CN110349233A - The single pixel dependent imaging that high quality is rebuild is realized using iterative phase searching algorithm - Google Patents

Abstract

The present invention is a single-pixel correlation imaging that uses an iterative phase retrieval algorithm to achieve high-quality reconstruction. The steps include: 1) based on a Hadamard matrix, pre-generate a series of intensity patterns, and use an iterative phase retrieval algorithm to decompose each intensity pattern into a Noisy phase profiles; 2) Collimated illumination of the laser beam, with two phase-only spatial light modulators embedded in each pair of phase profiles in turn; the free-space propagation field through the first phase-only plane is performed by using Fresnel diffraction. , the free-space propagating field through the second pure phase plane is also similar; the measured intensities are recorded by a barrel detector located behind the object that does not require spatial resolution; 3) the measured intensities that will be recorded will be recorded using the same cascade basis A series of intensity patterns generated and calculated by the facility are correlated with each other; 4) The calculated reference intensity patterns are correlated with the measured intensities, and the target is decrypted using the correlation function. The method of the present invention is simple and easy to implement.

Description

Single Pixel Correlation Imaging with High Quality Reconstruction Using Iterative Phase Retrieval Algorithm

technical field

The invention belongs to the technical field of image security, and relates to a single-pixel correlation imaging using an iterative phase retrieval algorithm to achieve high-quality reconstruction.

Background technique

Single-pixel correlation imaging, also known as ghost imaging, is one of the most attractive optical techniques and has received increasing attention due to its excellent physical properties. So far, applications based on single-pixel imaging have been widely developed. With the development of optical information encryption technology, the application research of single-pixel imaging technology in this field has attracted more and more attention. Most importantly, a large number of new configurations and algorithms for single-pixel imaging have been explored, however, these algorithms require not only reduced number of measurements and strict hardware constraints, but also improved robustness to noise and fast reconstruction of images.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a single-pixel correlation imaging that uses an iterative phase retrieval algorithm to achieve high-quality reconstruction, which solves the need for the prior art algorithm not only to reduce the number of measurements and strict hardware constraints, but also to improve the robustness against noise. sexual issues.

The technical solution adopted by the present invention is a single-pixel correlation imaging that utilizes an iterative phase retrieval algorithm to achieve high-quality reconstruction, and the method is implemented according to the following steps:

Step 1: Based on the Hadamard matrix with a certain order, a series of intensity patterns are pre-generated, and an iterative phase retrieval algorithm is used to decompose each intensity pattern into a pair of noisy phase profiles;

Step 2: During the imaging process, the laser beam is collimated and illuminated, and each pair of phase profiles is sequentially embedded with two pure-phase spatial light modulators; the free-space propagation field through the first pure-phase plane is carried out by using Fresnel diffraction, The free-space propagating field through the second pure phase plane is similar; the measured intensity _Bi is recorded by a barrel detector located behind the object which does not require spatial resolution;

Step 3: To reconstruct the image, the measured intensities recorded by the bucket detector will be correlated with a series of intensity patterns generated and calculated using the same cascade infrastructure;

Step 4: The calculated reference intensity pattern is correlated with the measured intensity, and the target is decrypted using the correlation function.

The beneficial effects of the present invention include the following aspects: 1) The decryption effect is very satisfactory, and the image content can be clearly observed without using post-processing such as Gaussian low-pass filtering. 2) When the measured intensity is less recorded with the bucket detector, the image with lower visual quality can also be decrypted during reconstruction. 3) For grayscale patterns, decryption results with high visual quality can also be efficiently obtained using the proposed single-pixel correlation imaging system. 4) The Walsh-Hadamard pattern is spatially orthogonal without any redundancy, and the reconstruction result is very clear, much better than the result of random pattern decryption. At the same time, the number of measured intensities is reduced, and the imaging efficiency is greatly improved.

