A single-lens achromatic computational imaging method and system based on deep learning

Abstract

The application discloses a kind of single-lens achromatic computational imaging method and system based on deep learning, comprising the following steps: step 1: after input image is imaged by single lens, the complex amplitude distribution of the light field of single-lens imaging is recovered from the input image by complex amplitude recovery network;Step 2: construct a virtual lens, according to the convolution of the complex amplitude distribution obtained in step 1 and the point spread function of the virtual lens, obtain the complex amplitude distribution on the virtual lens image;Step 3: according to the complex amplitude distribution in step 2, the achromatic image can be obtained;The application adopts network model and virtual lens, constructs the whole link differentiable computational imaging model, and can eliminate the chromatic aberration of the image obtained by single lens;Solve the problem that the existing achromatic imaging technology is low in efficiency, complex in production, high in engineering cost and limited in imaging quality in actual imaging use, avoid complex optical system design, realize high-fidelity wide-spectrum achromatic imaging of single lens.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of optical imaging technology, and in particular to a single-lens achromatic computational imaging method and system based on deep learning. BACKGROUND

[0002] In modern camera design, wide-spectrum achromatic imaging of small optical systems is very important. Even if the sensor has been greatly miniaturized, the complex optical lens makes it difficult for the entire camera to be very small. It is difficult to take high-fidelity images using a simple optical system, such as a single lens. Because the chromatic aberration of a single lens will cause serious image blurring. Chromatic aberration is due to the different refractive indices of lens materials for different wavelengths of light, resulting in different imaging positions and magnifications for the same object at different wavelengths. Traditional optical design uses at least two lenses to achieve chromatic aberration compensation, which compensates for chromatic aberration by complementary high and low refractive index lenses, but increases the volume of the optical system. On the basis of the traditional optical design method, reducing the size of the optical system is a very reliable and effective method. For example, the superlens has great advantages in small optical imaging systems due to its structural thickness being on the wavelength scale or below. However, the method based on optical superlens design requires higher experience for designers and has higher manufacturing costs.

[0003] Computational imaging is another method of achieving achromatic imaging through the coordinated design of optical systems and post-processing algorithms. By designing an optical system to encode the light field, the required information is decoded from the captured image using post-processing algorithms. With the rapid development of artificial intelligence technology, deep learning has shown great advantages in solving ill-posed inverse problems with noise. And the introduction of deep learning has gradually become the core force driving the development of the field of computational imaging. By combining the design of the front-end optical system and the optimization of the post-image reconstruction network, the existing computational imaging method achieves good achromatic imaging of small optical systems, but the lenses designed by these methods are generally diffractive lenses, and the manufacturing process is complex.

[0004] The existing solutions, such as superlenses, can adjust the properties of light at subwavelength resolution, which makes them promising for developing planar optical elements. By fine-tuned subwavelength structures, the refractive angles of light of different wavelengths are made the same, so as to converge to the same point. Superlenses achieve achromatic imaging from the visible light band. Compared with traditional multi-lenses, superlenses focus incident light with smaller size, realizing achromatic imaging of single-piece lenses. Traditional multi-lens groups rely on spherical or aspherical surfaces on multiple optical materials to obtain the required progressive phase. However, such superlens design requires very professional optical design knowledge and experience, and puts high requirements on the processing technology; the design is difficult and the processing cost is high; and the superlens designed can only be used for specific imaging tasks, such as achromatic imaging for specific waveband range.

[0005] Achromatic diffractive lenses make the PSF distribution the same for different wavelengths by designing special diffractive optical elements. This feature ensures good color characteristics and helps correct residual aberrations of the captured image in the subsequent fast two-step deconvolution algorithm without additional color priors. However, such customized diffractive lenses need to consider the errors introduced in the actual manufacturing process, resulting in a certain deviation between the imaging characteristics and the ideal, affecting the reconstruction quality of the post-processing algorithm. The traditional deconvolution algorithm used in this method relies heavily on the design of the front-end optical system, has high coupling, and has low imaging quality.

