CN113448233B - Under-sampling hologram compression holographic multi-scale self-focusing reconstruction method and system - Google Patents
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Abstract
The invention discloses an under-sampling hologram compression holographic multi-scale self-focusing reconstruction method and a system, belonging to the technical field of digital holography, comprising the steps of respectively carrying out down-sampling operation on holograms generated by irradiating different positions of an object in an optical structure by a light source to obtain down-sampling holograms at different positions; reconstructing the down-sampling holograms at different positions based on a CS algorithm to obtain amplitude images at different positions; estimating the position of a focal plane according to amplitude images at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm; and reconstructing the down-sampled hologram at the position of the focusing plane based on the TwinT algorithm. The invention provides an EIG-AF-CS self-focusing algorithm for realizing self-focusing under the condition of undersampling, combines the EIG-AF-CS self-focusing algorithm with compression reconstruction without twin images, and effectively overcomes the problems of twin image interference and lack of self-focusing capability in the traditional compression holographic reconstruction while ensuring the reconstruction quality.
Description
Technical Field
The invention relates to the technical field of digital holography, in particular to an under-sampling hologram compression holographic multi-scale self-focusing reconstruction method and system.
Background
Digital Holography (DH) is a holographic technique in which an intensity image is recorded by a CCD, and then the original object information is reconstructed by computer numerical calculations. Its disadvantage is the high storage capacity and bandwidth required, which greatly limits the wide-spread use of digital holography. In 2006, Cand, Donoho, Tao et al proposed the Compressed Sensing (CS) theory that if a signal is sparse or compressible, only limited measurements of the sparse signal are needed to reconstruct the original signal accurately, saving resources and time greatly, breaking through the limitation that the sampling rate specified by the traditional Nyquist sampling theorem must be at least twice the signal bandwidth.
In 2009, Brady et al combine compressed sensing and digital holography together, propose a compressed holographic method, build a bridge between the compressed sensing theory and the holographic display technology, and by using the compressed sensing theory, an original object can be accurately reconstructed from a 2D hologram by a small amount of measurement sample data, and a Brady group experiment realizes holographic layer chromatography reconstruction of two layers of dandelions with a long distance; subsequently, the group also successfully completed several studies, such as Compressive Holographic Tomography (CHT), Millimeter Wave (MWH), and blur (DH) holograms. In addition, in 2014, Stern et al in israel proposed a Compressive Fresnel Holography (CFH) based on a variable down-sampling strategy, and provided conditions required to be satisfied for realizing the actual Compressive Fresnel Holography, and then the extension of the CFH is applied to imaging fields such as multi-dimensional imaging, tomography, reconstruction of partially-occluded objects, and the like.
The traditional compression holographic reconstruction method mainly faces the interference of a twin image and a zero-order image, and the twin image and the zero-order image are usually eliminated by adopting a multi-exposure method. In 2018, Zhang et al, university of Qinghua, based on the sparsity difference between the reconstructed image and the twin image caused by the physical symmetry of the hologram, proposed a CS method to successfully realize the twin-image-free holographic reconstruction from the single-exposure hologram.
The method proposed by Zhang et al can realize twinning-free image reconstruction, but only aims at a 2D-2D full-sampling imaging model, lacks a compression sampling process, and has no self-focusing capability because the position of a focal plane must be known during reconstruction.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and realize the twinning-free image self-focusing compression holographic reconstruction from a single undersampled hologram.
To achieve the above object, in one aspect, the present invention employs an under-sampled hologram compression holographic multi-scale self-focusing reconstruction method, including:
carrying out down-sampling operation on the hologram generated by the object through the light source irradiation to obtain a down-sampled hologram;
and reconstructing the down-sampling hologram based on a TwinST algorithm to obtain a reconstruction result.
Further, the down-sampling operation is performed on the hologram generated by the object illuminated by the light source, so as to obtain a down-sampled hologram, and the formula is as follows:
wherein D is Ω Representing down-sampling, G representing forward transformation,. phi Ω Representing the term 2Re { D Ω G ρ } versus ρ, ρ representing the object density, e representing the model error.
Further, the down-sampling operation is performed on the hologram generated by the object illuminated by the light source to obtain a down-sampled hologram, and the method further includes:
and respectively carrying out down-sampling operation on the holograms generated by the irradiation of the light source at different positions of the object in the optical structure to obtain down-sampled holograms at different positions.