Description of drawings

Fig. 1 is the system principle diagram of single-pixel correlation imaging adopted by the present invention;

Figure 2a is a typical pattern generated from a row vector of the Hadamard matrix, Figure 2b is a first phase profile, Figure 2c is a second phase profile, and Figure 2d is a graph of the relationship between the number of iterations and the correlation coefficient;

Figure 3a is the correlation between each pair of phase profiles α _i (x, y) and β _i (ξ, η), and Figure 3b is the set and set ( ξ,η), Figure 3c is the correlation between the first phase contour in the set β(ξ,η) and all the contours in the set (x,y).

Figure 4a is the original binary image, Figure 4b is the distribution of the measured intensity, Figure 4c is the reconstruction using the second-order correlation algorithm, and Figure 4d is the optimized reconstruction using the _l0 smoothing algorithm;

Fig. 5a, Fig. 5b, Fig. 5c, Fig. 5d are the decryption of the recorded measured intensity using the phase profiles of 30%, 50%, 70%, and 90%, respectively;

Figure 6a is a decoding pattern using a phase profile pair of 1.5%, and Figure 6b is the corresponding nonlinear correlation diagram;

Figure 7a is the grayscale image, Figure 7b is the reconstructed image using the second-order correlation algorithm, Figure 7c is the reconstructed image using a 3.5% phase profile pair, and Figure 7d is the corresponding nonlinear correlation map.

In the figure, 1. laser, 2. lens, 3. spatial light modulator one, 4. spatial light modulator two, 5. object, 6. barrel detector, 7. processor.

Detailed ways

The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

In order to improve the quality of reconstructed images with less measured intensities, the present invention proposes a single-pixel correlation imaging (method) that uses an iterative phase retrieval algorithm to achieve high-quality reconstruction. As shown in FIG. 1 , the present invention uses single-pixel correlation imaging for An optical cascade sensing infrastructure is provided, the structure of which includes a laser 1, a lens 2, a spatial light modulator 1 3, a spatial light modulator 2 4, an object 5, and a barrel detector 6 arranged in sequence along the horizontal axis. and processor 7.

The method of the present invention utilizes the above-mentioned optical cascade sensing infrastructure, and is implemented according to the following steps:

Step 1: Based on the Hadamard matrix with a certain order, a series of intensity patterns are pre-generated, and an iterative phase retrieval algorithm is used to decompose each intensity pattern into a pair of noisy phase profiles. The specific process is:

Assuming K is the total number of patterns, a series of intensity patterns I _i (μ,ν)[i=1,2,3,...,K] are pre-generated Hadamard matrices with a certain order, and an iterative phase retrieval algorithm is used Decompose each intensity mode into a pair of noisy phase profiles α _i (x, y) and β _i (ξ, η), where (x, y) and (ξ, η) represent the coordinates of the plane of the two phases, respectively ,

Basic blocks of order 2 are often used to construct Hadamard matrices of arbitrary order, which are mathematically defined as:

Then, the Hadamard matrix with 2 ^k is obtained using the following recursive formula:

Hadamard matrices in any order are square and symmetric, where each element is equal to +1 or -1; suppose the size of the object to be imaged is M×N pixels, which satisfies the condition M×N=2 ^k ; with formula (1 ) and formula (2) After computing a Hadamard matrix with order ^2k , random permutations are applied between row vectors, and elements with -1 in each row vector are set to 0; then, the i-th row vector is The rearrangement into a two-dimensional intensity pattern I _i (μ,ν) has M×N pixels; thus, yielding a total of ^2k intensity patterns, which are fully or partially used in the process of single-pixel correlation imaging,

In order to obtain the corresponding phase profiles α _i (x, y) and β _i (ξ, η), an iterative phase recovery algorithm is used, and the specific process is as follows:

1.1) Two pure phase masks exp(jα _i (x, y)) and exp(jβ _i (ξ, η)) are generated to M×N pixels, where the two initial phase profiles are in the range [0, 2π] are randomly distributed within; in subsequent iterative steps, these phase profiles are updated by treating the intensity patterns as amplitude constraints;

1.2) In the nth round, the wave forward propagation between the first phase plane and the second phase plane is expressed as:

where d ₁ represents the axial distance between the two phase planes;

