scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain condition (isolated lighting or named separated lighting), a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered by the microscope, it is still possible to extract the full information from the low frequency part. Based on the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extract the full information of the sample’s structure directly from the diffraction-blurred image, while the other extract it directly from part of the observed image’s spectrum, e.g., low frequency part. Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Diffraction Limit ◽  
Full Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting super-resolution details directly from a diffraction-blurred image or part of its frequency spectrum

2019 ◽  
Author(s):  
Edward Y Sheffield
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Fourier Spectrum ◽  
Low Frequency ◽  
Super Resolution ◽  
Full Information ◽  
Structure Information ◽  
High Frequency Part ◽  
Blurred Image ◽  
Blurred Images

It is usually believed that the low frequency part of a signal’s Fourier spectrum represent its profile, while the high frequency part represent its details. Conventional light microscopes filter the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain condition (isolated lighting or named separated lighting), a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered by the microscope, it is still possible to extract the full information from the low frequency part. Based on the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extract the full information of the sample’s structure information directly from the diffraction-blurred image, while the other extract it directly from part of the observed image’s spectrum, e.g., low frequency part. Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.

scholarly journals Extracting Super-resolution Structures inside a Single Molecule or Overlapped Molecules from One Blurred Image

2019 ◽  
Author(s):  
Edward Y. Sheffield
Keyword(s):  
Single Molecule ◽  
High Frequency ◽  
Super Resolution ◽  
Region Of Interest ◽  
Diffraction Limit ◽  
Full Information ◽  
Simulation Experiments ◽  
Imaging Condition ◽  
Blurred Image ◽  
Frequency Components

AbstractIn some super-resolution techniques, adjacent points are illuminated at different times. Thereby, their locations and light intensities can be detected even if the images are very blurred due to diffraction. According to conventional theories, the points’ inner details cannot be recovered because the images’ high frequency components are removed due to the diffraction-limit. But this study finds an exception, and full information can be extracted from a diffraction-blurred image. In such a “resolvable condition”, neither profile nor detail information is damaged by diffraction. Thereby, it can be recovered reversibly by solving equation systems in spatial domain or frequency domain. This condition is tightly relevant to the imaging condition of existing super-resolution techniques. Based on the condition, a method is proposed which can achieve unlimited high resolutions in principle, and its effectiveness is demonstrated by both theoretical analysis and simulation experiments. It can also work without any observed image outside the region of interest. Simulation experiments also show its tolerance to certain level of noise.

Non-uniform dependence on initial data for the generalized Degasperis–Procesi equation on the line

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026
Author(s):  
Yanggeng Fu ◽  
Zanping Yu ◽  
Jianhe Shen
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
High Frequency ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Solution Map ◽  
High Frequency Part ◽  
Uniformly Continuous

In this paper, we show that the solution map of the generalized Degasperis–Procesi (gDP) equation is not uniformly continuous in Sobolev spaces [Formula: see text] for [Formula: see text]. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part. It also exploits the fact that the gDP equation conserves a quantity which is equivalent to the [Formula: see text] norm.

Dynamic relation between global Islamic and conventional sectoral stock and bonds indexes

2020 ◽  
Vol 07 (02) ◽  
pp. 2050006
Author(s):  
Sukriye Tuysuz
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Stock Index ◽  
High Frequency Part ◽  
Dynamic Relation ◽  
The Relationship

This paper examines the relationship between 10 Global sectoral conventional and Islamic assets. For each sector, a conventional, an Islamic stock index and a bond are retained. The analyzed relations are done by taking into account diverse investment horizons by using MODWT and GARCH-DCC-type models. Our results indicate that adding bond indexes into a portfolio composed with conventional stock or Islamic stock is efficient. As for the correlations between conventional and Islamic sectoral indexes, they depend on the sector. Relations between returns of securities are quite similar to the relations between high-frequency part of these series and are very volatile at low frequency.

Application with Wavelet Detection to Signal Process of SINS

2012 ◽  
Vol 571 ◽  
pp. 671-675
Author(s):  
Xiang Yuan Huang ◽  
Xia Qing Tang ◽  
Li Bi Guo ◽  
Xu Wei Cheng
Keyword(s):  
High Frequency ◽  
Simulation Experiment ◽  
Detection Method ◽  
Low Frequency ◽  
Frequency Noise ◽  
Wavelet Filter ◽  
Initial Alignment ◽  
Signal Process ◽  
Signal Characteristic ◽  
Alignment Process

Aimed at disturbance caused from motor running and personnel ambulation during initial alignment process of SINS, a new signal detection method of disturbance based on wavelet analysis is brought out. Through analyzing original signal characteristic of FOG and the data with wavelet filter on disturbance base, finds out wavelet filter just have effectiveness to high frequency noise. Then T&L signal detecting law is introduced, and builds T&L signal with high frequency part of wavelet decomposing to estimates interfere time and then resample. Offline simulation experiment results indicate the method can eliminate low frequency disturbance effectively and has certain apply value.

scholarly journals Analysis of the Wavelet Domain Filtering Approach for Video Super-Resolution

2021 ◽  
Vol 11 (4) ◽  
pp. 7477-7482
Author(s):  
M. V. Daithankar ◽  
S. D. Ruikar
Keyword(s):  
High Frequency ◽  
Low Frequency ◽  
Super Resolution ◽  
Visual Quality ◽  
Research Area ◽  
Wavelet Domain ◽  
Edge Information ◽  
Algorithm Efficiency ◽  
Frequency Components ◽  
Processing Techniques

The wavelet domain-centered algorithms for the super-resolution research area give better visual quality and have been explored by different researchers. The visual quality is achieved with increased complexity and cost as most of the systems embed different pre- and post-processing techniques. The frequency and spatial domain-based methods are the usual approaches for super-resolution with some benefits and limitations. Considering the benefits of wavelet domain processing, this paper deals with a new algorithm that depends on wavelet residues. The methodology opts for wavelet domain filtering and residue extraction to get super-resolved frames for better visuals without embedding other techniques. The avoidance of noisy high-frequency components from low-quality videos and the consideration of edge information in the frames are the main targets of the super-resolution process. This inverse process is carried with a proper combination of information present in low-frequency bands and residual information in the high-frequency components. The efficient known algorithms always have to sacrifice simplicity to achieve accuracy, but in the proposed algorithm efficiency is achieved with simplicity. The robustness of the algorithm is tested by analyzing different wavelet functions and at different noise levels. The proposed algorithm performs well in comparison to other techniques from the same domain.

Research of Image Compression Based on Fractal Coding

2012 ◽  
Vol 241-244 ◽  
pp. 418-422
Author(s):  
Dong Mei Wang ◽  
Jing Yi Lu
Keyword(s):  
Wavelet Transform ◽  
Theoretical Analysis ◽  
Image Compression ◽  
High Frequency ◽  
Wavelet Transformation ◽  
Simulation Experiment ◽  
Low Frequency ◽  
Reconstructed Image ◽  
Wavelet Domain ◽  
Fractal Coding

The EZW and Fractal Coding were researched and simulated in this paper. And two drawbacks were discovered in these algorithm:the coding time is too long and the effect of reconstructed image is not ideal. Therefore, The paper studied the wavelet transformation in the fractal coding application, The wavelet coefficients of an image present two characteristics when the image is processed by wavelet transform: first characteristic is that the energy of an image is strongly concentrated in low frequency sub-image, second characteristic is that there is a similarity between the same direction in high frequency sub-images.but the fractal coding essence was precisely uses the similarity of wavelet transform image. The paper designed one kind of new Image Compression based on Fractal Coding in wavelet domain. The theoretical analysis and the simulation experiment indicated that, to some extent the method can reduce the coding time and reduce the MSE and enhance compression ratio of the reconstructed image and improve PSNR of the reconstructed image..

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