Sparsity Based Super Resolution Using Color Channel Constraints

Background Color SR Color Dictionary Learning Experimental Results Conclusion

Sparsity Based Super ResolutionUsing Color Channel Constraints

Hojjat Mousavi, Vishal Monga

School of Electrical Engineering and Computer Science

The Pennsylvania State University

September 27, 2016

iPAL Color Super Resolution 1/28


Super Resolution - Problem Definition

• Multi-frame SR: Traditional Super-resolution problem is the process ofcombining multiple low resolution images to form a higher resolution one

• Resulting image should represent reality better than all the input images.

• Single-image SR: given a single low-resolution input, reconstruct ahigh-resolution version of the input.

• Advantage: more widely applicable than multi-frame approaches.• Challenge: single-image super-resolution is an extremely ill-posed

problem.



Sparsity-based Super resolution - Basic idea 1,2

• Construct two coupled dictionaries based on image patches inluminance (Y) channel

1 Low resolution dictionary: DDDl (High frequency features)

2 High resolution dictionary: DDDh (Actual high resolution patches)

• Atoms of each dictionary correspond to each other and are LR-HRcounterparts of each other extracted from the same locations

1Wright et al. CVPR 20082Wright et al. TIP 2009



Sparsity-based Super resolution

• SR for an unseen low resolution image:

1 Extract overlapping patches (overlapped tiling) (yyyl)

2 For each patch find the low resolution representation using DDDl

xxx∗ = argminxxx

12||yyyl−DDDlxxx||22 +λ ||xxx||1

Find the sparse linear representation of low resolution patch based on LRdictionary

3 Find the high resolution representation using DDDh and the same xxx∗.

yyyh =DDDhxxx∗

4 construct the high resolution image from high-res patches.



Color Super Resolution

• YCbCr space. Apply Bicubic interpolation on Cb and Cr channels.• Human eye is more sensitive to luminance than chrominance• Some images have varying amount of luminance and chrominance

geometry

• Chrominance channels also contain useful information• Super-resolution only on luminance channel may not get the best results• Luminance edge (in Y)→ present in R, G and B channels• Jointly account for cross channel information in an adaptive manner




• How to capture edge similarities?• Extract edge information in RGB channels

• Find patches that should have have high edge correlation based on amountof color information in each patch

• Encourage edge similarity in selected patches of high resolution image

• Similarity (Correlation) between edges in different channels. (Based on HRimage): Example: ‖SSSryyyhr −SSSgyyyhg‖2 Or correlation (SSSryyyhr )

T(SSSgyyyhg)

where SSSr,SSSg,SSSb are highpass edge detector filters

• Color constraints: Edge differences across color channels are minimizedfor selected patches3,4,5

‖SSSryyyhr −SSSgyyyhg‖2 < εrg

‖SSSgyyyhg −SSSbyyyhb‖2 < εgb

‖SSSbyyyhb −SSSryyyhr‖2 < εbr3Srinivas et al. CIC 20104Farsiu et al. TIP 20065Menon et al. TIP 2009




• High resolution representation of patches is incorporated in the costfunction by the following assumption of conventional SR methods.

yyyhr =DDDhrxxxr, yyyhg =DDDhgxxxg, yyyhb =DDDhbxxxb

• Incorporating RGB channel information and exploiting our multi-taskframework result in the following optimization problem:

argminxxxc

∑c={r,g,b}

(12‖yyylc −DDDlcxxxc‖2

2 +λ‖xxxc‖1

)+τ

[‖SSSrDDDhrxxxr−SSSgDDDhgxxxg‖2

2 +‖SSSgDDDhgxxxg−SSSbDDDhbxxxb‖22 +‖SSSbDDDhbxxxb−SSSrDDDhrxxxr‖2

2

].