Further, reconstructing the down-sampling hologram based on the TwIST algorithm to obtain a reconstruction result, further comprising:
estimating the position of a focal plane by adopting an evaluation method of a characteristic value algorithm for the downsampled holograms at different positions;
and reconstructing the down-sampling hologram at the focusing plane position based on the TWIST algorithm to obtain the reconstruction result.
Further, the estimating the focal plane position of the downsampled hologram at different positions by using an evaluation method of a characteristic value algorithm includes:
reconstructing the down-sampling holograms at different positions based on a CS algorithm to obtain amplitude images at different positions;
and estimating the position of the focal plane according to the amplitude images at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm.
Further, still include: and estimating the position of the focal plane by combining a multi-scale search strategy and adopting an evaluation method of a characteristic value self-focusing algorithm on the downsampled holograms at different positions, wherein the method specifically comprises the following steps:
1) setting a search start point of a first layer scale
Searching for an endpoint
And search spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
2) reconstructing the down-sampling hologram at each position in the current layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
3) the evaluation method of the characteristic value self-focusing algorithm is adopted to estimate and obtain the search result of the current layer scale according to the amplitude images at different positions
4) Taking the search result of the current layer scale as the search result of the previous layer scale, and taking the search result of the previous layer scale as the search result of the previous layer scale
As a central point, based on a relational expression
i 2,3, …, k obtaining the search starting point of the next layer search space
Searching for an endpoint
And search spacing
And the next layer position sequence, and repeatedly executing the steps 2) -4) until the self-focusing search result of the k-th layer scale is obtained
5) Reconstructing a location based on the TWIST algorithm
And (4) processing the down-sampling hologram to obtain the reconstruction result.
In another aspect, a compressed holographic multi-scale self-focusing reconstruction system using an under-sampled hologram comprises a down-sampling operation module and a reconstruction module, wherein:
the down-sampling operation module is used for performing down-sampling operation on the hologram generated by the object through the illumination of the light source to obtain a down-sampling hologram;
and the reconstruction module is used for reconstructing the down-sampling hologram based on a TwinT algorithm to obtain a reconstruction result.
Furthermore, the down-sampling operation module is further configured to perform down-sampling operations on holograms generated by the illumination of the object by the light source at different positions in the optical structure, so as to obtain down-sampled holograms at different positions.
Further, the reconstruction module further comprises a focal plane position estimation unit and a reconstruction unit, wherein:
the focal plane position estimation unit is used for estimating the focal plane position of the down-sampled holograms at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm;
the reconstruction unit is used for reconstructing the down-sampling hologram at the focusing plane position based on the TwinT algorithm to obtain the reconstruction result.
Further, the focal plane position estimation unit is configured to estimate the focal plane position by using an evaluation method of a feature value self-focusing algorithm for the downsampled holograms at different positions in combination with a multi-scale search strategy, and specifically includes:
1) setting a first layer dimensionIs searched for
Searching for an endpoint
And search spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
2) reconstructing the down-sampling hologram at each position in the current layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
3) the evaluation method of the characteristic value self-focusing algorithm is adopted to estimate and obtain the search result of the current layer scale according to the amplitude images at different positions
4) Taking the search result of the current layer scale as the search result of the previous layer scale, and taking the search result of the previous layer scale as the search result of the previous layer scale
As a central point, based on a relational expression
i 2,3, …, k obtaining the search starting point of the next layer search space
Searching for an endpoint
And search spacing
And the next layer position sequence, and repeatedly executing the steps 2) -4) until the self-focusing search result of the k-th layer scale is obtained
5) Reconstructing a location based on the TwinT algorithm
And (4) processing the down-sampling hologram to obtain the reconstruction result.
Compared with the prior art, the invention has the following technical effects: aiming at the lack of a compression sampling process in the traditional twin image-free reconstruction process, the invention carries out down-sampling on an under-sampled hologram to supplement the compression sampling process and establishes a compression holographic imaging model based on the under-sampled hologram; and aiming at the problem that accurate self-focusing is difficult to realize after the down-sampling operation is added, an EIG-AF-CS self-focusing algorithm is provided and is combined with the twin-free image compression reconstruction. The reconstruction can be realized by using less original data through down-sampling the hologram, the reconstruction quality can be ensured, the self-focusing reconstruction can be realized by combining an EIG-AF-CS self-focusing algorithm, and the problems of twin image interference and lack of self-focusing capability in the traditional compressed holographic reconstruction are effectively solved.
