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Abstract

The similarity measure plays the key role in the self-learning framework for single image super-resolution. This paper involves matrix regression with properties of robustness and two-dimensional structure to measure the similarity between image blocks and enhance the effect of super-resolution. Specifically, we use the minimal nuclear norm of representation error as a criterion, and the alternating direction method of multipliers (ADMM) to calculate the similarity between high- and low-resolution image blocks. Evaluation on several images with different interference and experimental results of super-resolution images clearly demonstrate the advantages of our proposed method in visual robustness and super-resolution effects.

Keywords

Computer Vision Fabric Imaging Processing Image Super-Resolution Matrix Regression Similarity Measure

Introduction

Image super-resolution refers to the process of using low-resolution observed images or multiple image sets to reconstruct high-resolution images with rich detailed features.¹ The super-resolution algorithm improves image visual quality by restoring hidden details and detailed structural features in low-resolution images. In the field of textiles, from the perspective of maintaining the continuity and integrity of fabric graphic patterns, the analysis of fabric structure is a very important part of the textile industry production process, and is the premise of counterfeiting or innovative textile products. Therefore, the research on image super-resolution technology is important to the analysis of low-resolution fabric image texture structures. It also has a wide range of applications in many other fields, such as digital high definition (HD), medical imaging, satellite image analysis, and security detection,^2,3 where the super-resolution technology is beneficial to improve the performance of pattern recognition. The high resolution image reconstructed by the super-resolution technology has higher pixel density and richer detail information content, which improves the accuracy of multi-target recognition and judgment in real-life applications.

Generally, we divide existing super-resolution methods into two broad categories: the interpolation-based methods and the learning-based methods.⁴ The interpolation-based methods can be further divided into the polynomial interpolation algorithms and the algorithms that use image edge steering for interpolation.⁵ The polynomial interpolation algorithms belong to traditional algorithms with the properties of simple and fast including the nearest neighbor interpolation, the bilinear interpolation, and the bicubic interpolation.⁶ However, their reconstruction effect of high-frequency detail information is very poor because they only consider pixel and motion information. It tends to generate image blurring edges, ringing, and silver-toothed artifacts in the reconstructed high-resolution image. Sun et al.^7,8 successfully preserved the boundary information in the super-resolution image restoration process by exploring the gradient contour prior to the local image structure. This kind of interpolation algorithm with prior information of the natural image could better preserve the structural features of the input observation image, but it is still limited to estimating the unknown pixels in the high-resolution grid using known neighborhoods.^9,10 Recently, the edge oriented interpolation methods have been proposed to make up for the shortcomings of traditional interpolation algorithms. Although these methods can preserve the edge structure of the image, they often produce speckle noise or distort the image around the texture regions.

The learning-based super-resolution methods mainly rely on the mapping relationship between the low-resolution image blocks and the high-resolution image blocks in the training set to predict the lost high frequency detail information in the test low-resolution image,¹¹ so as to realize the super-resolution task. In 2002, Freeman et al.¹² first proposed a single image super-resolution method, namely an instance-based method, which predicts degraded visual information in low-resolution images by learning from the training dataset. The algorithm can recover the high-frequency information of most images with a larger training dataset. However, the algorithm has low computational efficiency and poor anti-interference ability. In 2004, Chang et al.¹³ introduced the local linear embedding method and proposed a neighborhood embedding image super-resolution reconstruction algorithm. This algorithm takes a smaller training dataset to represent more image block patterns with low computation and high speed. However, it often leads to overfitting or underfitting and image blurring because the value of the nearest neighbor block is fixed. Yang et al.¹⁴ proposed a super-resolution reconstruction method based on sparse signal representation. By jointly training the high- and low-resolution image block dictionaries, the similarity of real dictionary sparse representations between high- and low-resolution image blocks is enhanced to reconstruct the target high-resolution image.^15–17 These methods can fully retain the prior knowledge and reduce the dimension during the training process to improve the computational efficiency. Nevertheless, all of them need an extra and well-constructed image data set to learn the mapping.

Generally, it is difficult to obtain multiple low- and high-resolution images of the same scene simultaneously because of the limitations of complex environments and hardware conditions. At this point, super-resolution technology of multiple images learning encountered a development bottleneck, and more scholars pay attention to the single image resolution technology.^18–21 In 2011, Freeman et al. proposed a single image super-resolution framework based on the self-learning theory, which completes the training process only with the feature information of the image itself. This self-learning super-resolution technology improves the image resolution by combining the symbiotic prior information of high- and low-resolution images with high-resolution image blocks containing rich details.^22,23 This technology solves the problem of multiple image acquisition difficulties in the same scene, and has become a research hotspot of image super-resolution technology.

In the self-learning framework, similarity matching plays the key role for boosting the image super-resolution effect.²⁴ However, the existing image blocks similarity measures ignore the two-dimensional structural information and are not robust for some interference. For example, because structural information is corrupted in a super-resolution scene of a textile image with stains, it is difficult for the traditional similarity measure methods of the single image super-resolution framework to accurately find similar low-resolution images of high-resolution images. Thus, this study aims to improve the super-resolution performance of the self-learning framework by introducing a robust image similarity measurement method. Recently, nuclear norm based matrix regression (NMR) analysis has become a popular tool for image recognition, which uses the low-rank to preserve two-dimensional structural information and promote robustness.^25,26 In image recognition, the essence of NMR is to measure the similarity of images by regression coefficients. Therefore, using the NMR to address the robustness and the two-dimension structure lost in the traditional self-learning super-resolution is theoretically feasible.

The motivation of this work is to establish a robust matrix regression model based self-learning super-resolution method that fully considers the two-dimensional structure of the image and ensures the robustness of the method on the premise of realizing super-resolution of a single image. Specifically, we substitute the nuclear norm with a non-convex function for characterizing the low-rank structure of the error image block. Based on this characterization, a robust nuclear norm based matrix regression model is introduced and applied to the self-learning framework to realize similarity matching between image blocks, so as to complete super-resolution reconstruction of a single image. In addition, we adopt the alternating direction method of multipliers (ADMM) to optimize our model. We hope that the jointly obtained components, like members with a team spirit, can create synergy through close interaction, and generate higher performance than traditional similarity measures in achieving single image super-resolution.

The contributions of this work are summarized as follows:

We propose an effective super-resolution method for a single image based on the self-learning framework and the robust matrix regression model, which can be applied in the field of textile image super-resolution.

The proposed method not only can preserve the two-dimensional structural information, but also can enhance the robustness of single image super-resolution.

We construct the fabric data set and carry out a large number of experiments on super- resolution reconstruction to prove the effectiveness of our proposed method. Experimental results show the advantages of our method in robustness and the image super-resolution reconstruction effect.

The rest of the paper is organized as follows. We briefly review the single image self-learning super-resolution framework, detail our proposed method, and provide the experimental results, followed by the conclusion.

Self-Learning Framework for Image Super-Resolution

In general, natural images usually contain a lot of visual repetition in different scales, which is called structural similarity.²⁷ Fig. 1 shows an example of an image with local self-similarity. The image block on the left petal and receptacle root has similarity inside the image rectangle. Although it varies slightly in scale, the image block on the right still shows a high degree of similarity. These features are often used as the prior knowledge to constrain the reconstruction process.^28,29 When the image is sub-pixel shifted, a similar image structure appears near the original image block, which indicates that the similarity between the same scale of the image can be used as the theoretical basis for image multi-frame reconstruction. The similarity between different scales of the image constitutes high- and low-resolution training samples, which improves the effective prior knowledge for the sample-based super-resolution reconstruction method. Therefore, self-learning reconstruction without any external training images not only saves time but also generates better results.

Fig. 1

An illustration of the image self-similarity.

The common singular points that improved resolution have singularity-invariant scaling transformations in natural images. Therefore, we can find related sample patches in a very limited set of patches. For each patch in the image, we can find the similar patches of its smoothed version near the same relative coordinates. The Freeman algorithm a classical one based on image self-similarity, which supplements the low-resolution image of the high-frequency patch. In one study,³⁰ they adopt small scale factors to scale the images, and then load the corresponding high-frequency image into the reconstruction image. The traditional self-learning algorithms usually take the sum of absolute differences (SAD, see Eq. 1) to determine the position of the absolute value difference between the high- and low-resolution images as their similarity matching criterion.

S (u, v) = \sum_{j = 1}^{n} \sum_{i = 1}^{m} | f_{l} (i, j) - f_{h} (i + u, j + v) |

Eq. 1

f_l and f_h represent the gray value of the low-resolution and high-resolution pixels, respectively, and m and n represent the size of the image block. The SAD searches for similar image blocks by matching the minimum gray value of the corresponding pixel points, which ignores the structural characteristics of the entire image. Besides, the method is prone to confusion and inaccurate matching in the condition that the image has more complex textures.

Proposed Method

For boosting the performance of the single image self-learning super-resolution, we introduce an improved similarity measure model with properties of robustness and two-dimensional structure to measure the similarity between image blocks in this section.

Similarity Measure with Matrix Regression

Given a set of n image block matrices D₁,…, D_n, ∈ R^p×q and an image block matrix B_i ∈ R^p×q. For ∀i, j, D_i ≠ D_j when i ≠ j. Our aim is to find the true nearest neighbors of B_i in D. Traditional algorithms accurately calculate each similarity indicator d (B_i, D_i) between B_i and D_i respectively with a variety of defined similarity functions, such as Euclidean distance, Manhattan distance, correlation coefficient, and so forth. Then the nearest neighbors of B_i are obtained by sorting them.

Here, we take full use of the matrix regression model to find the nearest image block of high-resolution image block. Specifically, we represent the image blocks in the form of a matrix and use nuclear norm based matrix regression (NMR, see Eq. 2) to preserve the low-rank structure information of the scaled image and enhance the robustness of the similarity degree of the image blocks.

\min {‖ D x - B_{i} ‖}_{*} + λ ‖ x ‖_{1}

Eq. 2

x = (x₁,…, x_n) represents the linear representation coefficients, which indicate the degree of similarity of the images,³¹ and λ donates the regularization parameter, which governs the relative importance between the regularization term and the reconstruction error term.

We take the ADMM algorithm to solve this regularized matrix regression problem. At this point, the model expressed by Eq. 2 can be rewritten as Eq. 3.

\min ‖ Y ‖_{*} + λ ‖ x ‖_{1} subject to D x - B_{i} = Y

Eq. 3

And the augmented Lagrangian function L_μ is defined by Eq. 4.

\begin{array}{l} L_{μ} (Y, x, Z) = ‖ Y ‖_{*} + \frac{1}{2} λ ‖ x ‖_{1} + Tr (Z^{T} \\ (A (x) - Y - B)) + \frac{μ}{2} ‖ A (x) - Y - B ‖_{2}^{F} \end{array}

Eq. 4

μ > 0 is a penalty parameter, Tr(·) is the trace operator, and Z is the array of Lagrange multipliers.

The ADMM algorithm mainly involves the following iterations (Eqs. 5–7):

(i)

Given Y = Y^k and Z = Z^k updating x by

x^{k + 1} = \arg \min_{x} L_{μ} (Y, x, Z)

Eq. 5

(ii)

Given x = x^k and Z = Z^k updating Y by

Y^{k + 1} = \arg \min_{Y} L_{μ} (Y, x, Z)

Eq. 6

(iii)

Given x = x^k and Y = Y^k updating Z by

Z^{k + 1} = Z^{k} + μ (A (x) - Y - B)

Eq. 7

The algorithm we adopted can be interpreted as a two-step iterative strategy for super-resolution. Updating x is the step used to determine the representation coefficient and representation error, while updating Y is actually an error support step used to determine the actual super-resolution fuzzy part. Therefore, the robust matrix regression based on nuclear norm provides a unified framework for integrating error detection and error support into a simple model.

In short, the NMR treats the query image block as a linear combination of the image blocks in the dictionary and determines the nearest neighbor of the query image block by sorting the minimum reconstruction coefficient. This similarity measure model considers both the two-dimensional structure of the image and the robustness for the interference.

Super-Resolution Algorithm

Assume that X_h represents a high-resolution image and X_l denotes the low-resolution image obtained by the optical quality reduction processing. Then the degradation model can be expressed as Eq. 8.

