CN108024037B - Hadamard matrix perception imaging system and imaging method thereof - Google Patents

Hadamard matrix perception imaging system and imaging method thereof Download PDF

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CN108024037B
CN108024037B CN201711232935.2A CN201711232935A CN108024037B CN 108024037 B CN108024037 B CN 108024037B CN 201711232935 A CN201711232935 A CN 201711232935A CN 108024037 B CN108024037 B CN 108024037B
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叶梅
叶虎年
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Huazhong University of Science and Technology
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Abstract

The Hadamard matrix perception imaging system provides an imaging method thereof, and solves the problem that the signal-to-noise ratio of a reconstructed image is not high enough in the existing DMD device imaging method. The Hadamard matrix perception imaging system comprises a first lens, a DMD device, a second lens, a first unit detector, an AD converter and a processor, and can further comprise a third lens and a second unit detector. The invention utilizes the unit detector, carries out Hadamard conversion by means of a DMD device, samples the target through a reflection light path, and obtains the sequence light signal digital quantity which is convenient to process and reconstruct the image by a compressed sensing method, and the finally obtained image has higher signal-to-noise ratio and better quality.

Description

Hadamard matrix perception imaging system and imaging method thereof
Technical Field
The invention belongs to an imaging system of an optical waveband.
Background
A digital Micromirror array (DMD) Device is composed of a block of independent micro-reflector, which is formed by adding a rotary mechanism capable of modulating the reflection surface on the standard semiconductor process of CMOS, and can be quickly turned to positive and negative directions (generally positive and negative 12 degrees) under the control of program to complete the light path modulation. At present, the dmd is mainly used in a Digital Light Processing (DLP) system as a core, i.e., a dmd chip adopted by an optical engine heart, so as to realize the functions of a modern projector. Researchers at the american RICE university in 2006 designed a single-pixel camera according to the compressive sensing theory, which generated a binary random sampling matrix by digital micromirror array (DMD) simulation, sampled the optical image linearly by a single detector element, and reconstructed the target image by a compressive sensing reconstruction algorithm, see TAKHAR d., LASKA j.n., WAKIN m., et al.a new compressive Imaging camera architecture using optical-domain compression [ J ]. in proc.is & T/SPIE Symposium Electronic Imaging: computational Imaging, 2006, 6065: 43-52.
The existing compressed sensing imaging method of the DMD device takes a Gaussian random matrix as a sampling matrix, and the sampling matrix cannot be optimal due to randomness, so that the peak signal-to-noise ratio of a reconstructed image is not high enough.
The hadamard matrix (H matrix) is an orthogonal square matrix composed of-1 and +1 elements, and among various construction methods of the H matrix, the Sylvester type H matrix is most widely used, the order of the H matrix is 2n, the direct product of the matrix can be applied, and the hadamard matrix is constructed by recursion from low order to high order:
Figure BDA0001484944550000021
in the formula:
Figure BDA0001484944550000022
is a 2 nd order H matrix whose other modes are:
Figure BDA0001484944550000023
all satisfy
Figure BDA0001484944550000024
By using the method, other modes of H matrix of each order can be obtained, and the maximum mode number is n2。
The different modes of the H matrix with the same order number are all composed of different modes of the H matrix with the order of 2: the following H4、H8Standard H matrix of order 4, 8:
Figure BDA0001484944550000025
different modes 2 order H matrix corresponding standard H4The matrix can be converted into other three other forms, and the requirement of the matrix is met
Figure BDA0001484944550000026
In total give 42A H4Matrix, order nThe maximum number of patterns of the H matrix is n2。
The method for imaging by using Hadamard matrix is to use the matrix as the construction mode of sampling template to make n on target2Sub-sampling, n being the order of the hadamard matrix used, n2Is the total number of pixels of the image formed. At most all n is completed2After sub-sampling, the value of each pixel can be solved. The imaging method has the advantage that the measurement accuracy of the solved pixel value and the value obtained by measuring one pixel by one same detector is higher.
The negative direction reflecting surface of the DMD device is a reflecting surface formed by rotating the reflecting surface anticlockwise, and the positive direction reflecting surface is a reflecting surface formed by rotating the reflecting surface clockwise.
