

21.78

22.77

15.06

11.86

12.24

13.26

12.65

12.45

12.74

12.16

11.88

12.64

10.63

9.87

21.38

16.59

16.06

14.02

10.72

9.03

27.78

23.82

22.56

6

10.30

6.72

4.84

11.27

9.88

8.26

9.51

8.73

6.55

12.95

14.69

9.05

7.13

6.50

5.67

5.41

5.46

4.50

5.49

5.39

4.20

5.90

5.61

4.63

9.25

9.01

7.52

10.17

7.44

4.81

11.43

12.41

10.53

7

4.79

3.23

2.90

8.67

7.46

6.06

5.99

4.80

4.34

10.16

7.26

6.95

4.81

4.03

3.81

4.38

4.44

4.08

4.17

4.10

4.15

4.47

3.92

3.54

6.98

5.49

5.19

5.47

4.00

3.33

9.85

8.33

7.84

8

32.37

16.62

10.72

23.69

21.07

12.84

19.49

18.84

11.88

29.50

42.52

14.17

14.15

13.50

9.80

11.62

11.96

9.06

11.39

11.73

8.49

11.78

11.73

9.20

18.78

18.35

12.63

32.65

18.34

10.11

23.72

24.33

17.33

9

5.29

3.59

2.70

7.18

6.34

4.61

5.44

4.71

3.67

8.22

7.16

5.04

4.41

3.90

3.24

4.04

4.10

3.37

3.81

3.87

3.18

4.10

3.75

3.15

5.91

5.03

4.14

5.61

4.20

2.98

8.35

7.68

5.61

10

4.40

3.52

3.07

7.26

6.23

5.14

5.35

4.56

4.05

7.45

6.16

5.50

4.44

3.75

3.52

4.18

4.05

3.71

3.64

3.65

3.18

3.80

3.37

3.15

7.44

5.71

5.53

4.58

3.84

3.16

9.74

8.31

6.66

11

8.96

6.75

5.05

12.45

11.00

8.75

9.81

8.91

7.11

14.30

13.26

9.88

7.56

7.04

6.18

6.29

6.35

5.42

6.07

6.04

5.20

6.18

6.09

5.30

10.23

9.60

8.15

9.04

7.24

5.51

13.09

13.25

11.58

12

4.12

2.81

2.41

4.86

4.60

3.61

4.03

3.62

3.10

6.00

5.81

4.30

3.16

2.84

2.61

2.75

2.92

2.53

2.65

2.76

2.35

2.79

2.62

2.32

4.39

3.83

3.40

4.40

3.03

2.46

5.41

5.25

5.18

13

21.67

22.48

17.20

35.74

33.57

27.91

31.43

31.28

24.86

40.77

37.86

32.77

25.65

25.17

21.95

18.70

19.11

15.63

19.55

19.79

15.04

20.57

21.59

16.82

32.18

33.29

27.13

22.25

25.49

18.25

40.62

44.05

36.08

14

22.80

14.57

12.17

34.72

27.02

24.40

25.12

18.84

18.04

40.71

27.08

28.43

20.13

15.76

16.14

17.75

17.89

15.85

16.63

16.41

16.81

18.83

15.61

15.53

28.72

21.53

22.96

23.26

15.90

14.34

38.88

31.08

33.48

15

7.43

6.45

6.28

11.53

10.51

10.00

9.58

8.35

8.59

13.15

10.89

11.52

7.71

6.85

7.15

6.85

7.12

7.33

6.63

6.87

6.81

6.76

6.25

6.37

10.67

9.46

9.67

8.13