Drawings
The following detailed description of embodiments of the invention refers to the accompanying drawings in which:
FIG. 1 is a flow chart of a method of compressed holographic reconstruction of an undersampled hologram;
FIG. 2 is a schematic down-sampling of an under-sampled hologram, wherein (a) the down-sampling of the under-sampled hologram is added and (b) the down-sampled hologram is up-sampled prior to two-way propagation;
FIG. 3 is a flow chart of a self-focusing reconstruction method for under-sampled hologram feature values;
FIG. 4 is an overall flow chart of an under-sampled hologram feature value self-focusing reconstruction method;
FIG. 5 is a flow chart of a method for multi-scale self-focusing reconstruction of an undersampled hologram.
Detailed Description
To further illustrate the features of the present invention, refer to the following detailed description of the invention and the accompanying drawings. The drawings are for reference and illustration purposes only and are not intended to limit the scope of the present disclosure.
As shown in fig. 1 to fig. 2, the present embodiment discloses a method for reconstructing a compressed hologram multi-scale self-focusing by under-sampling holograms, which includes the following steps S1 to S2:
s1, carrying out down-sampling operation on the hologram generated by the object through the illumination of the light source to obtain a down-sampled hologram;
s2, reconstructing the down-sampling hologram based on the TwinT algorithm to obtain a reconstruction result.
It should be noted that, for the problem that the existing twin image-free holography method (TIFH-CS) lacks a compressive sampling process and has no self-focusing capability, the present embodiment overcomes the disadvantage that the existing twin image-free holography method lacks a compressive sampling process, as shown in fig. 2, the undersampled hologram is downsampled to supplement the compressive sampling process, and the sampling operation formula is expressed as follows:
wherein D is Ω Representing down-sampling, e.g. uniform random down-sampling, G representing forward transformation, phi Ω Representing the term 2Re { D Ω G ρ } versus ρ, ρ representing the object density, e representing the model error,
representing a down-sampled hologram.
As a further preferred solution, the reconstruction needs to be known from
To solve ρ, this embodiment adopts a Two-step Iterative shrinkage/Threshold (TwIST-step Iterative shrinkage/Threshold) algorithm to solve the problem:
wherein the content of the first and second substances,
denotes the density of the object finally optimized by TWIST algorithm, i.e. the result of TWIST algorithm optimization, and τ denotes the residual error 2 Relative weight between norm and estimated TV norm.
It should be noted that, after down-sampling is added to the hologram in the twin image free holography method, it is difficult to achieve accurate self-focusing, and the evaluation method of the Eigenvalue (EIG) self-focusing algorithm of this embodiment is improved, and a TwIST algorithm is used instead of back propagation to reconstruct the down-sampled holograms at different positions to obtain amplitude images at different positions, so as to achieve the self-focusing of the twin image free holography. As shown in fig. 3 to 4, in order to implement the self-focusing function, the present embodiment provides an under-sampled hologram eigenvalue self-focusing reconstruction method (EIG-AF-CS), which includes the following steps:
1) respectively carrying out down-sampling operation on holograms generated by the irradiation of the light source at different positions of the object in the optical structure to obtain down-sampled holograms at different positions;
2) reconstructing the down-sampling holograms at different positions based on a CS algorithm to obtain amplitude images at different positions;
3) estimating the position of a focal plane according to amplitude images at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm;
4) and reconstructing the down-sampling hologram at the focusing plane position based on the TwinT algorithm to obtain the reconstruction result.
As a further preferred technical solution, the estimating method using the EIG algorithm estimates the position of the focal plane according to the amplitude images at different positions, specifically: from a distance z 1 ＝z s Starting to perform a hologram reconstruction with a reconstruction distance interval z step Let M X N and N z Representing the size of the hologram and the total number of reconstructed images, respectively, using the set of reconstructed images to perform automatic focal plane detection, comprising the steps of:
at a given reconstruction distance z, the corresponding amplitude image A z (x, y) by their energy classificationThe method comprises the following steps:
the average of the normalized amplitude images is calculated as:
covariance matrix Q z Comprises the following steps:
wherein the content of the first and second substances,
(·) T represents a matrix transpose, comprising Q z Column vector E of eigenvalues z Comprises the following steps:
E z ＝eig(Q z )
where the eigenvalue calculation function in MATLAB is represented. Taking into account the eigenvalues in the vector E z In ascending order, the metric L for detecting the focal plane is defined as:
where κ is a parameter that may be customized.
In the present case, the covariance matrix Q z Contains most of the information about spatial variations in the reconstructed image. Therefore, all these main eigenvalues should be utilized in the calculation of the metric L. However, the degree of spatial variation in the reconstructed image is almost monotonic with reconstruction distance, except in the focal plane. To compensate for this effect, a certain number of dominant eigenvalues need to be discarded in the computation of the autofocus metric. This number is given by the kappa parameter. In generalThe appropriate value of κ depends on the size of the reconstructed image. Due to Q z There are M eigenvalues, so the k value can be chosen as a percentage of M. Finally, z ═ z when the selection metric L takes the maximum/minimum value f The value serves as the position of the focal plane.
As shown in fig. 5, in order to improve the accuracy of self-focusing, the present embodiment combines a multi-scale search strategy to position a focal plane layer by layer, and implements multi-scale self-focusing (multi-scale EIG-AF-CS) under the condition of undersampling, which specifically includes the following steps:
1) respectively carrying out down-sampling operation on holograms generated by the irradiation of the light source at different positions of the object in the optical structure to obtain down-sampled holograms at different positions;
2) setting a search start point of a first layer scale
Searching for an endpoint
And search spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
3) reconstructing the down-sampling hologram at each position in the first layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
4) evaluation method using the eigenvalue autofocus algorithm
Estimating and obtaining a search result of a first-layer scale according to amplitude images at different positions
5) Search results at a first hierarchical scale
As a central point, based on a relational expression
i 2,3, …, k obtaining the search starting point of the next layer search space
Searching for an endpoint
And search spacing
And a second layer position sequence, which reduces the search space layer by layer until the self-focusing search result of the k-th layer scale is obtained
6) Reconstructing a location based on the TwinT algorithm
And (4) processing the down-sampling hologram to obtain the reconstruction result.
The embodiment provides an EIG-AF-CS self-focusing algorithm for realizing self-focusing under the undersampling condition, and combines the EIG-AF-CS self-focusing algorithm with twin-free image compression reconstruction. Experiments prove that reconstruction can be realized by using less original data for down-sampling the hologram, the reconstruction quality can be ensured, self-focusing reconstruction can be realized by combining an EIG-AF-CS self-focusing algorithm, and the problems of twin image interference and lack of self-focusing capability in the traditional compressed holographic reconstruction are effectively solved.
The embodiment also discloses an under-sampling hologram compression holographic multi-scale self-focusing reconstruction system, which is characterized by comprising a down-sampling operation module and a reconstruction module, wherein:
the down-sampling operation module is used for performing down-sampling operation on the hologram generated by the object through illumination of the light source to obtain a down-sampling hologram;
and the reconstruction module is used for reconstructing the down-sampling hologram based on a TwinT algorithm to obtain a reconstruction result.
As a further preferable technical solution, the down-sampling operation module is further configured to perform down-sampling operations on holograms generated by the illumination of the object by the light source at different positions in the optical structure, respectively, so as to obtain down-sampled holograms at different positions.
The reconstruction module further comprises a focal plane position estimation unit and a reconstruction unit, wherein:
the focal plane position estimation unit is used for estimating the focal plane position of the down-sampled holograms at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm;
the reconstruction unit is used for reconstructing the down-sampling hologram at the focusing plane position based on the TwinT algorithm to obtain the reconstruction result.
As a further preferred technical solution, the focal plane position estimating unit is configured to estimate the focal plane position by using an evaluation method of an EIG algorithm for the downsampled holograms at different positions in combination with a multi-scale search strategy, and specifically includes:
1) setting a search start point of a first layer scale
Search endpoint
And search spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
2) reconstructing the down-sampling hologram at each position in the current layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
3) the evaluation method of the characteristic value self-focusing algorithm is adopted to estimate and obtain the search result of the current layer scale according to the amplitude images at different positions
4) Taking the search result of the current layer scale as the search result of the previous layer scale, and taking the search result of the previous layer scale as the search result of the previous layer scale
As a central point, based on a relational expression
i 2,3, …, k obtaining the search starting point of the next layer search space
Searching for an endpoint
And search spacing
And the next layer position sequence, and repeatedly executing the steps 2) -4) until the self-focusing search result of the k-th layer scale is obtained
5) Reconstructing a location based on the TwinT algorithm
And (4) processing the down-sampling hologram to obtain the reconstruction result.
The system provided by the embodiment of the present invention is used for executing the above method embodiments, and for details of the process and the details, reference is made to the above embodiments, which are not described herein again.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.
