CN113709325A - Single-pixel imaging method based on Hadamard frequency domain transformation matrix threshold filtering - Google Patents

Single-pixel imaging method based on Hadamard frequency domain transformation matrix threshold filtering Download PDF

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CN113709325A
CN113709325A CN202110817757.XA CN202110817757A CN113709325A CN 113709325 A CN113709325 A CN 113709325A CN 202110817757 A CN202110817757 A CN 202110817757A CN 113709325 A CN113709325 A CN 113709325A
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matrix
frequency domain
hadamard
light source
threshold filtering
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陈希浩
吕瑞兵
宋成旭
孟少英
付强
鲍倩倩
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Liaoning University
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    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
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Abstract

A single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering. The method obtains a transform matrix sequence of a frequency domain of a Hadamard modulation matrix sequence by performing discrete cosine transform on the Hadamard modulation matrix sequence. Low-pass filtering the transformed matrix sequence in the frequency domain, and inversely transforming the matrix sequence back to the space domain. And then, modulating and sampling the target in a single-pixel imaging system by using the new matrix, and finally, reconstructing a target image at an ultralow sampling rate by using a compressed sensing algorithm. The method is based on the traditional passive single-pixel imaging system, has a simple structure, is easy to operate, and can recover a clear image of a measured object at a sampling rate lower than 10%. Compared with other modulation methods such as Hadamard and the like, the method has the advantage that the required sampling rate is lower under the condition of the same imaging quality and object sparsity. Therefore, the method is expected to have wide application value in the fields of remote sensing imaging and the like.