6.57

6.63

13.27

12.63

13.94

16

5.27

2.97

2.09

4.80

4.45

3.55

4.24

3.96

2.91

5.91

7.35

3.91

3.09

2.93

2.55

2.31

2.39

2.06

2.20

2.21

1.86

2.56

2.56

2.16

4.51

4.44

3.56

5.29

3.32

2.14

5.95

6.79

4.91

17

4.99

4.48

3.80

7.48

6.44

5.73

6.54

5.84

5.07

8.71

6.76

6.27

5.74

5.02

4.80

4.35

4.26

3.81

4.30

4.22

3.82

4.53

4.16

3.64

6.82

6.04

5.53

4.93

4.78

4.02

8.31

8.20

6.72

18

13.11

12.15

10.12

20.86

18.38

16.78

17.16

15.70

13.96

22.05

18.29

18.79

15.03

13.87

13.04

12.64

12.63

11.36

13.49

13.53

12.44

12.89

12.16

10.64

17.96

16.57

15.23

13.52

13.40

11.31

22.51

21.41

19.65

19

10.45

6.27

4.38

9.46

8.09

6.10

7.58

7.11

5.29

11.33

13.72

6.84

5.95

5.63

4.61

4.72

4.79

4.05

4.70

4.80

3.87

4.89

4.83

4.13

7.41

7.23

5.68

10.46

6.92

4.54

9.15

9.52

7.59

20

6.44

5.07

4.06

9.22

7.91

6.05

7.73

6.49

5.33

10.48

8.03

6.81

6.35

5.44

4.74

5.19

5.17

4.14

4.94

4.91

4.25

5.39

4.74

4.03

8.82

7.42

6.04

6.09

5.40

3.98

11.58

11.27

7.47

21

9.82

7.73

6.02

13.54

11.35

9.90

9.97

9.55

7.66

14.96

15.16

10.76

8.10

7.63

6.81

6.23

6.30

5.37

6.21

6.23

5.12

6.53

6.46

5.45

10.16

9.84

8.48

9.65

8.37

5.99

12.89

13.45

11.33

22

12.22

9.26

8.13

16.10

13.61

12.74

12.90

10.91

10.58

18.23

15.20

14.24

11.34

9.66

9.50

8.56

8.68

8.75

8.50

8.58

8.42

9.41

8.18

8.01

13.30

11.32

11.36

12.45

10.08

8.74

16.19

14.73

15.11

23

4.97

3.34

2.80

8.33

6.91

5.87

5.66

4.38

4.09

10.01

6.49

6.96

4.50

3.70

3.76

4.15

4.31

3.82

3.86

4.09

3.91

4.27

3.65

3.51

6.52

4.94

4.99

5.31

3.79

3.32

9.54

7.98

7.98

24

22.39

19.10

17.84

28.50

23.69

23.03

26.96

22.71

21.14

32.82

25.14

26.84

24.05

19.74

19.97

15.20

15.29

15.31

15.52

15.44

14.52

18.86

15.59

14.72

29.08

25.10

23.06

21.28

20.14

16.94

32.04

33.52

26.67

mean

10.74

7.96

6.46

14.38

12.42

10.50

11.58

10.23

8.69

16.82

14.90

12.10

9.41

8.34

7.70

7.57

7.68

6.83

7.46

7.52

6.64

7.94

7.34

6.52

12.48

11.08

9.90

10.96

8.72

6.79

15.79

15.15

13.57

 

Table 2: Demosaicking performance (CPSNR) on Kodak dataset (noise free) with all 11 CFAs