1.3) Forward propagation between the second phase plane and the object plane, the expression is:

Wherein, d ₂ represents the axial distance between the second phase plane and the object plane;

1.4) Apply the intensity mode I _i (μ,ν) as the amplitude constraint to update the complex-valued wave Then propagate backward, the expression is:

Among them, FWP _λ,-d represents free-space backpropagation, and |.| represents modulo operation;

1.5) Update the pure phase mask with the help of the acquired wavefront On the second-stage unique plane, the expression is:

1.6) Update complex-valued waves Then the wave backward propagation is performed, and the expression is:

1.7) Update the pure phase mask in the first pure phase plane, the expression is:

1.8) Estimate the correlation coefficient CC between the magnitudes of the objects, and the pre-generated pattern I _i (μ,ν) is calculated as the convergence criterion to determine whether the iterative process stops or not, the expression is:

where E[.] represents the expected value operator, and coordinates are omitted for brevity; usually, a real value very close to 1 is set as the threshold for the correlation coefficient to ensure the best iterative result;

1.9) Repeat the above steps 1.2)-step 1.8) until the CC value reaches the predetermined threshold; once the iterative process is over, the final updated result and will be considered as two decomposed phase profiles.

Step 2: During the imaging process, the laser beam is collimated and illuminated, and each pair of phase profiles is sequentially embedded with two pure-phase spatial light modulators; the free-space propagation field through the first pure-phase plane is carried out by using Fresnel diffraction, The free-space propagating field through the second pure phase plane is similar; the measured intensity B _i is recorded by a barrel detector located behind the object which does not require spatial resolution by:

During the imaging process, the laser beam is collimated and illuminated, and each pair of phase profiles is sequentially embedded with two phase-only spatial light modulators; the wave is formed by two phase-only masks exp( _jαi (x,y)) and exp( jβ _i (ξ,η)), The resulting speckle pattern traverses the object; the measured intensity B _i is recorded by a bucket detector located behind the object that does not require spatial resolution and is mathematically expressed as:

Among them, T(μ,ν) is the transfer function of the object, (μ,ν) is the truncation coordinate of the target plane, FWP _λ,d represents the propagation of the free space wave, λ is the wavelength of light, and d is the axial distance;

The free-space propagating field through the first phase plane is carried out using Fresnel diffraction and is expressed as:

Among them, * represents the convolution calculation, h(x, y, d ₁ ) is the point impulse function of Fresnel propagation, which is defined as:

Similarly, the free-space propagation field through the second phase plane is expressed as:

The corresponding point impulse function is expressed as:

Step 3: To reconstruct the image, the measured intensities recorded by the bucket detectors will be correlated with a series of intensity patterns generated and calculated using the same cascade infrastructure as:

To reconstruct the image, the measured intensities recorded by the bucket detectors will be correlated with a series of intensity patterns I _i '(μ,ν) [i=1,2,3,...,K] denoted as , using the same Cascade Infrastructure (Optical Cascade Sensing Infrastructure) is generated and calculated as

Step 4: The calculated reference intensity pattern is associated with the measured intensity, and the target is decrypted using the correlation function. The specific process is:

The reference intensity pattern I _i (μ,ν) is associated with the measured intensity B _i , and the target is decrypted using a correlation function whose expression is:

Serve.

Experiment on the effectiveness of the present invention

To evaluate the effectiveness of the single-pixel correlation imaging method of the present invention as shown in FIG. 1 , a plane wave with a wavelength of 632.8 nm and a 740.4 μm simulated illumination were used. When decomposing the pre-generated intensity pattern into two noisy phase profiles, the axial distances d1 and _{d2 were} set to 30 mm and 44 mm, respectively. Intensities measured during the recording process, a series of phase-only masks exp( _jαi (x,y)) and exp( _jβi (ξ,η))[i=1,2,3,...,K] cascaded and sequentially embedded into two 20 μm spatial light modulators with 64 × 64 pixel size and pixel pitch. For the sake of argument, the set denoted α(x,y) consists of the phase profiles retrieved in the first pure phase plane, and the set β(ξ,η) consists of the phase profiles in the second stage.