Description

Single-pixel imaging method based on Hadamard frequency domain transformation matrix threshold filtering
Technical Field
The invention relates to the technical field of single-pixel imaging, in particular to a single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering.
Background
The traditional single-pixel imaging method utilizes a Hadamard matrix or a random matrix as a measurement matrix, and has the disadvantages of poor imaging quality and low signal-to-noise ratio under a low sampling rate. The single-pixel imaging method based on Hadamard matrix optimization sorting can effectively solve the problem, but the situation that the target object is difficult to reconstruct under the ultra-low sampling rate still exists, and the imaging efficiency is seriously reduced.
Disclosure of Invention
The invention aims to solve the technical problem of providing a single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering, which utilizes high-frequency and low-frequency components with clear frequency domains to sample only in low-frequency information, thereby effectively improving the imaging efficiency.
In order to achieve the purpose, the invention adopts the following technical scheme:
a single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering comprises the following steps:
1. pretreatment:
1.1, generating a group of orthogonal Hadamard matrixes H by a computer, and transforming the H matrixes from a space domain to a frequency domain by utilizing discrete cosine transform, Fourier transform or wavelet transform, wherein the transformed matrixes are H1；
1.2 matching the matrix H in the frequency domain1Threshold filtering is carried out, high-frequency coefficients are abandoned, low-frequency coefficients are reserved, inverse discrete cosine transform is utilized to return to a space domain, and a matrix after transformation is H2；
1.3 finding H in step 1.22Minimum value a, maximum value b of the matrix let H2The matrix is added with | a | and divided by | a | + | b |, the transformed matrix is
Figure RE-RE-GDA0003302668060000011
1.4, mixing H obtained in the step 1.33Rounding each matrix element of the matrix, and reserving two decimal places to obtain a matrix H4Then adding H4Loading the matrix into a digital micromirror device;
2. imaging processing:
2.1, covering the light spots on an object by a light source through a collimation and beam expansion system;
2.2, light reflected by the object is imaged on the digital micromirror device through the imaging lens, and the total light intensity S reflected by the object modulated by the digital micromirror device is collected by the bucket detector through the collecting lens;
2.3 with H2Modulating the matrix to reconstruct the object, processing the data collected by the barrel detector, namely the total light intensity S, wherein the processed data is
S1＝S*(a|+|b|)-|a|*T(x,y)，
Where T (x, y) is the reflection function of the object and S is1Transmitting the data to a computer;
2.4, utilization data S1Sum matrix H2And performing coincidence operation to reconstruct a target image in the coincidence measurement system.
The imaging system used by the single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering comprises a light source, a target object, an imaging lens, a digital micromirror device, a collecting lens, a bucket detector and a coincidence measurement system; the light source covers the light spot on the object; the light reflected by the object is imaged on the digital micromirror device through the imaging lens; the bucket detector collects the total light intensity reflected by the object modulated by the digital micromirror device through a collecting lens; said H2Matrix sum S1The data is transmitted to a coincidence measurement system.
In 1.2, let the high frequency coefficient
Figure RE-RE-GDA0003302668060000021
Wherein
Figure RE-RE-GDA0003302668060000022
Preserving low frequency coefficients
Figure RE-RE-GDA0003302668060000023
Wherein
Figure RE-RE-GDA0003302668060000024
The light source is a helium neon laser light source, a thermal light source, a natural light source or an artificial pseudo-thermal light source.
The bucket detector is used for collecting total light intensity, and the total light intensity is S ═ I (x ^ I)1)dx1Wherein I (x)1) Is represented by x1The intensity of the light at.
In the step 2.4, the algorithm used for the coincidence operation is a compressed sensing algorithm or a traditional second-order correlation algorithm.
The beneficial effects created by the invention are as follows: the method comprises the steps that a computer generates an orthogonal Hadamard matrix, the orthogonal Hadamard matrix is converted into a frequency domain through discrete cosine transform, high-frequency coefficients are filtered out and then inversely converted into a space domain, finally, the matrix element value of the orthogonal Hadamard matrix is converted into a value between 0 and 1 and loaded to a digital micro-mirror device to be used for modulating a target object, a bucket detector detects the total light intensity reflected by the target and transmits the total light intensity to the computer, the computer conducts image reconstruction by using a new modulation matrix which is filtered through a frequency domain threshold based on the Hadamard modulation matrix, and the algorithm used for reconstruction is a TVAL3 algorithm, a compression sensing algorithm and can also be a traditional association algorithm or other compression sensing algorithms; according to the high-frequency and low-frequency components with clear frequency domains, sampling is only carried out at the low-frequency information position, and the imaging efficiency is effectively improved.
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FIG. 1: is a functional block diagram of an imaging system used in the creation of the present invention;
1. a light source; 2. a target object; 3. an imaging lens; 4. a digital micromirror device; 5. a collection lens; 6. a bucket detector; 7. in line with the measurement system.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only some embodiments of the present invention, not all embodiments.
Example 1: a single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering comprises the following steps:
1. pretreatment:
1.1, generating a group of orthogonal Hadamard matrixes H by a computer, and transforming the H matrixes from a space domain to a frequency domain by utilizing discrete cosine transform, Fourier transform or wavelet transform, wherein the transformed matrixes are H1. This can be achieved by using discrete cosine transform, fourier transform or wavelet transform, which works best when discrete cosine transform is used.
1.2 matching the matrix H in the frequency domain1Threshold filtering is carried out, high-frequency coefficients are abandoned, low-frequency coefficients are reserved, inverse discrete cosine transform is utilized to return to a space domain, and a matrix after transformation is H2. And low-frequency information is left, and the high-frequency information is abandoned, so that the contour of the target can be reconstructed more easily, and the reconstruction of the image of the object 2 under the low sampling rate is facilitated.
1.3 finding H in step 1.22Minimum value a, maximum value b of the matrix let H2The matrix is added with | a | and divided by | a | + | b |, the transformed matrix is
Figure RE-RE-GDA0003302668060000031
H2The elements of the matrix have a large number of negative values and the digital micromirror device 4 cannot read, let H2The matrix is added with | a | and divided by | a | + | b | to become H3Matrix, can be H2The value of the matrix element is between 0 and 1, so that the converted H is convenient3The matrix is loaded onto a digital micromirror device 4, where the modulation device can also be other spatial light modulators.
1.4, mixing H obtained in the step 1.33Rounding each matrix element of the matrix, and reserving two decimal places to obtain a matrix H4Then adding H4The matrix is loaded into the digital micromirror device 4. H3The matrix has 15 decimal places, and 2 decimal places are reserved for being read by the digital micro-mirror device 4, and the modulation device can also be a spatial light modulator.
2. Imaging processing:
2.1, covering the light spots on the object 2 by the light source 1 through a collimation and beam expansion system. The light source 1 may be a helium neon laser source, a thermal light source, a natural light source, or an artificial pseudo thermal light source.
2.2, the light reflected by the object 2 is imaged on the digital micromirror device 4 through the imaging lens 3, and the total light intensity S reflected by the object modulated by the digital micromirror device 4 is collected by the bucket detector 6 through the collecting lens 5. The instrument for collecting the total light intensity is a barrel detector 6 without spatial resolution capability or an area array camera with spatial resolution capability, and the total collected light intensity is S ═ I (x ═ I)1)dx1Wherein I (x)1) Is represented by x1The intensity of the light at.
2.3 with H2Modulating the matrix to reconstruct the object 2, processing the data collected by the barrel detector 6, namely the total light intensity S, and obtaining the processed data
S1＝S*(|a|+|b|)-|a|*T(x,y)，
Where T (x, y) is the reflection function of the object 2 and S is1And transmitting to the computer.
2.4, utilization data S1Sum matrix H2And performing coincidence operation to reconstruct a target image in the coincidence measurement system 7. The algorithm used by the coincidence operation is a compressed sensing algorithm and can also be a traditional second-order correlation algorithm.
Specifically, when the algorithm used is the TVAL3 algorithm, the solving method is as follows:
tMN×1＝argmin||t'MN×1||1s.t.||YK×1-φK×MNψt'MN×1||2<ε,
in the formula, phiK×MNIs a measurement matrix; noise is a random Noise term of the environment and the detector electric signals;
ψ＝[ψ1,ψ1,ψ1…,ψMN]is a specific sparse radical. Such as Noiselet, Dct, etc.; m and N are the pixel numbers of rows and columns of the image to be restored; the total number of measurements; l |. electrically ventilated margin1And |. non conducting phosphor2Respectively represent l1Norm sum l2A norm; with epsilon being the amplitude of the noiseA boundary.
The imaging system used in the above-described imaging method is shown in fig. 1. The device comprises a light source 1, a target object 2, an imaging lens 3, a digital micromirror device 4, a collecting lens 5, a barrel detector 6 and a coincidence measurement system 7; the light source 1 covers the light spot on the object 2; the light reflected by the object 2 is imaged on a digital micromirror device 4 through an imaging lens 3; the bucket detector 6 collects the total light intensity reflected by the object modulated by the digital micromirror device 4 through the collecting lens 5; said H2Matrix sum S1The data is transmitted to the coincidence measurement system 7.
Thus, it should be understood by those skilled in the art that while an exemplary embodiment of the present invention has been illustrated and described in detail herein, many other variations and modifications can be made, which are consistent with the principles of the invention, from the disclosure herein, without departing from the spirit and scope of the invention. Accordingly, the scope of the invention should be understood and interpreted to cover all such other variations or modifications.