• Note: Without color channel constraints→ Three independentoptimization problems

• With additional color constraints→ One optimization problem withquadratic constraints on pairs of channels

• τ is very crucial and we pick it in an adaptive manneriPAL Color Super Resolution 6/28



• Introducing DDD,DDDl,xxx,yyy, we can simply the cost function to

xxx = argminxxx xxxTDDDxxx−yyyTDDDlxxx+λ‖xxx‖1. → FISTA6

where

DDD =

12 DDDT

lrDDDlr +2τDDDT

hrSSST

r SSSrDDDhr −2τDDDThr

SSSTr SSSgDDDhg 000

000 12 DDDT

lgDDDlg +2τDDDT

hgSSST

g SSSgDDDhg −2τDDDThg

SSSTg SSSbDDDhb

−2τDDDThb

SSSTb SSSrDDDhr 000 1

2 DDDTlb

DDDlb+2τDDDT

hbSSST

b SSSbDDDhb

xxx =

xxxrxxxgxxxb

, yyy =

yyylryyylgyyylb

, DDDl =

DDDlr 000 000000 DDDlg 000000 000 DDDlb

• Note that matrix DDD can capture cross channel constraints by adding a

term to the appropriate locations• SSSr,SSSg,SSSb are gradient operators in RGB channels.6Beck et al. SIAM Journal of Imaging Sciences, 2009



Joint Dictionary Learning for Color Channels

• Correlation between color channels can be even better captured if theindividual color channel dictionaries are also designed to facilitate thesame.

• Given a set of N sampled training image patch pairs {YYYh,YYY l}.YYYh = {yyy1

h,yyy2h, ...,yyy

Nh }: set of HR patches sampled from training

YYY l = {yyy1l ,yyy

2l , ...,yyy

Nl }: set of corresponding LR patches.

• A new joint learning for multi channel dictionary learning is proposed:

arg minDDDh,DDDl,xxxi

1N

N∑i=1

γ

2‖yyyi

l−DDDlxxxi‖22 +

1− γ

2‖yyyi

h−DDDhxxxi‖22

+τ

[‖SSSrDDDhrxxx

ir−SSSgDDDhgxxxi

g‖22

+‖SSSgDDDhgxxxig−SSSbDDDhbxxxi

b‖22

+‖SSSbDDDhbxxxib−SSSrDDDhrxxx

ir‖2

2

]+λ‖xxxi‖1

st. ‖DDDh(:,k)‖22 ≤ 1, ‖DDDl(:,k)‖2

2 ≤ 1, k = 1,2, ...,K



Joint Dictionary Learning for Color Channels

L2 =1N

N∑i=1

γ

2‖yyyi

l−DDDlxxxi‖22 +

1− γ

2‖yyyi

h−DDDhxxxi‖22 +λ‖xxxi‖1

+2τxxxiT DDDThSSST(III−PPPT

s )SSSDDDhxxxiT

=γ

2N‖YYY l−DDDlXXX‖2

F +1− γ

2N‖YYYh−DDDhXXX‖2

F +λ

N‖XXX‖1

+2τ

NTr(

XXXTDDDThSSST(III−PPPT

s )SSSDDDhXXXT).

where XXX = [xxx1 xxx2 ... xxxN ].Alternatively solve for XXX, DDDl and DDDh

xxx =

xxxrxxxgxxxb

, yyy =

yyylryyylgyyylb

, DDDl =

DDDlr 000 000000 DDDlg 000000 000 DDDlb

, DDDh =

DDDhr 000 000000 DDDhg 000000 000 DDDhb

SSS =

SSSr 000 000000 SSSg 000000 000 SSSb

, PPPs =

000 000 IIIp2×p2

IIIp2×p2 000 000000 IIIp2×p2 000



Solution for XXX

• DDDl and DDDh fixed.• Optimize over XXX whose columns can be obtained independently.• For each column of XXX (i = 1...N) we can rewrite the cost function as:

xxxi = argminxxx

γ

2‖yyyi

l−DDDlxxx‖2F +

1− γ

2‖yyyi

h−DDDhxxx‖2F +λ‖xxx‖1

+2τxxxTDDDThSSST(III−PPPT

s )SSSDDDhxxxT

= argminxxx

xxxT [γ

2DDDT

l DDDl +1− γ

2DDDT

hDDDh

+2τDDDThSSST(III−PPPT

s )SSSDDDh]xxx

−(γyyyiT

l DDDl +(1− γ)yyyiTh DDDh

)xxx+λ‖xxx‖1

= argminxxx

xxxTAAAxxx−bbbTxxx +λ‖xxx‖1

AAA = γ

2DDDTl DDDl +

1−γ

2 DDDThDDDh +2τDDDT

hSSST(III−PPPTs )SSSDDDh

bbbiT = γyyyiTl DDDl +(1− γ)yyyiT

h DDDh.• Can be solved using FISTA7

7Beck et al. SIAM Journal of Imaging Sciences, 2009



Solution for DDDl

• Fix XXX and DDDh, the cost function reduces to:

DDDl = argminDDDl

‖YYY l−DDDlXXX‖2F

s.t. ‖DDDl(:,k)‖22 ≤ 1, k = 1,2, ...,K

DDDl is block diagonal .

