Single-Image Super-Resolution Based on Rational Fractal Interpolation.

Recent deep learning approaches in single image super-resolution (SISR) can generate high-definition textures for super-resolved (SR) images. However, they tend to hallucinate fake textures and even produce artifacts. An alternative to SISR, reference-based SR (RefSR) approaches use high-resolution (HR) reference (Ref) images to provide HR details that are missing in the low-resolution (LR) input image. We propose a novel framework that leverages existing SISR approaches and enhances them with RefSR. Specifically, we refine the output of SISR methods using neural texture transfer, where HR features are queried from the Ref images. The query is conducted by computing the similarity of textural and semantic features between the input image and the Ref images. The most similar HR features, patch-wise, to the LR image is used to augment the SR image through an augmentation network. In the case of dissimilar Ref images from the LR input image, we prevent performance degradation by including the similarity scores in the input features of the network. Furthermore, we use random texture patches during the training to condition our augmentation network to not always trust the queried texture features. Different from past RefSR approaches, our method can use arbitrary Ref images and its lower-bound performance is based on the SR image. We showcase that our method drastically improves the performance of the base SISR approach.

Fractal interpolation functions that share smoothness or nonsmoothness property of the prescribed interpolation data provide a novel method of interpolation. The present paper proposes a new type of rational cubic spline fractal interpolation function which involves two families of free shape parameters and which does not require derivatives at knots for its construction. The scaling factors inherent with the structure facilitate the proposed rational fractal interpolation function to recapture a classical rational cubic spline studied earlier in the literature as a special case. In addition, the scaling factors are the key ingredients that provide fractality to the derivative of the constructed interpolant. Thus, in contrast to the classical nonrecursive rational splines, the proposed rational cubic fractal spline can produce interpolants whose derivatives have irregularity in finite or dense subsets of the interpolation intervals depending on the nature of the problem. Assuming that the original data defining function belongs to the smooth class \(\fancyscript{C}^2\), an upper bound for the interpolation error with respect to the \(L_\infty \)-norm is obtained and the uniform convergence of the rational cubic fractal interpolant is deduced. The developed rational fractal interpolation scheme is illustrated with numerical examples and some possible extensions are exposed.KeywordsFractal SplineFractal Interpolation Functions (FIF)Rational SplineFree Shape ParametersIterated Function Systems (IFS)These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

MSAR-Net: Multi-scale attention based light-weight image super-resolution

Resolution enhancement (RE) schemes (which are not based on wavelets) suffer from the drawback of losing high-frequency contents (which results in blurring). The discrete-wavelet-transform-based (DWT) RE scheme generates artifacts (due to a DWT shift-variant property). A wavelet-domain approach based on dual-tree complex wavelet transform (DT-CWT) and nonlocal means (NLM) is proposed for RE of the satellite images. A satellite input image is decomposed by DT-CWT (which is nearly shift invariant) to obtain high-frequency subbands. The high-frequency subbands and the low-resolution (LR) input image are interpolated using the Lanczos interpolator. The high-frequency subbands are passed through an NLM filter to cater for the artifacts generated by DT-CWT (despite of its nearly shift invariance). The filtered high-frequency subbands and the LR input image are combined using inverse DT-CWT to obtain a resolution-enhanced image. Objective and subjective analyses reveal superiority of the proposed technique over the conventional and state-of-the-art RE techniques.

Positron Emission Tomography (PET) is a nuclear, in-vivo medical imaging technology which can make 3D images of tissue metabolic act, in which high dose of tracer is needed to obtain a high quality PET image, which affects patients' health. Due to the limitations of using high dose tracer and limitations of physical imaging systems, it is not easy to get an image in desired resolution. Simplest approach to generate a high resolution image is by post processing. Single Image Super Resolution (SISR) is a post processing procedure to retrieve a high resolution image from a low resolution input. We propose a convolutional neural network trained on PET images which can estimate a high resolution PET image from its input low resolution image.

The improvement of the spatial resolution of natural images is an important task for many practical applications of current image processing. The endeavor of applying single image super-resolution, which only uses one low-resolution input image, is frequently hampered by the presence of noise or artifacts in the input image, so denoising and super-resolution algorithms are usually applied to obtain a noiseless high-resolution image. In this work, several traditional and deep learning methods for denoising and super-resolution are hybridized to ascertain which combinations of them yield the best possible quality. The experimental design includes the introduction of Gaussian noise, Poisson noise, salt-and-pepper noise, and uniform noise into the low-resolution inputs. It is found that denoising must be carried out before super-resolution for the best results. Moreover, the obtained results indicate that deep learning techniques clearly outperform the traditional ones.

We present a self-learning approach for single image super-resolution (SR), with the ability to preserve high frequency components such as edges in resulting high resolution (HR) images. Given a low-resolution (LR) input image, we construct its image pyramid and produce a super pixel dataset. By extracting context information from the super-pixels, we propose to deploy context-specific contour let transform on them in order to model the relationship (via support vector regression) between the input patches and their associated directional high-frequency responses. These learned models are applied to predict the SR output with satisfactory quality. Unlike prior learning-based SR methods, our approach advances a self-learning technique and does not require the self similarity of image patches within or across image scales. More importantly, we do not need to collect training LR/HR image data in advance and only require a single LR input image. Empirical results verify the effectiveness of our approach, which quantitatively and qualitatively outperforms existing interpolation or learning-based SR methods.

Single image super resolution based on sparse domain selection

Problem statement: Existing lossless image compression schemes attempt to do prediction in an image data using their Local Binary Pattern ( LBP) and their spatial neighborhood based techniques. In the previous techniques such as Vec tor Quantization (VQ) and Gradient Adjusted Prediction (GAP) the texture and non-texture region s are not classified separately. Texture and Non- texture images prophecy has been a key factor in ef ficient lossless image compression. Hence, there is a need to develop a more efficient image prediction scheme to exploit these texture components. Approach: In this research, an efficient visual quality tech nique for image compression is proposed. The image is classified into texture and non-textur e regions by using an Artificial Neural Network (ANN) Classifier. The texture region is encoded wit h the Similar Block Matching (SBM) encoder and the non-texture region is encoded with SPIHT encoding. Results: The proposed texture prediction based compression is compared with the existing compression techniques such as H.264 and JPEG. From the result it reveals that the Peak Signal to Noise Ratio (PSNR) values of all the test images is higher in the proposed technique as compared to JPE G technique. Similarly PSNR values are low in H.264 for all the images except Boat image when compared to the proposed technique. This result concludes that the increase in PSNR indicates that the output image has less noise as compared to existing techniques. Conclusion: The compression of the proposed algorithm is superi or to JPEG and H.264. Our new method of compression algorithm can be used to improve the performance of Compression ratio and Peak Signal to Noise Ratio (P SNR). In future this study can be extended to real time applications for video compression in medical images.

In this paper, we have propounded a neoteric procedure for the super-resolution of an image using a single image. An image of low resolution is given as input which is upscaled to an image while preserving the information that is stored in textural and structural details of an image. The image provided as input which is of low resolution is segregated into two sections, namely textured and non-textured according to the features of the image. Rational fractal interpolation is employed in the section of the image considered as textured and rational interpolation is employed in the remaining image which is considered to be non-textured. Thereafter, pixel mapping is performed. The result obtained from interpolation is found to contain Gaussian noise. To subdue the effect of this noise, an adaptive Wiener filter is applied. Finally, an image of high resolution is obtained. Profound simulations and assessments demonstrate that competitive performance is achieved by our algorithm. The mean square error reduces approximately up to \(5\%\), whereas the structural similarity index improves marginally.KeywordsSingle-image super-resolutionRational fractal interpolationGaussian noiseWiener filter

Barycentric rational interpolation possesses various advantages in comparision with Thiele-type continued fraction, such as small amount of calculation, good numerical stability, no poles, no unattainable points and arbitrarily high approximation order regardless of the distribution of the points. In this paper, two new bivariate rational interpolation over triangular grids are presented, the first one is bivariate barycentric rational interpolation; the second one is a blending interpolation based on Newton interpolation and barycentric rational interpolation. One numerical example is given to show the effectiveness of the new approach.

Super-resolution (SR) has become more vital, because of its capability to generate high-quality ultra-high definition (UHD) high-resolution (HR) images from low-resolution (LR) input images. Conventional SR methods entail high computational complexity, which makes them difficult to be implemented for up-scaling of full-high-definition input images into UHD-resolution images. Nevertheless, our previous super-interpolation (SI) method showed a good compromise between Peak-Signal-to-Noise Ratio (PSNR) performances and computational complexity. However, since SI only utilizes simple linear mappings, it may fail to precisely reconstruct HR patches with complex texture. In this paper, we present a novel SR method, which inherits the large-to-small patch conversion scheme from SI but uses global regression based on local linear mappings (GLM). Thus, our new SR method is called GLM-SI. In GLM-SI, each LR input patch is divided into 25 overlapped subpatches. Next, based on the local properties of these subpatches, 25 different local linear mappings are applied to the current LR input patch to generate 25 HR patch candidates, which are then regressed into one final HR patch using a global regressor. The local linear mappings are learned cluster-wise in our off-line training phase. The main contribution of this paper is as follows: Previously, linear-mapping-based conventional SR methods, including SI only used one simple yet coarse linear mapping to each patch to reconstruct its HR version. On the contrary, for each LR input patch, our GLM-SI is the first to apply a combination of multiple local linear mappings, where each local linear mapping is found according to local properties of the current LR patch. Therefore, it can better approximate nonlinear LR-to-HR mappings for HR patches with complex texture. Experiment results show that the proposed GLM-SI method outperforms most of the state-of-the-art methods, and shows comparable PSNR performance with much lower computational complexity when compared with a super-resolution method based on convolutional neural nets (SRCNN15). Compared with the previous SI method that is limited with a scale factor of 2, GLM-SI shows superior performance with average 0.79 dB higher in PSNR, and can be used for scale factors of 3 or higher.

Multi-scale selective image texture smoothing via intuitive single clicks

Most of the previous models performed well for Single Image Super-Resolution (SISR). In these methods, the Low Resolution (LR) input image is amplified to the size of High Resolution (HR) through bicubic interpolation. However, bicubic interpolation can not represent the high frequency features of images with only one filter. Therefore, in this paper, we used a original framework which can effectively extract the feature maps from the input image space and transform to HR feature maps based on Spatial Transformer Networks (STN). In our STN-SR method, there are three kinds of parameters should be learned from the model: (i) a serial of filters to extract LR image feature maps; (ii)a local small network to learn parameters of the transformation $\Gamma_{\theta}(G)$ and (iii) the filter parameters to restore the HR patchs from the input HR feature maps through a restoring layer. Our model directly focus on the whole image, the proposed STN-SR method does not clip the image into many small size patches, and can use the image gobal message to rebuild more robust local texture. Compared to privious SR methods, the proposed STN-SR method can gain completely real image, while illustrating better edge and texture preservation performance.

Super-resolution (SR) brings an excellent opportunity to improve a wide range of different remote sensing applications. SR techniques are concerned about increasing the image resolution while providing finer spatial details than those captured by the original acquisition instrument. Therefore, SR techniques are particularly useful to cope with the increasing demand remote sensing imaging applications requiring fine spatial resolution. Even though different machine learning paradigms have been successfully applied in SR, more research is required to improve the SR process without the need of external high-resolution (HR) training examples. This paper proposes a new convolutional generator model to super-resolve low-resolution (LR) remote sensing data from an unsupervised perspective. That is, the proposed generative network is able to initially learn relationships between the LR and HR domains throughout several convolutional, downsampling, batch normalization, and activation layers. Then, the data are symmetrically projected to the target resolution while guaranteeing a reconstruction constraint over the LR input image. An experimental comparison is conducted using 12 different unsupervised SR methods over different test images. Our experiments reveal the potential of the proposed approach to improve the resolution of remote sensing imagery.