Claims (3)
1. An under-sampled hologram compression holographic multi-scale self-focusing reconstruction method is characterized by comprising the following steps:
carrying out down-sampling operation on the hologram generated by the object through the illumination of the light source to obtain a down-sampling hologram;
reconstructing the down-sampling hologram based on a TwinST algorithm to obtain a reconstruction result;
wherein, the down-sampling operation is carried out on the hologram generated by the object through the illumination of the light source to obtain the down-sampling hologram, and the method further comprises the following steps:
respectively carrying out down-sampling operation on the holograms generated by the object in different positions in the optical structure through light source illumination to obtain down-sampled holograms in different positions;
the reconstructing the down-sampling hologram based on the TwinT algorithm to obtain a reconstruction result specifically comprises:
estimating the position of a focal plane by adopting an evaluation method of a characteristic value self-focusing algorithm for the downsampling holograms at different positions;
reconstructing a down-sampling hologram at a focal plane position based on the TwinT algorithm to obtain a reconstruction result;
estimating the position of the focal plane by adopting an evaluation method of a characteristic value algorithm for the downsampled holograms at different positions, wherein the method comprises the following steps:
reconstructing the down-sampling holograms at different positions based on a CS algorithm to obtain amplitude images at different positions;
estimating the position of a focal plane according to amplitude images at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm;
further comprising: and estimating the position of the focal plane by combining a multi-scale search strategy and adopting an evaluation method of a characteristic value self-focusing algorithm on the downsampled holograms at different positions, wherein the method specifically comprises the following steps:
1) setting a search starting point of a first-tier scale
Searching for an endpoint
And searchCable spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
2) reconstructing the down-sampling hologram at each position in the current layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
3) the evaluation method of the characteristic value self-focusing algorithm is adopted to estimate and obtain the search result of the current layer scale according to the amplitude images at different positions
4) Taking the search result of the current layer scale as the search result of the previous layer scale, and taking the search result of the previous layer scale as the search result of the previous layer scale
As a central point, based on a relational expression
Obtaining a search starting point of a next search space
Searching for an endpoint
And search spacing
And the next layer position sequence, and repeatedly executing the steps 2) -4) until the self-focusing search result of the k-th layer scale is obtained
5) Reconstructing a location based on the TwinT algorithm
And (4) down-sampling the hologram to obtain the reconstruction result.
2. The method for reconstructing an under-sampled hologram by compressing a holographic multi-scale self-focusing according to claim 1, wherein the hologram generated by the object illuminated by the light source is down-sampled to obtain a down-sampled hologram, and the formula is as follows:
wherein D is Ω Representing down-sampling, G representing forward transformation,. phi Ω Representing the term 2Re { D Ω G ρ } versus ρ, ρ representing the object density, e representing the model error.
3. An under-sampled hologram compression holographic multi-scale self-focusing reconstruction system, comprising a down-sampling operation module and a reconstruction module, wherein:
the down-sampling operation module is used for performing down-sampling operation on the hologram generated by the object through illumination of the light source to obtain a down-sampling hologram;
the reconstruction module is used for reconstructing the down-sampling hologram based on a TwinT algorithm to obtain a reconstruction result;
the down-sampling operation module is also used for respectively performing down-sampling operation on the holograms generated by the object in the optical structure at different positions through the illumination of the light source to obtain down-sampling holograms at different positions;
the reconstruction module further comprises a focal plane position estimation unit and a reconstruction unit, wherein:
the focal plane position estimation unit is used for estimating the focal plane position of the down-sampled holograms at different positions by adopting an evaluation method of a characteristic value self-focusing algorithm;
the reconstruction unit is used for reconstructing a down-sampling hologram at a focusing plane position based on the TwinT algorithm to obtain a reconstruction result;
the focal plane position estimation unit is used for estimating the focal plane position by combining a multi-scale search strategy and adopting an evaluation method of a characteristic value self-focusing algorithm for the downsampling holograms at different positions, and specifically comprises the following steps:
1) setting a search start point of a first layer scale
Searching for an endpoint
And search spacing
Obtaining a first layer position sequence, wherein the total interval number of the first layer is N;
2) reconstructing the down-sampling hologram at each position in the current layer position sequence based on a CS algorithm to obtain amplitude images at different positions;
3) the evaluation method of the characteristic value self-focusing algorithm is adopted to estimate and obtain the search result of the current layer scale according to the amplitude images at different positions
4) Taking the search result of the current layer scale as the search result of the previous layer scale, and taking the search result of the previous layer scale as the search result of the previous layer scale
As a central point, based on a relational expression
Obtaining a search starting point of a next search space
Searching for an endpoint
And search spacing
And the next layer position sequence, and repeatedly executing the steps 2) -4) until the self-focusing search result of the k-th layer scale is obtained
5) Reconstructing a location based on the TwinT algorithm
And (4) processing the down-sampling hologram to obtain the reconstruction result.
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