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 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 ◽  
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 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.

Simulations of high-resolution images of amorphous silicon films

1986 ◽  
Vol 44 ◽  
pp. 544-545
Author(s):  
G. Y. Fan ◽  
J. M. Cowley
Keyword(s):  
Electron Microscope ◽  
High Frequency ◽  
Fourier Transformation ◽  
Amorphous Materials ◽  
Low Frequency ◽  
Chromatic Aberration ◽  
Structure Information ◽  
Frequency Components ◽  
High Resolution Images ◽  
Spatial Frequency Spectrum

It is well known that the structure information on the specimen is not always faithfully transferred through the electron microscope. Firstly, the spatial frequency spectrum is modulated by the transfer function (TF) at the focal plane. Secondly, the spectrum suffers high frequency cut-off by the aperture (or effectively damping terms such as chromatic aberration). While these do not have essential effect on imaging crystal periodicity as long as the low order Bragg spots are inside the aperture, although the contrast may be reversed, they may change the appearance of images of amorphous materials completely. Because the spectrum of amorphous materials is continuous, modulation of it emphasizes some components while weakening others. Especially the cut-off of high frequency components, which contribute to amorphous image just as strongly as low frequency components can have a fundamental effect. This can be illustrated through computer simulation. Imaging of a whitenoise object with an electron microscope without TF limitation gives Fig. 1a, which is obtained by Fourier transformation of a constant amplitude combined with random phases generated by computer.

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.

scholarly journals Brain Medical Image Fusion Based on Dual-Branch CNNs in NSST Domain

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Zhaisheng Ding ◽  
Dongming Zhou ◽  
Rencan Nie ◽  
Ruichao Hou ◽  
Yanyu Liu
Keyword(s):  
Image Fusion ◽  
High Frequency ◽  
Medical Image ◽  
Low Frequency ◽  
Structural Features ◽  
Functional Information ◽  
Convolutional Network ◽  
Structure Information ◽  
Medical Image Fusion ◽  
Research Challenge

Computed tomography (CT) images show structural features, while magnetic resonance imaging (MRI) images represent brain tissue anatomy but do not contain any functional information. How to effectively combine the images of the two modes has become a research challenge. In this paper, a new framework for medical image fusion is proposed which combines convolutional neural networks (CNNs) and non-subsampled shearlet transform (NSST) to simultaneously cover the advantages of them both. This method effectively retains the functional information of the CT image and reduces the loss of brain structure information and spatial distortion of the MRI image. In our fusion framework, the initial weights integrate the pixel activity information from two source images that is generated by a dual-branch convolutional network and is decomposed by NSST. Firstly, the NSST is performed on the source images and the initial weights to obtain their low-frequency and high-frequency coefficients. Then, the first component of the low-frequency coefficients is fused by a novel fusion strategy, which simultaneously copes with two key issues in the fusion processing which are named energy conservation and detail extraction. The second component of the low-frequency coefficients is fused by the strategy that is designed according to the spatial frequency of the weight map. Moreover, the high-frequency coefficients are fused by the high-frequency components of the initial weight. Finally, the final image is reconstructed by the inverse NSST. The effectiveness of the proposed method is verified using pairs of multimodality images, and the sufficient experiments indicate that our method performs well especially for medical image fusion.

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.

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