[0006] The achromatic imaging method of diffractive lenses based on deep learning optimizes the surface parameters of diffractive lenses as variables and parameters in the image reconstruction network, combines optical and deep learning networks, and realizes end-to-end optical system design and image reconstruction. What kind of optical system and reconstruction algorithm is determined by each other, only the final result needs to be constrained. However, the error between the ideal lens obtained by such optimization and the actually manufactured lens will affect the reconstruction quality of the network, and the customization cost is high, limited by the actual optical material, the application scene is narrow, and the designed lens can only be applied to a specific field and cannot be used twice. SUMMARY

[0007] The present application provides a single-lens achromatic computational imaging method and system based on deep learning to solve the problems in the prior art.

[0008] The technical scheme adopted by the present application is as follows:

[0009] A single-lens achromatic computational imaging method based on deep learning, comprising the following steps:

[0010] Step 1: After the input image is imaged by a single lens, the complex amplitude distribution of the single-lens imaging is recovered from the input image by a complex amplitude recovery network;

[0011] Step 2: Constructing a virtual lens, according to the convolution of the complex amplitude distribution obtained in step 1 and the point spread function of the virtual lens, the complex amplitude distribution on the virtual lens image plane is obtained;

[0012] Step 3: According to the complex amplitude distribution in step 2, the achromatic image is obtained;

[0013] The complex amplitude restoration network is a U-net network model, and a channel attention module is added to the bottom layer downsampling module of the U-net network model; the channel attention module includes a maximum pooling layer, an average pooling layer and two fully connected networks.

[0014] Further, the last layer of the complex amplitude restoration network is a convolution kernel with a dimension of N x 6, including three complex amplitudes A and three phases to form a three-channel complex amplitude distribution The N complex amplitude distributions recovered from the input image are:

[0015]

[0016]

[0017] In the formula: k is the kth amplitude or phase generated, N is the dimension, j is the imaginary symbol, and CWR(I) is the process of recovering the complex amplitude from the intensity image I by the complex amplitude restoration network CWR-Net constructed in the application.

[0018] Further, the imaging model of the complex amplitude restoration network and the virtual lens is constructed as follows:

[0019]

[0020]

[0021] In the formula: k is the wave number, x and y are the coordinates on the virtual lens plane, is the total phase introduced by the virtual lens, h is the point spread function of the virtual lens, x0 and y0 are the coordinates of the virtual imaging plane, x i and y i are the object plane coordinates, j is the imaginary symbol, d o is the object distance, d i is the distance, U' is the light field distribution of the point light source after passing through the virtual lens, and P(x, y) is the aperture function of the virtual lens.

[0022] Further, the complex amplitude distribution on the virtual lens image plane is as follows:

[0023]

[0024] In the formula: * is convolution;

[0025] achromatic image I in step 3 o is expressed as:

[0026]

[0027] wherein W3 is the total superposition light field complex amplitude.

[0028] Further, the total phase calculation method introduced by the virtual lens is as follows:

[0029]

[0030] wherein: is the basic phase provided by the ideal convex lens, is the additional phase introduced by the Zernike polynomial height map; the virtual lens includes an ideal convex lens and an additional Zernike polynomial height map;

[0031]

[0032] wherein k is the wave number, f is the focal length of the virtual lens, and x and y are the coordinates on the virtual lens plane;

[0033]

[0034] wherein m(x, y) is the Zernike polynomial height map, and n and n' are the refractive indexes of air and lens material respectively.

[0035] Further, the image processing process in the channel attention module is as follows:

[0036] The feature maps respectively enter the maximum pooling layer and the average pooling layer to obtain two channel descriptions;

[0037] Then, the two feature maps respectively enter two layers of neural networks; the two features output by the two layers of neural networks are added and then subjected to a Sigmoid activation function to obtain a weight coefficient; the input feature map is multiplied by the weight coefficient to obtain a new scaled feature.

[0038] An imaging system of a single-lens achromatic computational imaging method based on deep learning, comprising: a real lens, a complex amplitude restoration network, and a virtual lens arranged in sequence;

[0039] The complex amplitude restoration network is used to learn the chromatic aberration information of single-lens imaging;

[0040] The virtual lens is used to compensate for the chromatic aberration of the single lens.

[0041] A use method of a single-lens achromatic computational imaging system based on deep learning, comprising the following steps:

[0042] S1: Construct a complex amplitude restoration network;

[0043] S2: Construct an imaging model of a complex amplitude restoration network and a virtual lens;

[0044] S3: Obtain the initial values ​​of the virtual lens surface shape;

[0045] S4: Construct the loss function, minimize the loss function based on the backpropagation gradient descent algorithm, and obtain the structural parameters of the pre-trained complex amplitude restoration network and the virtual lens;

[0046] S5: Input the chromatic aberration image obtained through a single lens into the imaging model composed of a complex amplitude restoration network and a virtual lens to obtain an achromatic image.