Claims (6)

1. A single-pixel imaging method based on Hadamard frequency domain transform matrix threshold filtering is characterized by comprising the following steps:
1. pretreatment:
1.1, generating a group of orthogonal Hadamard matrixes H by a computer, and transforming the H matrixes from a space domain to a frequency domain by utilizing discrete cosine transform, Fourier transform or wavelet transform, wherein the transformed matrixes are H1；
1.2 matching the matrix H in the frequency domain1Threshold filtering is carried out, high-frequency coefficients are abandoned, low-frequency coefficients are reserved, inverse discrete cosine transform is utilized to return to a space domain, and a matrix after transformation is H2；
1.3 finding H in step 1.22Minimum value a, maximum value b of the matrix let H2The matrix is added with | a | and divided by | a | + | b |, the transformed matrix is
Figure RE-FDA0003302668050000011
1.4, will stepH obtained in step 1.33Rounding each matrix element of the matrix, and reserving two decimal places to obtain a matrix H4Then adding H4Loading the matrix into a digital micromirror device (4);
2. imaging processing:
2.1, covering the light spots on the object (2) by the light source (1) through a collimation and beam expansion system;
2.2, light reflected by the object (2) is imaged on the digital micromirror device (4) through the imaging lens (3), and the total light intensity S reflected by the object modulated by the digital micromirror device (4) is collected by the bucket detector (6) through the collecting lens (5);
2.3 with H2Modulating the matrix to reconstruct the object (2), processing the data collected by the barrel detector (6), namely the total light intensity S, and obtaining the processed data
S1＝S*(|a|+|b|)-|a|*T(x,y)，
Wherein T (x, y) is the reflection function of the object (2) and S is1Transmitting the data to a computer;
2.4, utilization data S1Sum matrix H2And performing coincidence operation to reconstruct a target image in the coincidence measurement system (7).
2. The imaging system for use in the Hadamard frequency domain transform matrix threshold filtering based single pixel imaging method as claimed in claim 1, characterized by comprising a light source (1), a target object (2), an imaging lens (3), a digital micromirror device (4), a collecting lens (5), a bucket detector (6) and a coincidence measurement system (7); the light source (1) covers the light spot on the object (2); the light reflected by the object (2) is imaged on the digital micromirror device (4) through the imaging lens (3); the bucket detector (6) collects the total light intensity reflected by the object modulated by the digital micromirror device (4) through the collecting lens (5); said H2Matrix sum S1The data are transmitted to a coincidence measurement system (7).
3. The method of claim 1 for single-pixel imaging based on Hadamard frequency domain transform matrix threshold filtering, characterized in that: in 1.2, let the high frequency coefficient
Figure RE-FDA0003302668050000012
Wherein
Figure RE-FDA0003302668050000013
Preserving low frequency coefficients
Figure RE-FDA0003302668050000014
Wherein
Figure RE-FDA0003302668050000021
4. The Hadamard frequency domain transform matrix threshold filtering based single-pixel imaging method of claim 1, wherein: the light source (1) is a helium neon laser light source, a thermal light source, a natural light source or an artificial pseudo-thermal light source.
5. The method of claim 1 for single-pixel imaging based on Hadamard frequency domain transform matrix threshold filtering, characterized in that: the barrel detector (6) is used for collecting total light intensity, and the total light intensity is S ═ I (x ═ I)1)dx1Wherein I (x)1) Is represented by x1The intensity of the light at.
6. The Hadamard frequency domain transform matrix threshold filtering based single-pixel imaging method of claim 1, wherein: in the step 2.4, the algorithm used for the coincidence operation is a compressed sensing algorithm or a traditional second-order correlation algorithm.
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