Disclosure of Invention
The invention provides a Hadamard matrix perception imaging system and an imaging method thereof, and solves the problem that the signal-to-noise ratio of a reconstructed image is not high enough in the existing DMD device imaging method.
The invention provides a Hadamard matrix perception imaging system, which comprises a first lens, a DMD device, a second lens, a first unit detector, an AD converter and a processor, and is characterized in that:
the micromirror array of the DMD device is arranged according to a Hadamard matrix and is driven by a processor to gradually perform H conversion;
the DMD device is positioned on a focal plane of the first lens, the second lens is positioned in an object distance range of a reflecting surface of the DMD device, the first unit detector is positioned on a focal point of the second lens, and the first total energy reflected by each step of H conversion of the DMD device is measured, converted into a first digital quantity through the AD converter and sent to the processor;
the first total energy is the sum of optical signal values of all reflection lenses of the DMD device in the negative direction in an overturning and reflecting mode;
the first digital quantity formed in each step of H transformation forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate a high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
The Hadamard matrix perception imaging system is characterized in that:
the Hadamard matrix is an H matrix of 128 th order, 256 th order, 512 th order, 1024 th order, 2048 th order or 4096 th order.
The Hadamard matrix perception imaging system can also be provided with a third lens and a second unit detector, wherein the third lens is positioned in the object distance range of the positive direction reflecting surface of the DMD device, and the second unit detector is positioned on the focus of the third lens; the second unit detector measures the second total energy reflected by each step of H conversion of the DMD device, converts the second total energy into second digital quantity through the AD converter and then sends the second digital quantity to the processor;
the second total energy is the sum of the light signal values of the positive direction reversal reflection of each reflector of the DMD device;
the second digital quantity formed in each step of H transformation forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate a high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method;
or the first digital quantity and the second digital quantity formed in each step of H conversion are combined into superposed digital quantity, sequence optical signal digital quantity is formed in the processor and provided for the processor to adopt an orthogonal matching tracking method in a compressed sensing method, and a high peak signal-to-noise ratio reconstructed image of the target image is calculated.
The compressed sensing imaging method based on the Hadamard matrix sensing imaging system comprises the following steps:
placing a target image in an object distance range of a first lens, wherein a DMD device is positioned on a focal plane of the first lens, a second lens is positioned in an object distance range of a negative direction reflecting surface of the DMD device, and a first unit detector is positioned on a focal point of the second lens;
step two, the processor controls the driver to gradually carry out H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction by the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by the first unit detector through the second lens to form first total energy reflected by the DMD device in the step of H conversion, and the first total energy is converted into first digital quantity through the AD converter and then sent to the processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the first digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
The compressed sensing imaging method based on the Hadamard matrix sensing imaging system can also comprise the following steps of:
placing a target image in an object distance range of a first lens, wherein a DMD device is positioned on a focal plane of the first lens, a third lens is positioned in an object distance range of a positive direction reflecting surface of the DMD device 3, and a second unit detector is positioned on a focal point of the third lens;
step two, the processor controls the driver to gradually carry out H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction by the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each positive direction reflecting lens of the DMD device is received by the second unit detector through the third lens to form second total energy reflected by the DMD device in the step of H conversion, and the second total energy is converted into second digital quantity through the AD converter and then sent to the processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the second digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
The compressed sensing imaging method based on the Hadamard matrix sensing imaging system can further comprise the following steps:
placing a target image in an object distance range of a first lens, wherein a DMD device is positioned on a focal plane of the first lens, a second lens is positioned in an object distance range of a negative direction reflecting surface of the DMD device, and a first unit detector is positioned on a focal point of the second lens; the third lens is positioned in the object distance range of the positive direction reflecting surface of the DMD device, and the second unit detector is positioned on the focus of the third lens;
step two, the processor controls the driver to gradually carry out H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction by the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by the first unit detector through the second lens to form first total energy reflected by the DMD device in the step of H conversion, and the first total energy is converted into first digital quantity through the AD converter and then sent to the processor for storage;
the sum of the light signal values reflected by each positive direction reflecting lens of the DMD device is received by the second unit detector through the third lens to form a second total energy reflected by the DMD device in the step H, and the second total energy is converted into a second digital quantity through the AD converter and then sent to the processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image size of the DMD device is driven to complete the whole H conversion, combining the first digital quantity and the second digital quantity formed in each step of H conversion into a superposed digital quantity, forming a sequence optical signal digital quantity in the processor, providing the sequence optical signal digital quantity to the processor, and calculating a high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
In the second step, when the H transformation is performed step by step, the H matrix is constructed in a recursive manner from a low order to a high order:
Figure BDA0001484944550000071
and is
Figure BDA0001484944550000072
Wherein 1n is an n-order identity matrix,
Figure BDA0001484944550000073
is a 2 nd order H matrix;
in the H transformation, the reflecting mirror plates corresponding to each element of the second-order H matrix are totally performed by 22The other modes of the secondary flip are as follows:
Figure BDA0001484944550000074
corresponding n-th order H matrix is performed by 22Step transformation, which can be used to obtain other modes of H matrix of each order, and the maximum mode number is n2。
The invention combines a DMD device and a Hadamard matrix together with a compressed sensing method to form an imaging method capable of obtaining an image with a high peak signal-to-noise ratio.