The derivation of pre-generated intensity patterns from a row vector of a Hadamard matrix with order 2 ¹² is shown in Figure 2a. It indicates that the size of each intensity pattern is 64×64 pixels. Two corresponding phase profiles are shown in Fig. 2b and Fig. 2c, respectively, which were extracted by using an iterative phase retrieval algorithm. The proposed phase retrieval procedure has a high convergence speed, and after performing 6 iterations, the correlation coefficient value between the original intensity pattern and its estimate reaches more than 0.99.

According to the intensity pattern shown in Fig. 2a, the relationship between the number of iterations and the correlation coefficient is shown in Fig. 2d. Similar relationships can be obtained for other intensity modes. In single-pixel correlation imaging methods, it is best to avoid extracted phase profiles that have strong correlations with each other. Figure 3a is the correlation between each pair of phase profiles α _i (x, y) and β _i (ξ, η), and Figure 3b is the set and set ( ξ,η), Figure 3c is the correlation between the first phase contour in the set β(ξ,η) and all the contours in the set (x,y). As can be seen from these figures, the retrieved phase profiles are very uncorrelated, which fulfills the requirements of a single-pixel correlated imaging system.

Figure 4a shows a 64 × 64 pixel binary image that will be encrypted using the proposed single-pixel correlation imaging method. When sequentially embedding all phase profile pairs, a one-dimensional vector consisting of 4096 measured intensities recorded by the bucket detector can be obtained. Figure 4b depicts the results of the measured intensities, from which it can be seen that the information of the original binary image is fully encrypted and the distribution of the measured intensities is random. In addition to all phase profile pairs, there are also optical parameters such as light wavelength and axial distance that can be considered the main key. When all keys are applied correctly, the original image can be decrypted using a second order correlation algorithm. As shown in Fig. 4c, it is clear that the decryption results are very satisfactory, where the structured content is clearly observed without the use of post-processing such as Gaussian low-pass filtering. To quantitatively evaluate the quality of the reconstruction results, the noise ratio (PSNR) between the original pattern and its reconstructed image is calculated as:

Among them, f represents the original pattern, and g represents the reconstruction result. The coordinates are omitted for brevity. The mean squared error (MSE) between them is expressed as:

For the reconstruction shown in Fig. 4c, the peak signal-to-noise ratio and correlation coefficient are 46.4176 dB and 0.999955, respectively. The use of optimization methods such as the smoothing l ₀ algorithm can further improve the quality of the reconstruction results. The optimized reconstruction with high fidelity is shown in Fig. 4d, with a peak signal-to-noise ratio equal to 1 and a correlation coefficient of 274.6880dB.

Validation of the invention

Patterns with lower visual quality can also be deciphered when a smaller number of measured intensities are recorded with the bucket detector for reconstruction. Therefore, it is an important issue to reduce the number of phase profile pairs as much as possible under the premise of certain visual requirements, which will facilitate key management. When 30.0%, 50.0%, 70.0% and 90.0% phase profile pairs were cascaded and sequentially embedded into two spatial light modulators to record the measured intensities, the deciphered patterns are shown in Fig. 5a, Fig. 5b, Fig. 5c and 5d, the corresponding peak signal-to-noise ratio, mean square error and correlation coefficient are listed in Table 1.

Table 1 is the PSNR, MSE and CC values of the reconstruction results using 30%, 50%, 70% and 90% of the phase profile respectively (Table 1 has been added to the accompanying drawings);

Table 1. Comparison of Four Phase Profile Reconstruction Results

It can be seen that as the number of phase profile pairs increases, the quality of the decrypted pattern keeps improving. It is worth noting that although the reconstructed image is very blurred with a phase profile of 30.0%, the information of the original pattern can still be seen. Furthermore, if there is no need to visually observe the original pattern, a nonlinear correlation algorithm can be used to verify its existence with a very small number of phase profile pairs. Figure 6a shows the decrypted noise pattern using only 1.5% of the phase profile pairs, from which no meaningful information can be obtained. However, the relationship between the corresponding nonlinear correlogram pattern and its reconstruction suggests the presence of the original object, as only one spike is observed in Fig. 6b.