X_{l} = G E X_{h} + N

Eq. 8

Where G and E denote the down-sampling and blurring operators respectively, and N is the additional noise.

Bevilacqua et al. proposed that it is better to use a small scale scaling factor to iteratively enlarge the high-resolution image, rather than directly magnifying it at once.³² Therefore, we followed this suggestion and took the small scale scaling factor to iteratively enlarge the low-resolution image in the self-learning Freeman framework. We used the nuclear norm based on the matrix regression model to measure the similarity of image patches, which not only improved the super-resolution quality, but also ran faster. Fig. 2 shows the pipeline of our method.

Fig. 2

The pipeline of our method.

Algorithm 1.

Self-learning with robust matrix regression

Input: The low-resolution image, the scalar parameter α and the parameter λ.

Do:

Step 1. Obtain the image I ₁ by enlarging the original image I₀ with the small scale factor α.

Step 2. By using the opposite magnification factor to scale the original image I₀ to generate image I₂, and then enlarge image I₂ to the same size image I₃ as the original image.

Step 3. Calculate the high frequency image I₄, I = I ₀ - I ₃.

Step 4. Overlap the image I₁ into sub-blocks and generate the search window with the entire image I₃.

Step 5. Match the image sub-block by NMR model in the neighborhood of the search window in the entire image I₃.

Step 6. Perform high-frequency synthesis on image I₁.

Step 7. Return to step 4 to update I₂ completely.

Step 8. Return to step 1 until we get the final magnification.

Output: The high-resolution image.

The complete algorithm of self-learning super-resolution with robust matrix regression is detailed in Algorithm 1.

In terms of our model complexity, given the image size n × n and the size of sub block m × m, the computational complexity of Step 4 is O((n - m)²) is determined by the size n and k, which is the number of iterations of our entire method step. The computational complexity of Step 5 is O(k₁n²), which is determined by the matrix multiplication and k₁ (the number of iterations to find the similarity image block (ADMM). So, the entire computational complexity of the Algorithm is O(k₂(k₁n² + (n - m)²)), where k₂ is the number of iterations.

Experiments

In this section, we evaluated the proposed model by several experiments. We first discuss the parameter selection of our model, then demonstrate the super-resolution visual effect in different situations, use objective indicators to evaluate the super-resolution effects of test images in different situations, and finally, we test and compare the efficiency of the proposed algorithm.

To illustrate the effectiveness of the super-resolution algorithm adopted in this study in terms of two-dimensional structure preserving and robustness, we selected the test samples in Fig. 3 as the representative test images. Our experiment mainly showed the super-resolution effect of the images under the influence of illumination and the images with complex texture and complex background. We also selected the natural low-resolution images as the testing images. The bilinear interpolation algorithm and the traditional Freeman algorithm were selected as the comparing methods in our experiment. The magnification was doubled using a combination of small scale factors 3:2 and 4:3. There were no additional high-resolution image data sets in all experiments.

Fig. 3

The test images.

Parameter Selection

In our proposed algorithm, there were two parameters. The significant parameter mainly used in our experiment was the size of the search window in the entire image I₃ and the regularization parameter lambda in the ADMM algorithm of our model. We did a lot of experiments; each experiment only used a single low-resolution image in the test sets.

In our proposed method, there were three parameters: the overrelaxation parameter α value from 1.0 to 1.8, parameter λ value from 0 to 1, and parameter k value from 1 to n (usually we set it as 3). Parameter k was the size of the sub block. A large value of k decreased the precision of the result, while a very small value of k will increase the computation time. Parameter λ is the augmented Lagrangian parameter. Parameter α enlarged the range of computing.

Here, we only provided a guidance for setting them. For many images, parameter α was typically set from 1.0 to 1.8, as a regulator of the result. Parameter λ was the augmented Lagrangian parameter, usually set as 0.01. For most images, k should be properly enlarged to accelerate the process. Next, we set specific values according to the above principles for the different images in the experiment.

Super-Resolution Visual Effects

Here, we mainly evaluate the super-resolution effects of different methods on images in different situations, including images with illumination effect, complex texture, and complex background.

Super-Resolution Effect with Illumination

Our claim is that the robust matrix regression model could boost the performance of the self-learning super-resolution in the presence of some noise, such as illumination. Thus, we firstly evaluated the performance of our proposed method, compared with the bilinear interpolation algorithm and the traditional Freeman algorithm, under the condition of illumination.

In this experiment, we constructed a fabric database and selected fabric images with illumination effects. For fairness, we randomly selected the images and conducted multiple experiments for verification. For the other comparison methods, the solution tools and parameter settings were carried out according to the author's suggestions. We show some effects of image processing with light effects using different super-resolution methods in Fig. 4. Fig. 4a shows the ground truth; Fig. 4b is the super-resolution image obtained by bilinear interpolation, and Figs. 4c and d show the resulting images which were obtained by traditional Freeman algorithm and our method, respectively.

Fig. 4

Super-resolution with illumination.

The super-resolution processing visual effect of the proposed method was the most natural and closest to the normal image among all methods (Fig. 4). In addition, our method can effectively eliminate the interference of bad illumination and maintain the clear texture of the image. These demonstrate the robustness of our method under illumination.

Super-Resolution Effect with Structural Keeping

To verify the performance of our method in super-resolution for two-dimensional structure preserving, we constructed the fabric image database and randomly selected fabric images with complex textures. Figs. 5–7 show the results of super-resolution of selected images.

Fig. 5

Super-resolution with structural preserving 1.

Fig. 6

Super-resolution with structural preserving 2.

Fig. 7

Super-resolution with structural preserving 3.

We can see from Fig. 5d that the letters on the fabric pattern were clearer and the textures outside the letters were relatively distinct. Similarly, we can see from Fig. 6 that, compared with other traditional methods, the vertical texture of the fabric image processed by our method was clearer and the two-dimensional structure of the image was better maintained. From the super-resolution effect of Fig. 7, the reconstruction of the bilinear interpolation image was fuzzy. The Freeman algorithm implementation effect of super-resolution was better than the bilinear interpolation, but the printing structure of the fabric image was not good. In contrast, our method kept the structure of the image better and was closer to the real value. In addition, our method performed well for the dot pattern fabric image as well, and was closer to the ground truth.

Super-Resolution Effect with Complex Background

Here we further evaluated our proposed method on natural images with complex backgrounds. Figs. 8 and 9 show the results of the experiment.

Fig. 8

Super-resolution with complex background 1.

Fig. 9

Super-resolution with complex background 2.

Fig. 8 shows the super-resolution reconstruction of an image with the same foreground and background color. The result of our method was more natural compared to the blurring effect of the bilinear interpolation and the sharpening effect of the traditional Freeman algorithm. In Fig. 9, our proposed method achieved a better overall two-dimensional image effect of super-resolution reconstruction in the case of a complex image background.

Peak Signal-to-Noise Comparison in Super-Resolution

Compared to visual effects, the peak signal-to-noise ratio (PSNR), which directly measures the difference of pixel values, is more commonly used for the quantitative evaluation of super-resolution. The index is calculated between the super-resolution results obtained by different methods and the ground truth. The larger the value, the smaller the distortion.

Assume that the two input images are X and Y respectively, and the calculation formula is given in Eq. 9.

PSNR (X, Y) = 10 \log (\frac{{(2^{n} - 1)}^{2}}{M S E})

Eq. 9

$M S E = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} (X (i, j) - Y (i . j))$ represents the Mean Square Error (MSE) of the super-resolution image X and the real image Y, M and N are the height and width of the image respectively, and n is the number of bits per pixel, which is 8, generally indicating that the gray order of pixels is 256. We used objective evaluation indexes to evaluate six randomly selected images and compared them with bilinear interpolation and Freeman algorithm. The results are shown in Fig. 10. Our algorithm had a better super-resolution effect for images, and had a higher PSNR through average operation, which further shows the effectiveness of our method.

Fig. 10

PSNR of the super-resolution images.

Efficiency Comparison in Super-Resolution

In this study, we randomly selected six pictures from the data set to test our algorithm model, as shown in Table I, where the unit of time is seconds. According to Table I, the efficiency of our algorithm was lower than that of bilinear interpolation and Freeman algorithm, but this did not affect the super-resolution effect of the algorithm model in this work. Compared with the operating efficiency, we preferred to consume a little more time to get a better super-resolution effect.

Table I.

Efficiency Test in Super-Resolution

Image	Bilinear Interpolation	Freeman Algorithm	Our Method
1	0.009	1.386	36.04
2	0.007	1.296	34.56
3	0.007	1.421	35.33
4	0.008	1.579	35.48
5	0.01	1.792	37.651
6	0.007	1.474	34.68
Average	0.008	1.4915	35.6235

These experimental results provided strong evidence for the motivation of this research. That is, the robust matrix regression model can boost the performance of the self-learning super-resolution in visual robust and super-resolution effects. Although our algorithm was not the most efficient compared with other traditional algorithms, it still had a certain efficiency, and the super-resolution reconstruction effect of our method completely made up for the lack of efficiency.

Conclusion

To improve the robustness and accuracy of single image super-resolution, we introduced robust matrix regression as the similarity measure model among image blocks in the self-learning super-resolution framework. The experimental results show that the robust matrix regression model can significantly improve the performance of the super-resolution effect with illumination variation, structure preserving, and complex background. However, the ADMM algorithm we used in robust matrix regression was slow, and we will focus on improving its computational efficiency in future work.

References

Chen

; He

; Qing

; Teng

Single image super-resolution via adaptive transform-based nonlocal self-similarity modeling and learning-based gradient regularization.

IEEE Transactions on Multimedia 2017, 19 (8), 1702–1717.

Park

S. C

.; Park

M. K.

; Kang

M. G.

Super-resolution image reconstruction: a technical overview.

Signal Processing Magazine IEEE 2003, 20 (3), 21–36.

Cruz

; Mehta

; Katkovnik

; Egiazarian

K. O.

Single image super-resolution based on Wiener filter in similarity domain.

IEEE Transactions on Image Processing 2017, 27 (99), 1376–1389.

Wang

; Zhang

; Liang

; Pan

Semi-coupled dictionary learning with applications to image super-resolution and photo-sketch synthesis, 2012 IEEE Conference on Computer Vision and Pattern Recognition, 2012, pp 2216–2223.

; Orchard

M. T.

New edge-directed interpolation.

IEEE Transactions on Image Processing, 2001, pp 1521–1527.

Hou

; Andrews

Cubic splines for image interpolation and digital filtering.

IEEE Transactions on Acoustics, Speech, and Signal Processing 1978, 26 (6), 508–517.

Sun

; Xu

; Shum

H. -Y.

Image super-resolution using gradient profile prior.

IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2008), 24-26 June 2008, Anchorage, AK, USA,

Lai

; Chen

; Wu

; Wong

W. K.

; Shen

Jointly sparse hashing for image retrieval.

IEEE Transactions on Image Processing 2018, 27 (12), 6147–6158.

Wen

; Xu

; Tang

; Zhan

; Lai

; Guo

Joint video frame set division and low-rank decomposition for background subtraction.

IEEE Transactions on Circuits and Systems for Video Technology 2014, 24 (12), 2034–2048.

10.

X. -L

.; Wen

; Lai

; Wong

W. K.

; Shen

Binary sparse signal recovery algorithms based on logic observation.

Pattern Recognition 2019, 90, 147–160.

11.

Choi

J. -S

.; Bae

S. -H.

; Kim

Single image super-resolution based on self-examples using context-dependent subpatches, 2015 IEEE International Conference on Image Processing (ICIP), 2015, pp 2835–2839.

12.

Freeman

W. T

.; Jones

T. R.

; Pasztor

E. C.

Applications, Example-based super-resolution.

Computer Graphics & Applications IEEE 2002, 22 (2), 56–65.

13.

Chang

; Yeung

D. -Y.

; Xiong

Super-resolution through neighbor embedding, Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2004.

14.

Yang

; Wright

; Huang

T. S.

; Ma

Image super-resolution via sparse representation.

IEEE Transactions on Image Processing 2010, 19 (11), 2861–2873.

15.

; Lai

; He

; Cheung

Y. -M.

; Liu

Joint sparse principal component analysis.

Pattern Recognition 2017, 61, 524–536.

16.

Lai

; Mo

; Wen

; Shen

; Wong

W. K.

Generalized robust regression for jointly sparse subspace learning.

IEEE Transactions on Circuits and Systems for Video Technology 2018, 29 (3), 756–772.

17.

X. -L

.; Wen

; Wong

W. K.

; Tong

; Cui

On uniqueness of sparse signal recovery.

Signal Processing: The Official Publication of the European Association for Signal Processing (EURASIP) 2018, 150, 66–74.

18.

Ren

; He

; Teng

; Wu

; Nguyen

T. Q.

Single image super-resolution using local geometric duality and non-local similarity.

IEEE Transactions on Image Processing 2016, 25 (5), 2168–2183.

19.

Fang

; Xu

; Li

; Lai

; Wong

W. K.

Robust semi-supervised subspace clustering via non-negative low-rank representation.

IEEE Transactions on Cybernetics 2015, 46 (8), 1828–1838.

20.

Zhang

; Zhang

; Dai

CCR: Clustering and collaborative representation for fast single image super-resolution.

IEEE Transactions on Multimedia 2015, 18 (3), 405–417.

21.

Jiang

; Ma

; Chen

; Lu

; Wang

; Ma

Single image super-resolution via locally regularized anchored neighborhood regression and nonlocal means.

IEEE Transactions on Multimedia 2016, 19 (1), 15–26.

22.

; Wong

W. K.

; Lai

; Li

Robust flexible preserving embedding.

IEEE Transactions on Cybernetics 2019, (99), 1–13.

23.

; Lai

; Li

; Wong

W. K.

; Yuan

; Zhang

Low-rank 2-D neighborhood preserving projection for enhanced robust image representation.

IEEE Transactions on Cybernetics 2018, 49 (5), 1859–1872.

24.

Zhao

; Wang

; Zuo

; Shen

; Shao

; Miao

Similarity learning with joint transfer constraints for person re-identification.

Pattern Recognition 2020, 97, 107014.

25.

Yang

; Luo

; Qian

; Tai

; Zhang

; Xu

Nuclear norm based matrix regression with applications to face recognition with occlusion and illumination changes.

IEEE Transactions on Pattern Analysis & Machine Intelligence 2016, 39 (1), 156–171.

26.

; Lai

; Xu

; Li

; Zhang

; Yuan

Low-rank preserving projections.

IEEE Transactions on Cybernetics 2015, 46 (8), 1900–1913.

27.

Fang

; Teng

; Lai

; He

; Xie

; Wong

W. K.

Robust latent subspace learning for image classification.

IEEE Transactions on Neural Networks & Learning Systems 2017, 29 (6), 2502–2515.

28.

Lai

; Mo

; Wong

W. K.

; Xu

; Miao

; Zhang

Robust discriminant regression for feature extraction.

IEEE Transactions on Cybernetics 2017, 48 (8), 2472–2484.

29.

Fang

; Xu

; Li

; Lai

; Wong

W. K.

; Fang

Regularized label relaxation linear regression.

IEEE Transactions on Neural Networks & Learning Systems 2018, 29 (4), 1006–1018.

30.

Osorio

; Carlos

Image and video upscaling from local self-examples.

Computing Reviews 2012, 53 (12), 764.

31.

Zhang

; Yang

Linear reconstruction measure steered nearest neighbor classification framework.

Pattern Recognition 2014, 47 (4), 1709–1720.

32.

Bevilacqua

; Roumy

; Guillemot

; Morel

M.-L. A.

Single-image super-resolution via linear mapping of interpolated self-examples.

IEEE Transactions on Image Processing 2014, 23 (12), 5334–5347.

Single Image Self-Learning Super-Resolution with Robust Matrix Regression

Abstract

Abstract

Keywords

Introduction

Self-Learning Framework for Image Super-Resolution

Proposed Method

Similarity Measure with Matrix Regression

Super-Resolution Algorithm

Experiments

Parameter Selection

Super-Resolution Visual Effects

Super-Resolution Effect with Illumination

Super-Resolution Effect with Structural Keeping

Super-Resolution Effect with Complex Background

Peak Signal-to-Noise Comparison in Super-Resolution

Efficiency Comparison in Super-Resolution

Conclusion

References