Compressed sensing, also called compressive sampling and compressive sensing, is used as a new sampling theory, and can acquire discrete samples of signals by random sampling under the condition of far less than a Nyquist sampling rate by developing the sparse characteristic of the signals, and then perfectly reconstruct the signals by a nonlinear reconstruction algorithm.
The sequence optical signal digital quantity provided by the invention is convenient to be applied to an Orthogonal Matching Pursuit (OMP) algorithm in a compressed sensing reconstruction method, and the core idea is to obtain a column vector for representing a column atom from an observation matrix in a mode of multiple iteration and gradual selection. In each iteration, the selected atom and the current residual (redundant) vector have the maximum correlation and can meet the criterion of the optimal atom matching, the step of subtracting the correlation part from the observation vector is completed to update the residual vector until the iteration frequency reaches the sparsity K, and then the iteration is stopped.
And obtaining a complete line of target images after the reconstruction by the OMP method, and obtaining the whole target image which is consistent with the DMD array size through line-by-line sampling and reconstruction.
The invention utilizes the unit detector, carries out Hadamard conversion by means of a DMD device, samples the target through a reflection light path, and obtains the sequence light signal digital quantity which is convenient to process and reconstruct the image by a compressed sensing method, and the finally obtained image has higher signal-to-noise ratio and better quality.
Drawings
FIG. 1 is a schematic view of an imaging system of the present invention;
the 3 images of fig. 2 are in turn corresponding reconstructed images.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
As shown in fig. 1, the Hadamard matrix-sensing imaging system of the present invention comprises a first lens 2, a DMD device 3, a second lens 4, a first unit detector 5, an AD converter 6 and a processor 10; there may also be a third lens 7 and a second elementary detector 8.
The compressed sensing imaging method A comprises the following steps:
firstly, a target image 1 is placed in the object distance range of a first lens 2, a DMD device 3 is positioned on the focal plane of the first lens 2, a second lens 4 is positioned in the object distance range of a negative direction reflecting surface of the DMD device 3, and a first unit detector 5 is positioned on the focal point of the second lens 4;
step two, the processor 10 controls the driver 9 to gradually perform H transformation on the reflection lens in the area with the size of the corresponding target image size of the DMD device, the corresponding reflection lens of the DMD device is turned to the negative direction by the H transformation in each step, and the rest reflection lenses are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by the first unit detector 5 through the second lens 4 to form first total energy reflected by the DMD device in the step of H conversion, and the first total energy is converted into first digital quantity through the AD converter and then sent to the processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the first digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
The compressed sensing imaging method B of the present invention may also include the steps of:
step one, a target image 1 is placed in an object distance range of a first lens 2, a DMD device 3 is located on a focal plane of the first lens 2, a third lens 7 is located in an object distance range of a positive direction reflecting surface of the DMD device 3, and a second unit detector 8 is located on a focal point of the third lens 7;
step two, the processor 10 controls the driver 9 to gradually perform H transformation on the reflection lens in the area with the size of the corresponding target image size of the DMD device, the corresponding reflection lens of the DMD device is turned to the negative direction by the H transformation in each step, and the rest reflection lenses are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each positive direction reflecting mirror of the DMD device is received by a second unit detector 8 through a third lens 7 to form a second total energy reflected by the DMD device in the step of H conversion, and the second total energy is converted into a second digital quantity through an AD converter and then sent to a processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the second digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
The compressed sensing imaging method C of the present invention may further include the steps of:
firstly, a target image 1 is placed in the object distance range of a first lens 2, a DMD device 3 is positioned on the focal plane of the first lens 2, a second lens 4 is positioned in the object distance range of a negative direction reflecting surface of the DMD device 3, and a first unit detector 5 is positioned on the focal point of the second lens 4; the third lens 7 is positioned in the object distance range of the positive direction reflecting surface of the DMD device 3, and the second unit detector 8 is positioned on the focus of the third lens 7;
step two, the processor 10 controls the driver 9 to gradually perform H transformation on the reflection lens in the area with the size of the corresponding target image size of the DMD device, the corresponding reflection lens of the DMD device is turned to the negative direction by the H transformation in each step, and the rest reflection lenses are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by the first unit detector 5 through the second lens 4 to form first total energy reflected by the DMD device in the step of H conversion, and the first total energy is converted into first digital quantity through the AD converter and then sent to the processor for storage;
the total sum of the light signal values reflected by each positive direction reflecting mirror of the DMD device is received by a second unit detector 8 through a third lens 7 to form a second total energy reflected by the DMD device in the step H, and the second total energy is converted into a second digital quantity through an AD converter and then sent to a processor for storage;
and step three, after the reflector lens of the area with the size corresponding to the target image size of the DMD device is driven to complete the whole H conversion, combining the first digital quantity and the second digital quantity formed in each step of H conversion into a superposed digital quantity, forming a sequence optical signal digital quantity in the processor, providing the sequence optical signal digital quantity to the processor, and calculating a high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
Example (b): sampling a target by implementing 1024-order hadamard matrix transformation by means of a DMD device and reconstructing a target image by using an OMP algorithm
TABLE 1 reconstruction characteristics of a single H-matrix under OMP using DMD
Figure BDA0001484944550000111
In the table, a 1024-order H matrix is a 1024-order Hadamard matrix and corresponds to a compressed sensing imaging method C;
h matrix (+) of order 1024 indicates that the +1 part of the Hadamard matrix is reserved, -1 is replaced by 0; corresponding to the compressed sensing imaging method B;
the H matrix (-) of order 1024 represents the part where-1 in the hadamard matrix is reserved, and +1 is replaced by 0, corresponding to the compressed sensing imaging method a.
MSE is mean square error, RE is relative error, PSNR is peak signal-to-noise ratio, MdBAn amount of signal to noise improvement. Compared with the signal-to-noise ratio improvement amount 32 of the classical Hadamard transform optical method, the existing method is improved by three times, and the quality of a reconstructed image is greatly improved.
In table 1, the compressed sensing results of the hadamard matrix of 1024 orders are calculated according to the three classifications, and we can see that the reconstructed image is very vivid by combining fig. 2.
In summary, the three methods of the present invention can be used to complete image acquisition by the DMD device, and then provide the acquired image to the reconstruction algorithm for calculation and recovery to obtain the final target image.

Claims (6)

1. A Hadamard matrix perception imaging system comprising a first lens (2), a DMD device (3), a second lens (4), a first cell detector (5), an AD converter (6), and a processor (10), characterized in that:
the micromirror array of the DMD device (3) is arranged according to a Hadamard matrix and is driven by the processor (10) to gradually carry out H conversion;
the DMD device (3) is located on a focal plane of the first lens (2), the second lens (4) is located in an object distance range of a reflecting surface of the DMD device (3), the first unit detector (5) is located on a focal point of the second lens (4), first total energy of each step of H conversion reflection of the DMD device is measured, converted into first digital quantity through an AD converter (6), and then sent to the processor (10);
the first total energy is the sum of optical signal values of all reflection lenses of the DMD device in the negative direction in an overturning and reflecting mode;
the first digital quantity formed in each step of H transformation forms a sequence optical signal digital quantity in a processor (10), and the sequence optical signal digital quantity is provided for the processor to calculate a high peak signal-to-noise ratio reconstructed image of a target image by adopting an orthogonal matching tracking method in a compressed sensing method;
when the processor (10) drives to carry out H transformation step by step, a Sylvester type H matrix is constructed in a low-order to high-order recursive mode, and the matrix is a Hadamard matrix:
Figure FDA0002661237600000011
wherein 1 isnIs an identity matrix of order n,
Figure FDA0002661237600000012
is a 2 nd order H matrix and satisfies
Figure FDA0002661237600000013
In the H transformation, the reflecting mirror plates corresponding to each element of the second-order H matrix are totally performed by 22The other modes of the secondary flip are as follows:
Figure FDA0002661237600000021
corresponding n-th order H matrix is performed by 22Step transformation, which can be used to obtain other modes of H matrix of each order, and the maximum mode number is n2I.e. making n for the target2Sub-sampling, n being the order of the hadamard matrix used, n2Is the total number of pixels of the image formed, and at most completes all n2After sub-sampling, the value of each pixel is solved.
2. The Hadamard matrix perception imaging system of claim 1, wherein:
the Hadamard matrix is an H matrix of 128 th order, 256 th order, 512 th order, 1024 th order, 2048 th order or 4096 th order.
3. The Hadamard matrix perception imaging system of claim 1 or 2, wherein:
the DMD device is also provided with a third lens (7) and a second unit detector (8), wherein the third lens (7) is positioned in the object distance range of the positive direction reflecting surface of the DMD device 3, and the second unit detector (8) is positioned on the focal point of the third lens (7); a second unit detector (8) measures the second total energy reflected by each step of H conversion of the DMD device, converts the second total energy into a second digital quantity through an AD converter and then sends the second digital quantity to a processor (10);
the second total energy is the sum of the values of the optical signals which are reversely reflected in the positive direction of each reflector of the DMD device (3);
the second digital quantity formed in each step of H transformation forms a sequence optical signal digital quantity in a processor (10), and the sequence optical signal digital quantity is provided for the processor to calculate a high peak signal-to-noise ratio reconstructed image of a target image by adopting an orthogonal matching tracking method in a compressed sensing method;
or the first digital quantity and the second digital quantity formed in each step of H conversion are combined into superposed digital quantity, and the superposed digital quantity forms a sequence optical signal digital quantity in a processor (10), and is provided for the processor to adopt an orthogonal matching tracking method in a compressed sensing method to calculate a high peak signal-to-noise ratio reconstructed image of a target image.
4. The compressed sensing imaging method based on the Hadamard matrix sensing imaging system of claim 1 or 2, characterized by comprising the following steps:
placing a target image (1) in an object distance range of a first lens (2), positioning a DMD (digital micromirror device) device (3) on a focal plane of the first lens (2), positioning a second lens (4) in an object distance range of a negative direction reflecting surface of the DMD device (3), and positioning a first unit detector (5) on a focal point of the second lens (4);
step two, the processor (10) controls the driver (9) to gradually perform H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction through the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by a first unit detector (5) through a second lens (4), so that first total energy reflected by the DMD device in the step of H conversion is formed, and the first total energy is converted into first digital quantity through an AD converter and then sent to a processor for storage;
when H transformation is carried out step by step, an H matrix is constructed in a recursive mode from a low order to a high order:
Figure FDA0002661237600000031
wherein 1 isnIs an identity matrix of order n,
Figure FDA0002661237600000032
is a 2 nd order H matrix and satisfies
Figure FDA0002661237600000033
In the H transformation, the reflecting mirror plates corresponding to each element of the second-order H matrix are totally performed by 22The other modes of the secondary flip are as follows:
Figure FDA0002661237600000034