• Split into three separate dictionary learning procedures as follows wherec ∈ {r,g,b}.

DDDlc = argminDDDlc

‖YYY lc −DDDlcXXXc‖2F

s.t. ‖DDDlc(:,k)‖22 ≤ 1, k = 1,2, ...,K

where XXXc = [xxx1c xxx2

c ... xxxNc ], YYY lc = [yyy1

c yyy2c ... yyyN

c ] and c takes the subscripts from{r,g,b} indicating a specific color channel.

• Each of the above dictionaries are learnt by the ODL method8.8Mairal et al. ICML, 2009.



Solution for DDDh• Finally when XXX and DDDl are fixed, L2 reduces to:

DDDh = argminDDDh

1N

N∑i=1

1− γ

2‖yyyi

h−DDDhxxxi‖22


s )SSSDDDhxxxiT

s.t ‖DDDh(:,k)‖22 ≤ 1, k = 1,2, ...,K.

• Not very straight forward to solve→ ADMM9.• Define the function g(DDDh,ZZZ) as follows:

g(DDDh,ZZZ) =1N

N∑i=1

1− γ

2‖yyyi

h−DDDhxxxi‖22 +2τxxxiT DDDT

hSSST(III−PPPTs )SSSZZZxxxiT

• Solve the equivalent bi-convex problem:DDDh = argmin

DDDh,ZZZg(DDDh,ZZZ)

s.t DDDh−ZZZ = 000,‖DDDh(:,k)‖2

2 ≤ 1, k = 1,2, ...,K.9Boyd et al. Foundations and Trends in Machine Learning, 2011



Solution for DDDh

Iterative steps of ADMM until a convergence is achieved are as follows:1 Find DDDt+1

h :DDDt+1

h = argminDDDh

( 1N

N∑i=1

1− γ

2‖yyyi

h−DDDhxxxi‖22


s )SSSZZZtxxxiT)

+ρ

2‖DDDh−ZZZt +UUUt‖2

F

s.t. ‖DDDh(:,k)‖22 ≤ 1, k = 1, ...,K.

2 Find ZZZt+1:ZZZt+1 = argmin

ZZZ

(2τ

N

N∑i=1

xxxiT DDDt+1T

h SSST(III−PPPTs )SSSZZZtxxxiT

)+

ρ

2‖DDDt+1

h −ZZZ +UUUt‖2F

3 Find UUUt+1: UUUt+1 =UUUt +DDDt+1h −ZZZt+1

Solutions to steps 1 and 2 of the ADMM procedure are not straightforwardand details are in the paper.



• More analytical Results on how to solve optimization problems at eachstage

• Extensive experimental validations in addition to high quality images

• Implementation and MATLAB toolbox

All Available online at:http://signal.ee.psu.edu/MCcSR.html


http://signal.ee.psu.edu/MCcSR.html


State of the art methods to compare with

Single image super resolution methods that incorporate sparsity methods:1 Sparsity Constrained super resolution (ScSR)10

2 Single Image Scale-up using Sparse Representation 11

3 Adjusted Anchored Neighborhood Regression for Fast Example-BasedSuper-Resolution (ANR+)12

4 Global Regression for Fast Super-Resolution (GR)13

5 Neighbor Embedding with Locally Linear Embedding (NE+LLE) 14

6 Neighbor Embedding with NonNegative Least Squares (NE+NNLS) 15

7 Single Image SR using sparse regression and natural image prior16:Using sparse kernel ridge regression and natural image priors.

8 Image and Video Upscaling from Local Self-Examples17

10Yang, IEEE TIP, 201211Zeyde et al, Springer, Curves and Surfaces, 201212Timofte et al. ACCV 201413Timofte et al. ICCV 201314Chang et al. CVPR 200415Bevilazqua et al. BMVC 201216Kim et al. IEEE Tran on PAMI, 201017Freeman et al, ACM Transactions on Graphics, 2011



Experimental Set Up

• Dictionary size: 512 atoms - 100,000 image patches are sampled• Scaling factor: 2x, 3x, 4x• Patch size: 5×5, 7×7, 9×9 pixels.• Quantitative measures: PSNR, SSIM, S-CIELAB18

18Zhang et al., in Proc. IEEE COMPCON Symp. Dig., 1997.



(a) PSNR and SSIM - scale 2:Top: Original, Bicubic (30.46, 0.840), Zeyde et al. (31.97, 0.887),Middle: GR (31.70, 0.879), ANR (32.09, 0.889), NENNLS (31.87, 0.884)Bottom: NELLE (32.03, 0.889), MCcSR (32.23, 0.899), ScSR (32.14,0.893) .

(b) SCIELAB error map - scale 2:Top: Original, Bicubic (1.898e4), Zeyde et al. (1.127e4),Middle: GR (1.198e4), ANR (1.077e4), NENNLS (1.159e4)Bottom: NELLE (1.099e4), MCcSR (9.770e3) , ScSR (1.014e4).



(c) PSNR and SSIM - scale 3:Top: Original, Bicubic (27.51, 0.685), Zeyde et al. (28.28, 0.737),Middle: GR (28.15, 0.729), ANR (28.36, 0.742), NENNLS (28.17, 0.730)Bottom: NELLE (28.30, 0.738), MCcSR (28.51, 0.758), ScSR (28.25,0.740) .

(d) SCIELAB error map - scale 3:Top: Original, Bicubic (3.423e4), Zeyde et al. (2.896e4),Middle: GR (3.008e4), ANR (2.865e4), NENNLS (2.961e4)Bottom: NELLE (2.905e4), MCcSR (2.709e4) , ScSR (3.002e4).



(e) PSNR and SSIM - scale 4:Top: Original, Bicubic (26.05, 0.566), Zeyde et al. (26.61, 0.615),Middle: GR (26.51, 0.607), ANR (26.63, 0.618), NENNLS (26.50, 0.606)Bottom: NELLE (26.57, 0.614), MCcSR (26.74, 0.632), ScSR (26.35,0.608) .

(f) SCIELAB error map - scale 4:Top: Original, Bicubic (4.369e4), Zeyde et al. (3.923e4),Middle: GR (4.045e4), ANR (3.928e4), NENNLS (3.984e4)Bottom: NELLE (3.967e4), MCcSR (3.818e4) , ScSR (4.002e4).



Results - Scale 3

Table: PSNR results of different methods for various images with scaling factor of 3.

Images PSNR (dB)Bicub Zeyde GR ANR NENNLS NELLE MCcSR ScSR

baby 38.42 39.51 39.38 39.56 39.22 39.49 39.51 39.40butterfly 28.73 30.60 29.73 30.57 30.29 30.42 30.59 30.64bird 36.37 37.90 37.44 37.92 37.68 37.90 38.02 37.59face 35.96 36.44 36.40 36.50 36.39 36.47 36.48 36.37foreman 35.76 37.67 36.84 37.71 37.37 37.69 37.74 37.64coastguard 31.31 31.91 31.78 31.84 31.77 31.83 31.95 31.83flowers 30.92 31.84 31.62 31.88 31.68 31.80 32.07 31.87head 36.02 36.47 36.42 36.52 36.40 36.50 36.51 36.42lenna 35.26 36.23 35.99 36.29 36.11 36.24 36.33 36.14man 31.78 32.68 32.44 32.71 32.50 32.65 32.75 32.68pepper 35.25 36.27 35.77 36.13 35.99 36.12 36.30 36.20average 33.08 34.06 33.76 34.07 33.88 34.03 34.14 34.00



Results - Scale 3

Table: SSIM results of different methods for various images with scaling factor of 3.

Images SSIMBicub Zeyde GR ANR NENNLS NELLE MCcSR ScSR

baby 0.88 0.90 0.90 0.90 0.89 0.90 0.90 0.89butterfly 0.79 0.85 0.80 0.84 0.84 0.84 0.85 0.85bird 0.90 0.92 0.91 0.92 0.92 0.92 0.93 0.91face 0.72 0.74 0.74 0.74 0.74 0.74 0.75 0.74foreman 0.89 0.91 0.90 0.91 0.90 0.91 0.91 0.90coastguard 0.57 0.62 0.63 0.62 0.61 0.62 0.63 0.62flowers 0.77 0.80 0.79 0.80 0.79 0.80 0.81 0.80head 0.72 0.74 0.74 0.75 0.74 0.74 0.75 0.74lenna 0.78 0.80 0.80 0.80 0.80 0.80 0.81 0.80man 0.72 0.76 0.76 0.77 0.76 0.76 0.76 0.76pepper 0.78 0.80 0.79 0.80 0.79 0.79 0.80 0.79average 0.745 0.776 0.769 0.778 0.771 0.775 0.785 0.774



Results - Scale 3

Table: S-CIELAB error results of different methods for various images with scalingfactor of 3.

Images S-CIELABBicub Zeyde GR ANR NENNLS NELLE MCcSR ScSR

baby 2.07E+04 1.36E+04 1.40E+04 1.32E+04 1.47E+04 1.34E+04 1.34E+04 1.50E+04butterfly 2.28E+04 1.55E+04 1.84E+04 1.55E+04 1.60E+04 1.60E+04 1.54E+04 1.49E+04bird 1.07E+04 7.36E+03 8.02E+03 7.21E+03 7.73E+03 7.30E+03 6.50E+03 7.81E+03face 3.79E+03 2.71E+03 2.73E+03 2.57E+03 2.73E+03 2.61E+03 2.47E+03 2.70E+03foreman 8.46E+03 3.90E+03 4.79E+03 3.48E+03 4.01E+03 3.62E+03 3.72E+03 3.89E+03coastguard 1.96E+04 1.71E+04 1.70E+04 1.70E+04 1.76E+04 1.71E+04 1.69E+04 1.70E+04flowers 4.47E+04 3.75E+04 3.89E+04 3.69E+04 3.84E+04 3.74E+04 3.29E+04 3.70E+04head 3.79E+03 2.69E+03 2.74E+03 2.54E+03 2.79E+03 2.61E+03 2.42E+03 2.65E+03lenna 2.44E+04 1.74E+04 1.85E+04 1.67E+04 1.79E+04 1.69E+04 1.58E+04 1.72E+04man 3.80E+04 2.91E+04 3.03E+04 2.84E+04 3.02E+04 2.89E+04 2.88E+04 2.95E+04pepper 2.48E+04 1.91E+04 2.15E+04 1.96E+04 2.02E+04 1.95E+04 1.73E+04 1.91E+04

average 2.79E+04 2.27E+04 2.36E+04 2.24E+04 2.33E+04 2.26E+04 2.14E+04 2.28E+04



Effect of RGB constraints

Figure: Visual Images as well as S-CIELAB error maps are shown for a scaling factorof 3. From left to right for each row images correspond to: Original image, applyingSR separately on RGB channels (36.26, 0.83, 1.57e4), ScSR (36.13, 0.83, 1.67e4)and MCcSR (36.67, 0.85, 1.43e4). Numbers in parenthesis are PSNR, SSIM andSCIELAB error measures.



Effect of RGB constraints

Figure: Visual Images as wellas S-CIELAB error maps areshown for a scaling factor of 3.From left to right for each rowImages correspond to: OriginalImage, applying SR separatelyon RGB channels, ScSR,MCcSR

Table: Quantitative measures to show effectiveness of color constraints in SR for a scaling factor of 3.

Images PSNR SSIM S-CIELABSeparate RGB ScSR MCcSR Separate RGB ScSR MCcSR Separate RGB ScSR MCcSR

comic 28.37 28.25 28.51 0.74 0.74 0.75 2.80e4 3.00e4 2.70e4baboon 26.95 26.95 27.11 0.53 0.52 0.54 9.93e4 1.01e5 9.57e4pepper 36.14 35.85 36.30 0.79 0.77 0.81 1.93e4 2.27e5 1.73e4bird 37.71 37.59 38.02 0.92 0.912 0.93 7.28e3 8.54e3 6.50e3



Performance Under Noise

Figure: Super Resolution performance under difference noisestandard deviations: 4,6,8,12 (from top to bottom ) with different methods:Original, bicubic, MCcSR, ScSR (from left to right)

Table: Average performance under differentnoise levels.

Measure Method σ = 0 σ = 4 σ = 6 σ = 8 σ = 12

PSNRBicubic 33.08 32.99 32.75 32.50 31.88ScSR 34.00 33.95 33.92 33.90 33.86

MCcSR 34.14 34.11 34.09 34.09 34.07

SSIMBicubic 0.745 0.731 0.698 0.672 0.619ScSR 0.774 0.772 0.766 0.761 0.752

MCcSR 0.785 0.783 0.780 0.775 0.768

SCIELABBicubic 2.79E4 2.92E4 4.40E4 5.25E4 6.31E4ScSR 2.28E4 2.31E4 2.36E4 2.39E4 2.43E4

MCcSR 2.14E4 2.16E4 2.20E4 2.21E4 2.23E4



Dictionary size

• Dictionaries of size 16,32,64,128,256 and 512 are trained.

Figure: Effect of dictionary size on PSNR, SSIM and S-CIELAB erroriPAL Color Super Resolution 26/28


Conclusion and Future Work

• Sparsity→ powerful prior for the ill-posed problem of single image superresolution

• Cross channel information and color constraints→ Regularizing theoptimization problem for boosting SR performance

• Under different scaling factors, different noise levels, different dictionarysizes the proposed MCcSR method outperforms the state of the art.

• Expedite the sparse coding problem using neural networks

• Introduce other objective measurements rather than MSE for qualityassessment or in the objective function

• Apply other cross channel constraints or color constraint that canimprove super resolution performance



Thank you!


Backup Slides


Dictionary Atoms

• Low resolution dictionary atoms - Red channel only- 9 by 9 pixelspatches - Extracted from features

Figure: Low resolution dictionary atoms -Red channel only- 9 by 9 pixels patches -Extracted from features

Figure: High resolution dictionary atoms -RGB - 9 by 9 pixels patches


Color Adaptive Patch Processing

• Not all image patches have the same color information (chrominance)

• Parameter τ can be used to control high frequency correlation amongcolor channels.

• Calculate the variations in color information→ Adaptively control τ.

β =12s

(‖HHH1yyyCb‖+‖HHH1yyyCr‖‖HHH1yyyY‖

+‖HHH2yyyCb‖+‖HHH2yyyCr‖

‖HHH2yyyY‖

)where s is normalization parameter, HHH1 and HHH2 are high-pass Scharroperators.


(a) PSNR and SSIM - scale 2:Top: Original, Bicubic (28.19, 0.635), Zeyde et al. (28.62, 0.683),Middle: GR (28.63, 0.690), ANR (28.67, 0.689), NENNLS (28.58, 0.680)Bottom: NELLE (28.66, 0.688), MCcSR (28.78, 0.705, ScSR (28.69, 0.692).

(b) SCIELAB error map - scale 2:Top: Original, Bicubic (7.856e4), Zeyde et al. (6.570e4),Middle: GR (6.388e4), ANR (3.287e4), NENNLS (6.585e4)Bottom: NELLE (6.421e4), MCcSR (5.799e4) , ScSR (6.296e4).


(c) PSNR and SSIM - scale 3:Top: Original, Bicubic (26.71, 0.480), Zeyde et al. (26.94, 0.520),Middle: GR (26.95, 0.529), ANR (26.97, 0.527), NENNLS (26.92, 0.518)Bottom: NELLE (26.97, 0.526), MCcSR (27.11, 0.549), ScSR (26.95,0.524) .

(d) SCIELAB error map - scale 3:Top: Original, Bicubic (1.078e5), Zeyde et al. (1.008e5),Middle: GR (1.000e5), ANR (9.962e4), NENNLS (1.010e5)Bottom: NELLE (9.998e4), MCcSR (9.574e4) , ScSR (1.018e5).


(e) PSNR and SSIM - scale 4:Top: Original, Bicubic (26.00, 0.390), Zeyde et al. (26.17, 0.420),Middle: GR (26.17, 0.428), ANR (26.19, 0.426), NENNLS (26.15, 0.419)Bottom: NELLE (26.18, 0.425), MCcSR (26.25, 0.446), ScSR (26.11,0.415) .

(f) SCIELAB error map - scale 4:Top: Original, Bicubic (1.237e5), Zeyde et al. (1.186e5),Middle: GR (1.183e5), ANR (1.180e5), NENNLS (1.190e5)Bottom: NELLE (1.183e5), MCcSR (1.136e5) , ScSR (1.185e5).