CPSNR

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random CFA

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

Hao50

Hao60

image

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

1

37.02

38.32

39.56

36.73

36.99

38.09

37.50

37.21

38.42

35.57

34.95

36.98

38.75

38.56

39.33

39.74

39.40

40.29

39.66

39.33

40.92

39.78

39.24

40.27

37.18

36.94

37.96

36.90

37.85

39.62

36.20

35.82

36.32

2

39.04

39.99

41.48

38.13

38.35

39.55

38.83

39.26

40.24

37.25

37.95

38.80

39.66

39.91

40.69

40.15

39.75

40.68

40.26

39.84

40.86

40.17

40.22

40.66

38.59

38.97

39.69

38.92

39.96

40.98

37.94

38.49

38.10

3

40.77

42.63

42.99

39.20

39.83

41.10

39.89

41.22

41.65

38.12

40.12

40.10

40.72

41.86

42.24

41.89

41.89

42.61

42.16

42.28

42.61

41.18

42.19

42.73

38.66

40.06

40.34

40.52

42.28

43.01

37.22

37.94

38.28

4

40.15

41.14

41.24

38.07

38.61

38.71

39.27

39.99

39.85

37.22

38.40

37.82

40.20

40.77

40.58

40.59

40.50

40.31

40.78

40.74

40.59

40.84

41.25

41.10

38.71

39.52

39.20

39.62

41.03

40.54

38.05

38.61

37.17

5

36.94

38.44

38.89

33.71

34.82

35.24

35.35

36.42

36.75

32.90

34.75

34.56

36.35

37.39

37.25

36.91

37.11

37.18

37.08

37.28

37.38

37.11

37.87

38.19

34.83

35.93

36.07

36.66

37.83

38.57

33.69

34.36

34.60

6

38.00

39.86

41.28

37.61

38.18

38.96

38.35

38.72

39.97

37.01

36.46

38.56

39.60

40.00

40.59

40.80

40.76

41.60

40.73

40.81

41.90

40.43

40.64

41.48

38.47

38.59

39.37

38.06

39.42

41.31

37.55

37.19

37.91

7

41.33

43.04

43.51

38.75

39.40

40.31

40.36

41.31

41.76

38.06

39.52

39.71

41.31

42.07

42.33

41.71

41.66

42.03

41.93

42.01

41.95

41.63

42.19

42.64

39.69

40.73

40.98

40.75

42.11

42.91

38.19

38.93

39.19

8

33.03

35.93

37.83

34.39

34.89

37.05

35.23

35.38

37.38

33.43

31.85

36.62

36.62

36.83

38.22

37.48

37.35

38.56

37.56

37.44

38.84

37.42

37.44

38.50

35.39

35.49

37.12

32.99

35.50

38.08

34.38

34.27

35.74

9

40.89

42.58

43.82

39.57

40.11

41.49

40.77

41.40

42.49

38.98

39.58

41.11

41.69

42.22

43.02

42.06

42.00

42.85

42.33

42.25

43.11

42.01

42.39

43.15

40.41

41.12

41.96

40.64

41.90

43.39

38.91

39.28

40.64

10

41.70

42.67

43.26

39.52

40.19

41.02

40.85

41.54

42.06

39.41

40.23

40.73

41.66

42.39

42.66

41.92

42.06

42.43

42.52

42.51

43.11

42.33

42.86

43.14

39.42

40.57

40.71

41.53

42.29

43.13

38.24

38.94

39.89

11

38.61

39.84

41.10

37.18

37.72

38.71

38.22

38.63

39.61

36.58

36.90

38.18

39.34

39.66

40.22

40.15

40.10

40.79

40.30

40.32

40.97

40.22

40.28

40.88

38.03

38.31

39.02

38.57

39.53

40.72

36.96

36.91

37.49

12

41.98

43.64

44.32

41.27

41.51

42.55

42.07

42.54

43.22

40.35

40.49

41.79

43.14

43.60

43.97

43.73

43.47

44.10

43.89

43.72

44.42

43.68

43.95

44.48

41.70

42.30

42.82

41.69

43.31

44.23

40.80

40.93

40.99

13

34.77

34.61

35.78

32.60

32.87

33.67

33.16

33.18

34.18

32.03

32.35

32.98

34.04

34.12

34.72

35.41

35.32

36.19

35.22

35.17

36.36

35.00

34.79

35.87

33.05

32.91

33.80

34.66

34.07

35.52

32.04

31.69

32.56

14

34.55

36.50

37.28

32.73

33.81

34.26

34.13

35.38

35.57

32.03

33.80

33.59

35.09

36.16

36.05

35.64

35.60

36.13

35.92

35.98

35.88

35.38

36.20

36.22

33.55

34.80

34.52

34.46

36.12

36.57

32.23

33.21

32.88

15

39.42

40.04

40.15

37.51

37.92

38.13

38.32

38.92

38.79

36.94

37.76

37.52

39.26

39.77

39.59

39.77

39.61

39.48

39.91

39.76

39.80

39.83

40.17

40.09

37.85

38.37

38.28

39.03

39.96

39.92

36.90

37.12

36.69

16

40.91

43.40

44.93

41.32

41.65

42.63

41.86

42.15

43.49

40.42

39.47

42.21

43.23

43.46

44.06

44.49

44.35

44.99

44.71

44.68

45.43

44.06

44.05

44.78

41.59

41.66

42.62

40.90

42.92

44.84

40.38

39.81

41.22

17

41.15

41.62

42.34

39.39

40.04

40.55

39.97

40.46

41.08

38.73

39.83

40.15

40.54

41.12

41.32

41.75

41.83

42.32

41.80

41.88

42.31

41.57

41.94

42.52

39.79

40.32

40.70

41.21

41.33

42.09

38.93

38.99

39.85

18

36.96

37.29

38.08

34.94

35.49

35.88

35.79

36.17

36.68

34.70

35.51

35.39

36.36

36.71

36.98

37.11

37.12

37.58

36.83

36.82

37.18

37.03

37.28

37.86

35.59

35.94

36.30

36.82

36.86

37.60

34.61

34.82

35.20

19

37.94

40.16

41.72

38.37

39.05

40.28

39.33

39.61

40.90

37.59

36.76

39.78

40.38

40.62

41.49

41.39

41.33

42.06

41.41

41.32

42.26

41.24

41.29

41.98

39.44

39.54

40.58

37.93

39.73

41.56

38.52

38.34

39.33

20

40.04

41.08

42.05

38.48

39.15

40.32

39.25

40.01

40.87

37.93

39.08

39.80

40.10

40.78

41.37

40.98

40.99

41.96

41.19

41.22

41.85

40.82

41.38

42.08

38.68

39.43

40.32

40.28

40.81

42.14

37.49

37.61

39.40

21

38.21

39.25

40.33

36.81

37.58

38.18

38.14

38.33

39.29

36.38

36.32

37.81

39.05

39.31

39.80

40.18

40.14

40.83

40.20

40.18

41.03

39.98

40.03

40.76

38.06

38.20

38.85

38.29

38.90

40.35

37.03

36.84

37.59

22

37.26

38.46

39.03

36.06

36.79

37.08

37.02

37.75

37.89

35.52

36.31

36.59

37.59

38.28

38.36

38.81

38.75

38.71

38.84

38.80

38.88

38.39

39.01

39.09

36.89

37.59

37.58

37.18

38.10

38.72

36.04

36.45

36.34

23

41.16

42.89

43.65

38.92

39.74

40.45

40.60

41.71

42.02

38.13

40.01

39.70

41.60

42.45

42.38

41.95

41.79

42.31

42.26

42.01

42.20

41.83

42.50

42.68

39.99

41.20

41.15

40.88

42.35

42.92

38.34

39.11

39.11

24

34.63

35.32

35.62

33.58

34.38

34.51

33.82

34.57

34.88

32.97

34.13

33.84

34.32

35.18

35.13

36.31

36.29

36.28

36.22

36.24

36.51

35.38

36.20

36.45

33.50

34.13

34.50

34.85

35.09

35.84

33.07

32.88

33.87

mean

38.60

39.95

40.84

37.29

37.88

38.70

38.25

38.83

39.54

36.59

37.19

38.10

39.19

39.72

40.10

39.34

39.28

39.79

39.40

39.37

39.91

39.89

40.22

40.73

37.88

38.44

38.93

38.47

39.55

40.61

36.82

37.02

37.51

 

Table 3: Demosaicking performance (mean CIE Lab error) on Kodak dataset (noise free) with all 11 CFAs

LAB

Bayer CFA

Kodak CFA2.0

Fuji X-Trans

Sony RGBW

Random CFA

Hirakawa 4 color

Condat 6 color

Hao4x4

Hao40

Hao50

Hao60

image

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

Var

Rad

Ours

1

1.750

1.561

1.325

2.247

2.145

1.895

1.857

1.881

1.632

2.476

2.572

2.075

1.612

1.622

1.480

1.723

1.769

1.575

1.700

1.743

1.482

1.788

1.852

1.703

2.118

2.147

1.921

2.130

1.956

1.666

2.603

2.686

2.502

2

1.957

1.663

1.374

2.442

2.200

1.876

2.035

1.814

1.599