corresponding n-th order H matrix is performed by 22Step transformation, which can be used to obtain other modes of H matrix of each order, and the maximum mode number is n2；
And step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the first digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
5. The compressed sensing imaging method of the Hadamard matrix sensing imaging system according to claim 3, comprising the following steps:
placing a target image (1) in an object distance range of a first lens (2), positioning a DMD (digital micromirror device) device (3) on a focal plane of the first lens (2), positioning a third lens (7) in an object distance range of a positive direction reflecting surface of the DMD device (3), and positioning a second unit detector (8) on a focal point of the third lens (7);
step two, the processor (10) controls the driver (9) to gradually perform H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction through the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each positive direction reflecting mirror of the DMD device is received by a second unit detector (8) through a third lens (7), so that second total energy reflected by the DMD device in the step of H conversion is formed, and the second total energy is converted into second digital quantity through an AD converter and then sent to a processor for storage;
when H transformation is carried out step by step, an H matrix is constructed in a recursive mode from a low order to a high order:
Figure FDA0002661237600000041
wherein 1 isnIs an identity matrix of order n,
Figure FDA0002661237600000042
is a 2 nd order H matrix and satisfies
Figure FDA0002661237600000043
In the H transformation, the reflecting mirror plates corresponding to each element of the second-order H matrix are totally performed by 22The other modes of the secondary flip are as follows:
Figure FDA0002661237600000044
corresponding n-th order H matrix is performed by 22Step transformation, which can be used to obtain other modes of H matrix of each order, and the maximum mode number is n2；
And step three, after the reflector lens of the area with the size corresponding to the target image of the DMD device is driven to complete the whole H conversion, the second digital quantity formed in each step of H conversion forms a sequence optical signal digital quantity in the processor, and the sequence optical signal digital quantity is provided for the processor to calculate the high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
6. The compressed sensing imaging method of the Hadamard matrix sensing imaging system according to claim 3, comprising the following steps:
placing a target image (1) in an object distance range of a first lens (2), positioning a DMD (digital micromirror device) device (3) on a focal plane of the first lens (2), positioning a second lens (4) in an object distance range of a negative direction reflecting surface of the DMD device (3), and positioning a first unit detector (5) on a focal point of the second lens (4); the third lens (7) is positioned in the object distance range of the positive direction reflecting surface of the DMD device (3), and the second unit detector (8) is positioned on the focus of the third lens (7);
step two, the processor (10) controls the driver (9) to gradually perform H transformation on the reflecting mirror plates in the area with the size of the corresponding target image of the DMD device, the corresponding reflecting mirror plates of the DMD device are turned to the negative direction through the H transformation in each step, and the rest reflecting mirror plates are turned to the positive direction:
in each step of H conversion, the sum of the light signal values reflected by each negative direction reflecting mirror of the DMD device is received by a first unit detector (5) through a second lens (4), so that first total energy reflected by the DMD device in the step of H conversion is formed, and the first total energy is converted into first digital quantity through an AD converter and then sent to a processor for storage;
the total sum of the light signal values reflected by each positive direction reflecting lens of the DMD device is received by a second unit detector (8) through a third lens (7), so that the second total energy reflected by the DMD device is converted by the step H, converted into a second digital quantity through an AD converter and sent to a processor for storage;
when H transformation is carried out step by step, an H matrix is constructed in a recursive mode from a low order to a high order:
Figure FDA0002661237600000051
wherein 1 isnIs an identity matrix of order n,
Figure FDA0002661237600000061
is a 2 nd order H matrix and satisfies
Figure FDA0002661237600000062
In the H transformation, the reflecting mirror plates corresponding to each element of the second-order H matrix are totally performed by 22The other modes of the secondary flip are as follows:
Figure FDA0002661237600000063
corresponding n-th order H matrix is performed by 22Step transformation, which can be used to obtain other modes of H matrix of each order, and the maximum mode number is n2；
And step three, after the reflector lens of the area with the size corresponding to the target image size of the DMD device is driven to complete the whole H conversion, combining the first digital quantity and the second digital quantity formed in each step of H conversion into a superposed digital quantity, forming a sequence optical signal digital quantity in the processor, providing the sequence optical signal digital quantity to the processor, and calculating a high peak signal-to-noise ratio reconstructed image of the target image by adopting an orthogonal matching tracking method in a compressed sensing method.
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