[0047] Furthermore, the loss function is as follows:

[0048] l = PL(I o I GT )+α×MSE(I o I GT )+β×SSIM(I o I GT )

[0049] In the formula: l is the loss function, PL(I) o ,I GT ) represents the perceived loss, MSE(I) o ,I GT ) represents the root mean square error, SSIM(I) o ,I GT ) represents structural similarity, and α and β are weighting factors, both set to 1. GT For the true value image, I o To achromatic image.

[0050] The beneficial effects of this invention are:

[0051] (1) The present invention uses a network model and a virtual lens to construct a fully differentiable computational imaging model, which can eliminate the chromatic aberration of images obtained by a single lens;

[0052] (2) The present invention constructs a complex amplitude restoration network to learn the complex amplitude distribution characteristics of single lens imaging, obtains the complex amplitude phase distortion caused by its chromatic aberration, and then optimizes it together with a virtual lens and the complex amplitude restoration network to correct the chromatic aberration of the single lens.

[0053] (3) The virtual lens of the present invention includes an ideal convex lens and a Zernike height. The convex lens is used to provide a basic phase so that the light rays converge and the image is formed behind the lens. The Zernike height provides an additional phase to correct the distortion of the incident complex amplitude, that is, to correct the chromatic aberration of the imaging single lens.

[0054] (4) The present application solves the problems of low efficiency, complex production, high engineering cost and limited imaging quality in the actual imaging use of the existing achromatic imaging technology, avoids complex optical system design, and realizes high-fidelity wide-spectrum achromatic imaging of a single lens. BRIEF DESCRIPTION OF DRAWINGS

[0055] Figure 1 The flowchart of the calculation method of the present application is shown.

[0056] Figure 2 The structure diagram of the complex amplitude recovery network of the present application is shown.

[0057] Figure 3 The schematic diagram of the virtual lens of the present application is shown.

[0058] Figure 4 The schematic diagram of the achromatic imaging result obtained by the method of the present application is shown.

[0059] Figure 5 The schematic diagram of the image reconstruction comparison between the present application and the traditional U-Net network is shown. DETAILED DESCRIPTION

[0060] The present application will be further described below in combination with the drawings and specific embodiments.

[0061] As shown in the figure, a single lens achromatic computational imaging method based on deep learning includes the following steps: Figure 1 Step 1: After the input image is imaged by a single lens, the complex amplitude distribution of the single lens imaging is recovered from the input image by a complex amplitude recovery network;

[0062] As shown in the figure, the complex amplitude recovery network is a U-net network model, and a channel attention module is added in the bottom layer downsampling module of the U-net network model; the channel attention module includes a maximum pooling layer, an average pooling layer and two layers of fully connected network.

[0063] Figure 2

[0064] ​​The complex amplitude restoration network CWR-Net is based on a traditional U-Net network model; the traditional U-Net network model is composed of five down-sampling modules and four up-sampling modules. In particular, a channel attention module is added to the bottom down-sampling module of the network. The input of the channel attention module is a feature map F of size HxWx512 output by the bottom down-sampling module (H and W represent the pixel size). The feature map F is subjected to a spatial global maximum pooling and an average pooling respectively to obtain two channel descriptions of 1x1x512. Then they are respectively sent into a two-layer neural network (full connection network), the first layer has 512 / r neurons, and the activation function is ReLU, and the second layer has 512 neurons. The parameters of the two-layer neural network are shared. After adding the two features output by the two-layer neural network, a Sigmoid activation function is used to obtain the weight coefficient Mc. Finally, the input feature map F is multiplied by Mc to obtain the scaled new feature. The addition of the channel attention module enables the network model to perceive the differences between different channels, which is conducive to the elimination of color differences.

[0065] A convolution kernel with a dimension of Nx6 is used in the last layer of the complex amplitude restoration network model. Three complex amplitudes A and three phases A 3-channel complex amplitude distribution is composed of The final network model restores N complex amplitude distributions from the input single image I

[0066]

[0067]

[0068] In the formula, k represents the kth amplitude or phase generated, N is the dimension, j is the imaginary symbol, and CWR(I) is the process of restoring the complex amplitude from the intensity image I by the complex amplitude restoration network CWR-Net constructed by the application.

[0069] Step 2: Construct a virtual lens, and obtain the complex amplitude distribution on the virtual lens image plane according to the convolution of the complex amplitude distribution obtained in step 1 and the point spread function of the virtual lens;

[0070] After the complex amplitude distribution of the real lens imaging is restored, a virtual lens is designed to compensate for its color difference. Based on the Huygens-Fresnel principle and the Kirchhoff diffraction theory, the image field distribution corresponding to a point light source is represented by the PSF of the optical system. The output complex amplitude distribution can be calculated by the convolution of the input complex amplitude and the PSF of the system.

[0071] The constructed virtual lens is composed of an ideal convex lens and an additional Zernike polynomial height map. The ideal convex lens provides a basic phase The input diverging wave is converted into a converging wave, so that the object can be imaged behind the virtual lens.

[0072]

[0073] where k is the wave number, f is the focal length of the virtual lens, and x and y are the coordinates on the virtual lens plane.

[0074] The Zernike polynomial height map introduces a phase The variable is set to the wavefront shaping and aberration compensation. The additional phase is expressed as:

[0075]

[0076] where n and n' are the refractive indices of air and lens material, respectively

[0077] The total phase introduced by the virtual lens is calculated as follows:

[0078]

[0079] where: is the basic phase provided by the ideal convex lens, is the additional phase introduced by the Zernike polynomial height map.

[0080] The complex amplitude recovery network and the imaging model of the virtual lens are as follows:

[0081]

[0082]

[0083] where k is the wave number, x and y are the coordinates on the virtual lens plane, is the total phase introduced by the virtual lens, h is the virtual lens point spread function, x0 and y0 are the coordinates of the virtual imaging plane, x i and y i are the object plane coordinates, j is the imaginary symbol, d o is the object distance, d i is the distance, U' is the light field distribution of the point source after passing through the virtual lens, and P(x, y) is the aperture function of the virtual lens.

[0084] Step 3: According to the complex amplitude distribution in step 2, the achromatic image can be obtained;

[0085] Assuming that the paraxial approximation is feasible, the complex amplitude distribution on the image plane of the virtual lens The complex amplitude distribution obtained by the CWR-Net network and the PSF convolution are obtained:

[0086]

[0087] where * is a convolution.

[0088] achromatic image I o is represented as:

[0089]

[0090] where W3 is the total distribution of superimposed complex amplitudes of the light field obtained by the complex amplitude restoration network.

[0091] An imaging system of a single-lens achromatic computational imaging method based on deep learning, comprising: a real lens, a complex amplitude restoration network and a virtual lens arranged in sequence;

[0092] The complex amplitude restoration network is used to learn chromatic aberration information of single-lens imaging.

[0093] The virtual lens is used to compensate for single-lens chromatic aberration.

[0094] A use method of a single-lens achromatic computational imaging system based on deep learning, comprising the following steps:

[0095] S1: constructing a complex amplitude restoration network;

[0096] S2: constructing an imaging model of the complex amplitude restoration network and the virtual lens;

[0097] S3: obtaining an initial value of a surface shape of the virtual lens; in order to provide a better initial value for the virtual lens parameters, accelerate the network model and the virtual lens optimization process, and make the final imaging quality better. Based on the traditional two-lens achromatic principle, the initial Zernike surface shape parameters of the virtual lens can be obtained. As shown in Table 1, the initial structure can meet the physical rules and compensate for part of the chromatic aberration of the real single lens.

[0098] Table 1. Initial parameters of the virtual lens

[0099] Object distance 49.65 mm, 50 mm, 50.60 mm Focal length 31.65 mm, 31.79 mm, 32.04 mm Refractive index 1.538，1.531，1.528 Wavelength 486 nm, 587 nm, 656 nm Image distance 87.36 mm Diameter 5 mm Virtual sensor resolution 5.86 x 5.86 μm Zernike polynomial coefficients 0

[0100] S4: constructing a loss function, minimizing the loss function based on the back propagation gradient descent algorithm, obtaining the pre-training complex amplitude restoration network and the structure parameters of the virtual lens;

[0101] The CWR-Net and the surface shape of the virtual lens are optimized together, and the two can be matched with each other to achieve the best achromatic imaging effect. The loss function is used to evaluate the difference between the output predicted value of the neural network model and the true value, and the smaller the loss function is, the better the performance of the model is. The loss function is crucial for the training of the deep learning network, and plays a role in optimizing the network and the surface shape parameters of the virtual lens. The perceptual loss PL is used to calculate the high-dimensional feature map difference in order to better evaluate the observation performance. The MSE loss and the SSIM loss are used to calculate the pixel-level brightness mismatch and structural difference, respectively.

[0102] The loss function is as follows:

[0103] l = PL(I o ,I GT ) + alpha * MSE(I o ,I GT ) + beta * SSIM(I o ,I GT )

[0104] In the formula, l is the loss function, PL(I o ,I GT ) is the perceptual loss, MSE(I o ,I GT ) is the root mean square error, SSIM(I o ,I GT ) is the structural similarity, alpha and beta are weight factors, both of which are set to 0.1, I GT is the true value image, and I o is the achromatic image.

[0105] S5: The chromatic aberration image obtained through the single lens is input into the imaging model composed of the complex amplitude restoration network and the virtual lens, so that the achromatic image can be obtained.

[0106] The 512-channel feature map in the middle of the network is processed through the channel attention module, which can perceive the chromatic aberration information between different channels. An N*6-dimensional convolution kernel is used, and the output can adjust the number of complex amplitudes for different imaging tasks. The virtual lens is used to provide additional phase to the complex amplitude distribution of the single lens imaging to correct the phase distortion caused by chromatic aberration. The CWR-Net and the surface shape of the virtual lens are optimized together, and the two cooperate with each other to achieve the optimal achromatic imaging effect.

[0107] The network model and the virtual lens are jointly designed, and a full-link differentiable computational imaging model is constructed. The CWR-Net learns the complex amplitude distribution characteristics of the single lens imaging, and obtains the complex amplitude phase distortion caused by the chromatic aberration. Then the virtual lens and the CWR-Net are optimized together to correct the chromatic aberration of the single lens. The optimized virtual lens is as follows: Figure 3As shown, it is composed of an ideal convex lens and a Zernike height. The convex lens is used to provide a basic phase so that the light converges and images behind the lens. The Zernike height provides an additional phase to correct the distortion of the incident complex amplitude, that is, to correct the chromatic aberration of the imaging single lens.

[0108] The results of imaging by the method of the present application are shown in Figure 4 The first row in the figure is the chromatic aberration image of the single lens, and the second row is the high-definition image after the chromatic aberration is compensated by the CWR-Net and the virtual lens. The chromatic aberration blur of the edges of the toys, plants and books is well compensated. The average reconstruction time of each image is 0.103s. In addition, the average PSNR (peak signal-to-noise ratio) and SSIM of 50 verification images are quantitatively evaluated. Taking the true value image as the standard, the average PSNR and SSIM of the original single lens image are 18.723 and 0.355 respectively. Through the chromatic aberration compensation of the virtual lens, the PSNR and SSIM of the output image are increased to 33.490 and 0.935 respectively.

[0109] The results of the comparison between the method of the present application and the traditional method of using only U-Net network for image reconstruction are shown in Figure 5 There are some serious color deviations in the U-Net results. For example, in the U-Net results, the clothes of the animation characters are orange, while those of our method and the true value are pink. The white puzzle results of U-Net have obvious pseudo-edges. The average PSNR and SSIM of 50 images reconstructed by U-Net are 29.006 and 0.823 respectively, while those of our method are 33.49 and 0.935 respectively, and the image quality is greatly improved. This obvious difference is due to the essential difference between our method and the pure image processing method, that is, the chromatic aberration is eliminated through optical correction, instead of relying entirely on the research and reasoning of the image.

[0110] The present application adopts a network model and a virtual lens to construct a full-link differentiable computational imaging model, which can eliminate the chromatic aberration of the image obtained by the single lens; a complex amplitude restoration network is constructed to learn the complex amplitude distribution characteristics of the single lens imaging, to obtain the complex amplitude phase distortion caused by the chromatic aberration, and then to optimize the chromatic aberration of the single lens through the virtual lens and the complex amplitude restoration network; the virtual lens includes an ideal convex lens and a Zernike height, and the convex lens is used to provide a basic phase so that the light converges and images behind the lens; the Zernike height provides an additional phase to correct the distortion of the incident complex amplitude, that is, to correct the chromatic aberration of the imaging single lens; the problems of low efficiency, complex production, high engineering cost and limited imaging quality in the actual imaging use of the existing chromatic aberration correction imaging technology are solved, the complex optical system design is avoided, and the high-fidelity wide-spectrum chromatic aberration correction imaging of the single lens is realized.

Claims

1. A deep learning-based single-lens achromatic computational imaging method, characterized in that, The method comprises the following steps: Step 1: after the input image is imaged by a single lens, the complex amplitude distribution of the single lens imaging is recovered from the input image by a complex amplitude recovery network; Step 2: a virtual lens is constructed, and the complex amplitude distribution on the image plane of the virtual lens is obtained according to the convolution of the complex amplitude distribution obtained in step 1 and the point spread function of the virtual lens; Step 3: the achromatic image can be obtained according to the complex amplitude distribution in step 2; The complex amplitude recovery network is a U-net network model, and a channel attention module is added to the bottom layer downsampling module of the U-net network model; the channel attention module comprises a max-pooling layer, an average-pooling layer and two layers of full connection networks; The imaging model of the complex amplitude recovery network and the virtual lens is constructed as follows: wherein: k is the wave number, x and y is the coordinate on the virtual lens plane, is the total phase introduced by the virtual lens, h is the point spread function of the virtual lens, x 0and y 0is the virtual imaging plane coordinate, x i and y i is the object plane coordinate, j is the imaginary symbol, is the object distance, is the separation distance, is the light field distribution of the point source after passing through the virtual lens, is the aperture function of the virtual lens; Complex amplitude distribution on the virtual lens image plane As follows: In the formulae: is a convolution; achromatic image in step 3 I o is represented as: In the formula: W 3 is the total distribution of the superimposed complex amplitudes of the optical field obtained by the complex amplitude recovery network; The total phase calculation method introduced by the virtual lens is as follows: wherein: the basic phase provided by an ideal convex lens, the additional phase introduced by the Zernike polynomial height map; the virtual lens comprises an ideal convex lens and the additional Zernike polynomial height map; wherein: k is the wave number, f is the focal length of the virtual lens, x and y is the coordinate on the virtual lens plane; wherein: is a Zernike polynomial height map, and n and n' are the refractive indices of air and the lens material, respectively; The last layer of the complex amplitude restoration network is a convolution kernel with dimensions N × 6, including three complex amplitude A and three phase The processing process of the image in the channel attention module is as follows: , which constitutes a three-channel complex amplitude distribution The recovered N complex amplitude distributions from the input image are: In the formula: k For the obtained first k One amplitude or phase, N As a dimension, j It is the symbol for imaginary numbers. The complex amplitude restoration network CWR-Net constructed for this invention is based on the intensity map. I The process of restoring the amplitude.

2. The single-lens achromatic computational imaging method based on deep learning according to claim 1, characterized in that, The feature map respectively enters the max-pooling layer and the average-pooling layer to obtain two channel descriptions; Then, the two layers of neural networks are entered; the two features output by the two layers of neural networks are added and then subjected to a Sigmoid activation function to obtain a weight coefficient; the input feature map is multiplied by the weight coefficient to obtain a new scaled feature. The method comprises the following steps:

3. The imaging system of any of claims 1-2, wherein the method further comprises: The real lens, the complex amplitude recovery network and the virtual lens are sequentially arranged; The complex amplitude recovery network is used to learn the chromatic aberration information of single lens imaging; The virtual lens is used to compensate for the chromatic aberration of the single lens. The method comprises the following steps:

4. The method of claim 3, wherein the method further comprises: S1: constructing a complex amplitude recovery network; S2: constructing an imaging model of the complex amplitude recovery network and the virtual lens; S3: obtaining an initial value of the virtual lens surface shape; S4: constructing a loss function, minimizing the loss function based on a back propagation gradient descent algorithm, and obtaining structure parameters of the pre-trained complex amplitude recovery network and the virtual lens; S5: inputting the chromatic aberration image obtained by the single lens into the imaging model composed of the complex amplitude recovery network and the virtual lens, so that an achromatic image can be obtained. The loss function is as follows:

5. The method of claim 4, wherein the method is performed by a computer system. ​ wherein: is a loss function, is a perceptual loss, is a root mean square error, is a structural similarity, α and β are weight factors, all set to 0.1, is a ground truth image, is an achromatic image.

Images