Showing papers on "Phase correlation published in 2016"

Off-the-Grid Recovery of Piecewise Constant Images from Few Fourier Samples

Abstract: We introduce a method to recover a continuous domain representation of a piecewise constant two-dimensional image from few low-pass Fourier samples. Assuming the edge set of the image is localized to the zero set of a trigonometric polynomial, we show that the Fourier coefficients of the partial derivatives of the image satisfy a linear annihilation relation. We present necessary and sufficient conditions for unique recovery of the image from finite low-pass Fourier samples using the annihilation relation. We also propose a practical two-stage recovery algorithm that is robust to model-mismatch and noise. In the first stage we estimate a continuous domain representation of the edge set of the image. In the second stage we perform an extrapolation in Fourier domain by a least squares two-dimensional linear prediction, which recovers the exact Fourier coefficients of the underlying image. We demonstrate our algorithm on the superresolution recovery of MRI phantoms and real MRI data from low-pass Fourier sam...

Fast large scale structure perturbation theory using one-dimensional fast Fourier transforms

Abstract: Author(s): Schmittfull, M; Vlah, Z; McDonald, P | Abstract: The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small density fluctuations, usually written in terms of convolutions in Fourier space, can be written as a series of products of these fields evaluated at the same location in configuration space. Based on this, we establish a new method to numerically evaluate the 1-loop power spectrum (i.e.; Fourier transform of the 2-point correlation function) with one-dimensional fast Fourier transforms. This is exact and a few orders of magnitude faster than previously used numerical approaches. Numerical results of the new method are in excellent agreement with the standard quadrature integration method. This fast model evaluation can in principle be extended to higher loop order where existing codes become painfully slow. Our approach follows by writing higher order corrections to the 2-point correlation function as, e.g.; the correlation between two second-order fields or the correlation between a linear and a third-order field. These are then decomposed into products of correlations of linear fields and derivatives of linear fields. The method can also be viewed as evaluating three-dimensional Fourier space convolutions using products in configuration space, which may also be useful in other contexts where similar integrals appear.

Phase preserving Fourier descriptor for shape-based image retrieval

Abstract: Shape is one of the most important discriminative elements for the content based image retrieval and the most challenging for quantification and description. Fourier descriptors are a very efficient shape description method used in shape-based image retrieval tasks. In order to achieve invariance under rotation and starting point change, most Fourier descriptor implementations disregard the phase of Fourier coefficients, consequently losing valuable information about the shape. This paper proposes a novel method of extracting Fourier descriptors that preserve the phase of Fourier coefficients. We introduce specific points, called pseudomirror points, and use them as a shape orientation reference. They facilitate the extraction of phase-preserving Fourier descriptors which are invariant under translation, scaling, rotation and starting point change. The proposed descriptor was tested on four popular benchmarking datasets: MPEG7 CE-1 Set B, Swedish leaf, ETH-80 and Kimia99 datasets. Performance and computational complexity measures indicate that the proposed method outperforms other state-of-the-art phase-based Fourier descriptors. In addition, it outperforms other state-of-the-art magnitude-based Fourier descriptors, and many non-Fourier based shape description methods in terms of performance - complexity ratio. HighlightsMagnitude-based Fourier descriptors discard information contained in phase.Invariant phase-preserving Fourier descriptor is proposed.Pseudomirror points are introduced, and used as shape orientation references.The proposed descriptor is compact, effective and simple to extract and compare.Retrieval performance is improved without increasing computational complexity.

A Non-iterative Method for (Re)Construction of Phase from STFT Magnitude

Abstract: A non-iterative method for the construction of the Short-Time Fourier Transform (STFT) phase from the magnitude is presented. The method is based on the direct relationship between the partial derivatives of the phase and the logarithm of the magnitude of the un-sampled STFT with respect to the Gaussian window. Although the theory holds in the continuous setting only, the experiments show that the algorithm performs well even in the discretized setting (Discrete Gabor transform) with low redundancy using the sampled Gaussian window, the truncated Gaussian window and even other compactly supported windows like the Hann window. Due to the non-iterative nature, the algorithm is very fast and it is suitable for long audio signals. Moreover, solutions of iterative phase reconstruction algorithms can be improved considerably by initializing them with the phase estimate provided by the present algorithm. We present an extensive comparison with the state-of-the-art algorithms in a reproducible manner.

Hierarchical and Adaptive Phase Correlation for Precise Disparity Estimation of UAV Images

Abstract: When using fixed-window phase correlation (PC) to estimate the disparity of stereo images, the precision is usually rather poor due to large depth differences of scenes and noise, and this problem is specially severe when using unmanned aerial vehicle (UAV) image pairs to extract the digital elevation model of mountain land. To tackle this problem, this paper proposes a hierarchical and adaptive PC, which includes three steps: First, PC with the initialized window is performed to coarsely estimate a disparity value, along with the peak of the Dirichlet function for each pixel; then, an additional round of PC is performed for each pixel using the window of smaller size and with being guided by the coarsely estimated disparity; finally, the previous two steps are iteratively performed until convergence. In particular, using the peak of the Dirichlet function of each pixel in step two, we can drop out the influence of dramatically changing areas such as river; moreover, the scheme can minimize the influence of boundary overreach. The novel scheme has been tested on a large number of UAV images captured at mountainous regions in southwest China, showing that the proposed method is superior to the state-of-the-art methods, especially in handling UAV images of the high mountains and rivers.

Registration of retinal sequences from new video-ophthalmoscopic camera

Abstract: Analysis of fast temporal changes on retinas has become an important part of diagnostic video-ophthalmology. It enables investigation of the hemodynamic processes in retinal tissue, e.g. blood-vessel diameter changes as a result of blood-pressure variation, spontaneous venous pulsation influenced by intracranial-intraocular pressure difference, blood-volume changes as a result of changes in light reflection from retinal tissue, and blood flow using laser speckle contrast imaging. For such applications, image registration of the recorded sequence must be performed. Here we use a new non-mydriatic video-ophthalmoscope for simple and fast acquisition of low SNR retinal sequences. We introduce a novel, two-step approach for fast image registration. The phase correlation in the first stage removes large eye movements. Lucas-Kanade tracking in the second stage removes small eye movements. We propose robust adaptive selection of the tracking points, which is the most important part of tracking-based approaches. We also describe a method for quantitative evaluation of the registration results, based on vascular tree intensity profiles. The achieved registration error evaluated on 23 sequences (5840 frames) is 0.78 ± 0.67 pixels inside the optic disc and 1.39 ± 0.63 pixels outside the optic disc. We compared the results with the commonly used approaches based on Lucas-Kanade tracking and scale-invariant feature transform, which achieved worse results. The proposed method can efficiently correct particular frames of retinal sequences for shift and rotation. The registration results for each frame (shift in X and Y direction and eye rotation) can also be used for eye-movement evaluation during single-spot fixation tasks.

Area-efficient scaling-free DFT/FFT design using stochastic computing

Abstract: Among various discrete transforms, discrete Fourier transformation (DFT) is the most important technique that performs Fourier analysis in various practical applications, such as digital signal processing, wireless communications, to name a few. Due to its ultra-high computing complexity as O(N2), in practice the N-point DFT is usually performed in the form of fast Fourier transformation (FFT) with complexity as O(NlogN). Despite this significant reduction in computing complexity, the hardware cost of the multiplication-intensive N-point FFT is still very prohibitive; especially for many large-scale applications that requires large N.

Estimation of glacier surface motion by robust phase correlation and point like features of SAR intensity images

Abstract: For monitoring of glacier surface motion in pole and alpine areas, radar remote sensing is becoming a popular technology accounting for its specific advantages of being independent of weather conditions and sunlight. In this paper we propose a method for glacier surface motion monitoring using phase correlation (PC) based on point-like features (PLF). We carry out experiments using repeat-pass TerraSAR X-band (TSX) and Sentinel-1 C-band (S1C) intensity images of the Taku glacier in Juneau icefield located in southeast Alaska. The intensity imagery is first filtered by an improved adaptive refined Lee filter while the effect of topographic reliefs is removed via SRTM-X DEM. Then, a robust phase correlation algorithm based on singular value decomposition (SVD) and an improved random sample consensus (RANSAC) algorithm is applied to sequential PLF pairs generated by correlation using a 2D sinc function template. The approaches for glacier monitoring are validated by both simulated SAR data and real SAR data from two satellites. The results obtained from these three test datasets confirm the superiority of the proposed approach compared to standard correlation-like methods. By the use of the proposed adaptive refined Lee filter, we achieve a good balance between the suppression of noise and the preservation of local image textures. The presented phase correlation algorithm shows the accuracy of better than 0.25 pixels, when conducting matching tests using simulated SAR intensity images with strong noise. Quantitative 3D motions and velocities of the investigated Taku glacier during a repeat-pass period are obtained, which allows a comprehensive and reliable analysis for the investigation of large-scale glacier surface dynamics.

Neural network calibration of a snapshot birefringent Fourier transform spectrometer with periodic phase errors

Abstract: Systematic phase errors in Fourier transform spectroscopy can severely degrade the calculated spectra. Compensation of these errors is typically accomplished using post-processing techniques, such as Fourier deconvolution, linear unmixing, or iterative solvers. This results in increased computational complexity when reconstructing and calibrating many parallel interference patterns. In this paper, we describe a new method of calibrating a Fourier transform spectrometer based on the use of artificial neural networks (ANNs). In this way, it is demonstrated that a simpler and more straightforward reconstruction process can be achieved at the cost of additional calibration equipment. To this end, we provide a theoretical model for general systematic phase errors in a polarization birefringent interferometer. This is followed by a discussion of our experimental setup and a demonstration of our technique, as applied to data with and without phase error. The technique's utility is then supported by comparison to alternative reconstruction techniques using fast Fourier transforms (FFTs) and linear unmixing.

A Registration Scheme for Multispectral Systems Using Phase Correlation and Scale Invariant Feature Matching

Abstract: In the past few years, many multispectral systems which consist of several identical monochrome cameras equipped with different bandpass filters have been developed. However, due to the significant difference in the intensity between different band images, image registration becomes very difficult. Considering the common structural characteristic of the multispectral systems, this paper proposes an effective method for registering different band images. First we use the phase correlation method to calculate the parameters of a coarse-offset relationship between different band images. Then we use the scale invariant feature transform (SIFT) to detect the feature points. For every feature point in a reference image, we can use the coarse-offset parameters to predict the location of its matching point. We only need to compare the feature point in the reference image with the several near feature points from the predicted location instead of the feature points all over the input image. Our experiments show that this method does not only avoid false matches and increase correct matches, but also solve the matching problem between an infrared band image and a visible band image in cases lacking man-made objects.

Frequency-Domain Imaging Algorithm for Single-Input–Multiple-Output Array

Abstract: In this letter, a novel frequency-domain imaging method is proposed for a single-input–multiple-output array, which avoids the frequency-domain interpolation. This method transforms the measurements into the wavenumber domain for compensation. The spectrum data at each frequency are proved to be the Fourier transform of the phase-modulated reflectivity function; therefore, a subimage at a specific frequency can be produced by inverse fast Fourier transform and phase demodulation. The final image is obtained by coherent accumulation of all subimages. This method does not take the plane wave approximation and can be applied in short-range imaging scenes. It has the same imaging accuracy as the backprojection algorithm but greatly reduces the computational load. Both two- and three-dimensional imaging experiments verify its performance.

Image deblurring by sparsity constraint on the Fourier coefficients

Abstract: This paper is concerned with the image deconvolution problem. For the basic model, where the convolution matrix can be diagonalized by discrete Fourier transform, the Tikhonov regularization method is computationally attractive since the associated linear system can be easily solved by fast Fourier transforms. On the other hand, the provided solutions are usually oversmoothed and other regularization terms are often employed to improve the quality of the restoration. Of course, this weighs down on the computational cost of the regularization method. Starting from the fact that images have sparse representations in the Fourier and wavelet domains, many deconvolution methods have been recently proposed with the aim of minimizing the l1-norm of these transformed coefficients. This paper uses the iteratively reweighted least squares strategy to introduce a diagonal weighting matrix in the Fourier domain. The resulting linear system is diagonal and hence the regularization parameter can be easily estimated, for instance by the generalized cross validation. The method benefits from a proper initial approximation that can be the observed image or the Tikhonov approximation. Therefore, embedding this method in an outer iteration may yield further improvement of the solution. Finally, since some properties of the observed image, like continuity or sparsity, are obviously changed when working in the Fourier domain, we introduce a filtering factor which keeps unchanged the large singular values and preserves the jumps in the Fourier coefficients related to the low frequencies. Numerical examples are given in order to show the effectiveness of the proposed method.

On convexity and identifiability in 1-D Fourier phase retrieval

Abstract: This paper considers phase retrieval from the magnitude of 1-D oversampled Fourier measurements. We first revisit the well-known lack of identifiability in this case, and point out that there always exists a solution that is minimum phase, even though the desired signal is not. Next, we explain how the least-squares formulation of this problem can be optimally solved via PhaseLift followed by spectral factorization, and this solution is always minimum phase. A simple approach is then proposed to circumvent non-identifiability: adding an impulse to an arbitrary complex signal (offset to the Fourier transform) before taking the quadratic measurements, so that a minimum phase signal is constructed and thus can be uniquely estimated. Simulations with synthetic data show the effectiveness of the proposed method.

Robust Multi-Source Image Registration for Optical Satellite Based on Phase Information

Abstract: Robust image registration is a vital challenging task, especially for multi-source satellite images that may have significant different illumination. A coarse-to-fine registration algorithm based on phase information is proposed. The coarse registration is implemented using Fourier-polar transform and phase correction based on phase congruency. The fine registration is first implemented by dividing large images into blocks. Then, the uniformly distributed corners and Principal Phase Congruency ( ppc ) images are extracted. After that, the corresponding points of extracted corners are obtained based on Phase Correlation of Principal Phase Congruency ( pcppc ), followed by a new outlier removal method. Experiment results revealed the robustness, accuracy, and distribution quality less than 1.0 of the proposed algorithm. The matching correct rate is about 94.7 percent for Data Set 2 due to considerable topography variations, and more than 96.6 percent for data set 4 despite significant different or inverse intensity, which can reach 100 percent with our outlier removal method.

Phase retrieval from multiple-window short-time Fourier measurements

Abstract: In this paper, we introduce two symmetric directed graphs depending on supports of signals and windows, and we show that the connectivity of those graphs provides either necessary and sufficient conditions to phase retrieval of a signal from magnitude measurements of its multiple-window short-time Fourier transform. Also we propose an algebraic reconstruction algorithm, and provide an error estimate to our algorithm when magnitude measurements are corrupted by deterministic/random noises.

A novel sub-pixel matching algorithm based on phase correlation using peak calculation

Abstract: . The matching accuracy of homonymy points of stereo images is a key point in the development of photogrammetry, which influences the geometrical accuracy of the image products. This paper presents a novel sub-pixel matching method phase correlation using peak calculation to improve the matching accuracy. The peak theoretic centre that means to sub-pixel deviation can be acquired by Peak Calculation (PC) according to inherent geometrical relationship, which is generated by inverse normalized cross-power spectrum, and the mismatching points are rejected by two strategies: window constraint, which is designed by matching window and geometric constraint, and correlation coefficient, which is effective for satellite images used for mismatching points removing. After above, a lot of high-precise homonymy points can be left. Lastly, three experiments are taken to verify the accuracy and efficiency of the presented method. Excellent results show that the presented method is better than traditional phase correlation matching methods based on surface fitting in these aspects of accuracy and efficiency, and the accuracy of the proposed phase correlation matching algorithm can reach 0.1 pixel with a higher calculation efficiency.

Fourier bases and Fourier frames on self-affine measures

Abstract: This paper gives a review of the recent progress in the study of Fourier bases and Fourier frames on self-affine measures. In particular, we emphasize the new matrix analysis approach for checking the completeness of a mutually orthogonal set. This method helps us settle down a long-standing conjecture that Hadamard triples generates self-affine spectral measures. It also gives us non-trivial examples of fractal measures with Fourier frames. Furthermore, a new avenue is open to investigate whether the Middle Third Cantor measure admits Fourier frames.

Enhanced phase correlation for image registration

Abstract: An image registration system and method for matching images having fundamentally different characteristics. One exemplary feature of the system and method includes the use of an enhanced phase correlation method combined with a coarse sensor model to hypothesize and match a custom match metric to determine a best solution. The system and method may be operated on a non-transitory computer-readable medium storing a plurality of instructions which when executed by one or more processors causes the one or more processors to perform the image registration method utilizing the enhanced phase correlation.

Side-scan sonar image registration based on modified phase correlation for AUV navigation

Abstract: In this paper, we propose a novel approach for SSS registration based on modified phase correlation, which is capable of handling low resolution and noise. The modified phase correlation combines threshold segmentation with phase correlation to carry out side-scan sonar (SSS) image registration. Image registration aims to transform images obtained from different views to the same coordinate. Underwater environment has poor visibility and the registration for optical underwater images faces various challenges. The registration method for SSS image is different from that for optical image. Region-based registration is more robust than feature-based registration for side-scan image because there are featureless areas in underwater environment and region-based registration can handle this. When an autonomous underwater vehicle (AUV) equipped with the SSS is navigating an unknown underwater environment, the ability to realize the registration between the current sonar image and the previous ones accurately and fast does matter. When compared to a state-of-art region-based and feature-based technique, our approach shows superior performance in accuracy and time-consuming.

Nanoparticle flow velocimetry with image phase correlation for confocal laser scanning microscopy

Abstract: We present a new particle image correlation technique for resolving nanoparticle flow velocity using confocal laser scanning microscopy (CLSM). The two primary issues that complicate nanoparticle scanning laser image correlation (SLIC)–based velocimetry are (1) the use of diffusion-dominated nanoparticles as flow tracers, which introduce a random decorrelating error into the velocity estimate, and (2) the effects of the scanning laser image acquisition, which introduces a bias error. To date, no study has quantified these errors or demonstrated a means to deal with them in SLIC velocimetry. In this work, we build upon the robust phase correlation (RPC) and existing methods of SLIC to quantify and mitigate these errors. First, we implement an ensemble RPC instead of using an ensemble standard cross-correlation, and develop a SLIC optimal filter that maximizes the correlation strength in order to reliably and accurately detect the correlation peak representing the most probable average displacement of the nanoparticles. Secondly, we developed an analytical model of the SLIC measurement bias error due to image scanning of diffusion-dominated tracer particles. We show that the bias error depends only on the ratio of the mean velocity of the tracer particles to that of the laser scanner and we use this model to correct the induced errors. We validated our technique using synthetic images and experimentally obtained SLIC images of nanoparticle flow through a micro-channel. Our technique reduced the error by up to a factor of ten compared to other SLIC algorithms for the images tested in this study. Moreover, our optimized RPC filter reduces the number of image pairs required for the convergence of the ensemble correlation by two orders of magnitude compared to the standard cross correlation. This feature has broader implications to ensemble correlation methods and should be further explored in depth in the future.

UAV image registration algorithm based on overlapping region detrction

Abstract: UAV image registration is a key in the process of UAV image matching and application. Based on a large number of images, overlapping irregular and lack of ground control point, paper put forward the image registration algorithm based on overlapping area detection. Firstly the algorithm uses the improved distributed search method based on phase correlation method to search overlapping area and get the translation and rotation parameters of the original image, which is very effective for rotating image. Then a new angular point matching method combined with the offset and rotation angle is used, which is based on Harris. The experimental results show that the method can be applied to UAV remote sensing image registration properly, and has the characteristics of efficiency, accuracy and robustness.

Hartley transform based correlation filters for face recognition

Abstract: This paper explores the viability of Hartley Transforms as an alternative to Fourier Transforms for Face Recognition. The paper provides a brief introduction to Hartley Transform, which is a reasonable alternate to Fourier Transform due to its similarities in the choice of basis function. Correlation filter is a pattern recognition tool that is efficient and robust. This includes extraction of features from the face images and development of various discriminant functions in the form of correlation planes. The correlation filters produce a sharp peak if an image similar to the trained image is present. The decision is based on the peak to side lobe ratio of the correlation plane. Results obtained from various classes of correlation filter indicate that Hartley Transform is a reasonable alternative to Fourier Transform.

Statistical power of intensity- and feature-based similarity measures for registration of multimodal remote sensing images

Abstract: This paper investigates performance characteristics of similarity measures (SM) used in image registration domain to discriminate between aligned and not-aligned reference and template image (RI and TI) fragments. The study emphasizes registration of multimodal remote sensing images including optical-to-radar, optical-to-DEM, and radar-to- DEM scenarios. We compare well-known area-based SMs such as Mutual Information, Normalized Correlation Coefficient, Phase Correlation, and feature-based SM using SIFT and SIFT-OCT descriptors. In addition, a new SM called logLR based on log-likelihood ratio test and parametric modeling of a pair of RI and TI fragments by the Fractional Brownian Motion model is proposed. While this new measure is restricted to linear intensity change between RI and TI (assumption somewhat restrictive for multimodal registration), it takes explicitly into account noise properties of RI and TI and multivariate mutual distribution of RI and TI pixels. Unlike other SMs, distribution of logLR measure for the null hypothesis does not depend on registration scenario or fragments size and follows closely chi-squared distribution according to Wilks’s theorem. We demonstrate that a SM utility for image registration purpose can be naturally represented in (True Positive Rate, Positive Likelihood Rate) coordinates. Experiments on real images show that overall the logLR SM outperforms the other SMs in terms of area under the ROC curve, denoted AUC. It also provides the highest Positive Likelihood Rate for True Positive Rate values below 0.4-0.6. But for certain registration problem types, logLR can be second or third best after MI or SIFT SMs.

Image mosaicing using phase correlation and feature based approach: a review

Abstract: Mosaicing is a computer-vision-based approach to attain high field of view without compromising the image quality. Image Mosaicing technique enables to combine together many small images into a single large image, which represents more information. In this paper, images with overlapping regions are mosaiced using the phase correlation and feature based approaches. Phase correlation involves featureless registration, followed by mosaicing of images, and blending of image mosaic in order to reduce seams that may arise due to different environmental conditions such as lighting, camera focusing etc. In the efficient feature based approach involves in taking scale invariant features (using SIFT) in both the images. Later to find by using the perfectly matched corner pairs, homography is done to do mosaicing. A weighted average blending algorithm is used to seamlessly blend the two images.

An Improved Super-resolution Image Reconstruction Algorithm

Abstract: The paper introduces the Keren registration method and points out its disadvantage which means it will become inaccuracy on the large scale parameters. To reduce the error on large scale parameters of Keren registration, a two step method is proposed, which the phase correlation algorithm is used to estimate the large translation and rotation angle roughly and the improved Keren algorithm is used to estimate accurately the small translation and rotation angle. The experimental results show that the two step method makes less absolute error of angle than Keren method in the situation of large translation and rotation angle. A new method of estimating the standard deviation of noise is introduced to the robust certainty function, which reduces the impact of noise in the process of interpolation using normalized convolution algorithm. By the edge detection of fusion image in the first stage of the interpolation process of normalized convolution algorithm, a calculation method of long axis and short axis of the structure self-adaptive function is improved. The experimental results show that the proposed interpolation method can improve the performance of the original algorithm and enhance the effect of image super-resolution reconstruction.

Precise and fast spatial-frequency analysis using the iterative local Fourier transform.

Abstract: The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method’s superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.

Phase correlation based acquisition method and system for self-learning super-resolution image

Abstract: The present invention discloses a phase correlation based acquisition method and system for a self-learning super-resolution image. The method comprises: acquiring a first low-frequency image, only comprising original image low-frequency information, of a low-resolution image, and acquiring a first high-frequency image only comprising original image high-frequency information according to the first low-frequency image; acquiring an amplified second low-frequency image after performing interpolation amplification calculation on the low-resolution image; matching positions of the second low-frequency image and the first low-frequency image; and filling a corresponding position of the matched second low-frequency image with the first high-frequency image to generate a final super-resolution image. According to the acquisition method and system, the matching between image blocks in a self-learning process can be completed quickly and accurately without the need for search, the computational complexity is reduced, the reconstruction speed of the super-resolution image is increased, and the clear super-resolution image can be obtained.