For grayscale images, decryption results with high visual quality can also be efficiently obtained using the proposed single-pixel correlation imaging system. As shown in Fig. 7a, the pattern with 64 × 64 pixels cropped from the central part of the image "Lena" was considered as the original information, which was selected from the USC-SIPI image database. By using a second-order correlation algorithm, reconstructions were decrypted from all measured intensities, which were recorded with 4096 pairs of phase profiles, as shown in Fig. 7b. Similar to the results shown in Fig. 4c, the structured content of the original pattern can be completely distinguished. The peak signal-to-noise ratio and correlation coefficient are 47.0479dB and 0.9998, respectively. The reconstruction when only 3.5% of the phase profile pairs are used is shown in Fig. 7c, where no meaningful information is presented. The nonlinear correlation plot between the pattern and its reconstruction is depicted in Fig. 7d, where only one significant peak on the noisy background is observed to demonstrate the presence of the original object. It is worth noting that the number of phase profile pairs applied in a single-pixel correlation imaging system increases to a certain extent, because the grayscale mode has a larger spectral range and more information compared to the binary mode.

A Walsh-Hadamard pattern is applied to illuminate the object to record measured pairs of intensities, and the difference between a pair of measured intensities is taken as the result. Because the Walsh-Hadamard patterns are spatially orthogonal without any redundancy, the reconstruction results are very clean and much better than decrypted with random patterns. At the same time, the number of measured intensities is reduced, so that the imaging efficiency can be greatly improved. Compared with this imaging scheme, the proposed single-pixel correlation imaging system has higher efficiency. According to the 64×64 pixel object shown in Fig. 4a, in the above scheme, a total of 8192 measured intensities need to be recorded with the bucket detector 6, while only 4096 measured values are collected in the imaging method proposed in the present invention.

Claims (5)

1. a kind of single pixel dependent imaging for realizing that high quality is rebuild using iterative phase searching algorithm, which is characterized in that according to Following steps are implemented:

Step 1: based on the hadamard matrix with certain order, having pre-generated a series of intensity modes, and used iteration phase Each intensity mode is decomposed into a pair of noisy phase outline by position searching algorithm；

Step 2: in imaging process, collimated illumination being carried out to laser beam, it is empty that each pair of phase section is sequentially embedded two pure phase positions Between optical modulator；It is carried out by the free-space propagation field of the first pure phase bit plane by using Fresel diffraction, passes through second The free-space propagation field of pure phase bit plane is also similar；The intensity B of measurement_iThe space that do not need by being located at object rear is divided The bucket detector of resolution records；

Step 3: for reconstruction image, the measurement intensity of bucket detector record will generate simultaneously with identical cascaded basis facility is used A series of intensity modes calculated are interrelated；

Step 4: calculated referenced strength mode is associated with the intensity measured, is solved using correlation function to target It is close.

2. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm, It is characterized in that, detailed process is in the step 1:

Assuming that K is the sum of pattern, a series of intensity mode I_i(μ, ν) [i=1,2,3 ..., K] it is pre-generated with certain The Hadamard matrix of order, and each intensity mode is decomposed by a pair of noisy phase using iterative phase searching algorithm Profile α_i(x, y) and β_i(ξ, η), wherein (x, y) and (ξ, η) respectively indicates the plane in two stages of coordinate,

The basic block of 2 ranks is mathematically defined as commonly used in the hadamard matrix of building arbitrary order:

Then, being obtained using following recurrence formula has 2^kHadamard matrix:

The Hadamard matrix of any sequence is all square and symmetrical, wherein each element is equal to+1 or -1；Assuming that will be at The size of the object of picture is M × N pixel, meets condition M × N=2^k；Being calculated with formula (1) and formula (2) has order 2^k's After Hadamard matrix, random permutation is applied between row vector, and the element in each row vector with -1 is set It is set to 0；Then, the i-th row vector is rearranged into two-dimensional intensity mode I_i(μ, ν) has M × N pixel；Therefore, it generates in total 2^kA intensity pattern, during being completely or partially used for single pixel dependent imaging,

In order to obtain corresponding phase outline α_i(x, y) and β_i(ξ, η), using a kind of Phase Retrieve Algorithm of iteration, detailed process It is as follows:

1.1) by two phase-only mask exp (j α_i(x, y)) and exp (j β_i(ξ, η)) M × N number of pixel is generated, at the beginning of two of them Beginning phase outline random distribution in [0,2 π] range；In subsequent iterative step, by the way that intensity mode is considered as amplitude about Beam updates these phase outlines；

1.2) in being taken turns n-th, the wave propagated forward between first phase plane and second phase plane, expression formula are as follows:

Wherein, d₁Indicate the axial distance between two phase planes；

1.3) propagated forward between second phase plane and object plane, expression formula are as follows:

Wherein, d₂Indicate the axial distance between second phase plane and object plane；

1.4) intensity mode I is applied_i(μ, ν) is that amplitude constrains to update complex value wave V_i ⁽ⁿ⁾(μ, ν), then back-propagation, expression formula Are as follows:

Wherein, FWP_λ,-dIndicate free space backpropagation, | | indicate modulo operation；

1.5) in the case where obtaining wavefront and helping, phase-only mask is updatedIn the unique plane of second stage, Expression formula are as follows:

1.6) complex value wave W is updated_i ⁽ⁿ⁾(ξ, η) then executes wave back-propagating, expression formula are as follows:

1.7) phase-only mask in first pure phase bit plane is updated, expression formula are as follows:

1.8) estimate the related coefficient CC between object amplitude, | V_i ⁽ⁿ⁾(μ,ν)|²With pre-generated mode I_i(μ, ν) is calculated as Convergence, to determine whether iterative process stops, expression formula are as follows:

Wherein, E [] indicates desired value operator；Set very close 1 real number value to the threshold value of related coefficient；

1.9) repeat the above steps 1.2)-step 1.8), until CC value reaches predetermined threshold；Once at the end of iterative process, most The result updated afterwardsWithIt will be considered as the phase outline of two decomposition.

3. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm, It is characterized in that, detailed process is in the step 2:

In imaging process, collimated illumination is carried out to laser beam, each pair of phase section is sequentially embedded two pure phase bit space light tune Device processed；Wave is by two phase-only mask exp (j α_i(x, y)) and exp (j β_i(ξ, η)),Obtained speckle pattern is worn Cross object；The intensity B of measurement_iBy being located at the bucket detector record for not needing spatial resolution at object rear, mathematical expression Formula are as follows:

Wherein, T (μ, ν) is the transmission function of object, and (μ, ν) is the transversal coordinate of objective plane, FWP_λ,dIndicate free space wave Propagation, λ is optical wavelength, and d is axial distance；

It is carried out by the free-space propagation field of first phase plane using Fresel diffraction, expression formula are as follows:

Wherein, * indicates convolutional calculation, h (x, y, d₁) be Fresnel propagation point impulse function, is defined as:

Similarly, pass through the free-space propagation field expression formula of second phase plane are as follows:

Corresponding impulse function indicates are as follows:

4. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm, It is characterized in that, detailed process is in the step 3:

For reconstruction image, the measurement intensity recorded by bucket detector by with a series of intensity mode I ' for being expressed as_i(μ,ν)[i =1,2,3 ..., K] it is interrelated, it generates and is calculated as using identical cascaded basis facility

5. the single pixel dependent imaging according to claim 1 for realizing that high quality is rebuild using iterative phase searching algorithm, It is characterized in that, detailed process is in the step 4:

Referenced strength mode I_i(μ, ν) and the intensity B measured_iIt is associated, target is decrypted using correlation function, the phase Close the expression formula of function are as follows: