CN114066735B - Least-squares-based sparse sampling Fourier stacked imaging artificial neural network reconstruction method - Google Patents
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Abstract
The invention belongs to the technical field of Fourier laminated imaging, and particularly relates to a least square sparse sampling Fourier laminated imaging reconstruction method based on an artificial neural network, which comprises the following steps: sparse sampling is carried out on the images by adopting Fourier laminated imaging equipment, so that a series of low-resolution acquired images are obtained; establishing a Fourier laminated imaging forward model, sequentially inputting acquired low-resolution images into the forward model, comparing the minimum absolute deviation between an artificial neural network simulation generated image and the acquired image, and solving the problem of least square with solution constraint; training and updating artificial neural network weights by utilizing error back propagation to obtain a reconstructed high-resolution phase recovery image; according to the invention, a random gradient descent optimization method is adopted to optimize the loss function of the model, so that the trained model is more accurate, and the definition of a high-resolution reconstruction graph constructed by sampling sparse sampling data is higher.
Description
Technical Field
The invention belongs to the technical field of Fourier stacked imaging, and particularly relates to a least square based sparse sampling Fourier stacked imaging artificial neural network reconstruction method.
Background
In recent years, proposed stacked imaging technologies (two types of space stacked imaging and fourier stacked imaging) are utilized, the synthetic aperture (SYNTHETIC APERTURE) and phase recovery (PHASE RETRIEVAL) technologies are utilized to scan only a sub-region of a sample or a low-resolution image of the sample at a time, and a high-resolution complex amplitude (including attenuation and phase information) optimization solution of the sample is solved through a computational imaging method. And the lamination imaging technology can keep the unification of a large view field and high resolution of image acquisition, and reconstruct sample phase information and attenuation information (sample depth information can be further reconstructed by applying a specific algorithm). The method mainly comprises the following steps: the first class is formed by evolution of classical GS algorithm (Gerchberg Saxton proposed in 1972), although various GS algorithms are different in form, the core ideas are the same: simulating forward propagation of the intermediate solution to an image space in the optical path system, performing assignment operation to enable the amplitude of the intermediate solution after forward propagation to be equal to a measured value, inverting the updated intermediate solution until an incident plane after constraint, and performing the next forward reverse circulation; the second type of method is a gradient descent-based method. The gradient descent method establishes a system objective function, compares the total difference (energy function) between the measured intensity image and the corresponding calculated image, and updates the calculated parameters by the gradient descent (or similar algorithm) method until convergence by solving the total difference and the calculated parameter bias analysis expression. The limitation of laminated imaging application is that the large sample size of the data acquisition image results in slower acquisition speed and the implementation of high-resolution real-time imaging is impossible.
Disclosure of Invention
In order to solve the problems in the prior art, the invention provides a sparse sampling Fourier stacked imaging artificial neural network reconstruction method based on least square, which comprises the following steps: acquiring a sparse image to be reconstructed, and sampling the acquired sparse image to be reconstructed to obtain a low-resolution sub-image; inputting all the obtained low-resolution sub-images into a trained artificial neural network to obtain reconstructed super-resolution images;
the training process of the artificial neural network comprises the following steps:
S1: acquiring an original image data set, and performing interval sampling on each image data in the original image data set to obtain a low-resolution sub-image; dividing the obtained low-resolution sub-images to obtain a training set and a testing set;
S2: constructing an artificial neural network; processing the low-resolution sub-images in the training set by adopting an artificial neural network model to obtain the intensity of the images;
s3: constructing a loss function of the model according to the intensity of the reconstructed Fourier laminated image;
S4: optimizing the loss function by adopting a random gradient descent optimization method;
s5: and inputting all data in the training set into the model for iteration, and obtaining the amplitude and phase information of the reconstructed high-resolution image after the iteration is completed, thereby completing the training of the model.
Preferably, the process of processing the low resolution sub-images in the training set by using the artificial neural network model includes: acquiring the size of a low-resolution sub-image, extracting initial features of the low-resolution sub-image, and performing Fourier forward transformation on the acquired initial features; acquiring a frequency domain center origin of a low-resolution sub-image; processing the frequency domain center origin, the Fourier positive transformation of the initial characteristic and the size of the low-resolution sub-image by adopting two-dimensional fftshift operation, cutting the processing result, and carrying out inverse Fourier transformation on the cut image to obtain an emergent wave of the low-resolution sub-image; the intensity of the low resolution sub-image is calculated from the exit wave.
Further, the formula of the outgoing wave of the low resolution sub-image is:
Wherein, AndRepresenting the two-dimensional fourier and inverse transforms respectively,For the two-dimensional fftshift operation, crop is an image cropping operation, (k x,ky) represents the frequency domain center origin coordinates of the low resolution sub-image, and (Nx, ny) represents the size of the low resolution sub-image.
Further, the formula for calculating the intensity of the low resolution sub-image is:
wherein, ψ exit represents the outgoing wave of the low resolution sub-image, Representing convolution operation, LF representing lens transfer function.
Preferably, the loss function of the model is:
Wherein J i is a measured image, TV is a total variation function, lambda is a weight coefficient of a balance data item and a constraint item, and n is the number of low-resolution images used for training the artificial neural network.
Preferably, the formula for optimizing the loss function by adopting the random gradient descent optimization method is as follows:
Wherein, And alpha is the learning rate for solving partial derivatives by utilizing neural network error reverse conduction.
According to the invention, the random gradient descent optimization method is adopted to optimize the loss function of the model, so that the trained model is more accurate, and the reconstructed high-resolution reconstruction map has higher definition.
Drawings
FIG. 1 is a graph of amplitude and phase of reconstructed simulation data comparing the present invention with a conventional method;
fig. 2 is a graph of amplitude and phase of experimental data reconstructed by the present invention and a conventional method.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
A least-squares-based sparse sampling Fourier stacked imaging artificial neural network reconstruction method comprises the following steps: the Fourier laminated imaging equipment performs sparse image sampling to obtain a series of low-resolution acquisition images; and (3) establishing a Fourier laminated imaging forward model, sequentially inputting acquired low-resolution images into the forward model, comparing an artificial neural network simulation generated image with acquired image differences (comprising minimum absolute deviation and image sparse prior), establishing a system loss function based on least one multiplication, and training and updating artificial neural network weights by utilizing error back propagation to obtain a reconstructed high-resolution phase recovery image.
Unlike traditional optimization method of Fourier laminated image, such as Gerchberg-Saxton algorithm or Wirtingerflow algorithm, the optimization target is average mean square error, the invention fully considers the signal characteristics of the image acquired by Fourier laminated imaging, i.e. the acquired image is mostly dark field image. Such acquired dark field images are distinguished from bright field images in that the primary signal is distributed in areas where the image brightness is darker. Under the condition of Fourier stacked imaging sparse sampling, the situation that an image cannot be reconstructed occurs by adopting the traditional average mean square error, and the invention provides that the image phase recovery can be successfully carried out based on least square.
The training process of the artificial neural network comprises the following steps:
S1: acquiring an original image data set, and performing interval sampling on each image data in the original image data set to obtain a low-resolution sub-image; dividing the obtained low-resolution sub-images to obtain a training set and a testing set;
S2: constructing an artificial neural network; processing the low-resolution sub-images in the training set by adopting an artificial neural network model to obtain the intensity of the images;
s3: constructing a loss function of the model according to the intensity of the reconstructed Fourier laminated image;
S4: optimizing the loss function by adopting a random gradient descent optimization method;
S5: and inputting all data in the training set into the model for iteration, and obtaining the amplitude and phase information of the reconstructed high-resolution image after the iteration is completed, thereby completing the training of the model.
The process of processing the low resolution sub-images in the training set using the artificial neural network model includes: acquiring the size of a low-resolution sub-image, extracting initial features of the low-resolution sub-image, and performing Fourier forward transformation on the acquired initial features; acquiring a frequency domain center origin of a low-resolution sub-image; processing the frequency domain center origin, the Fourier positive transformation of the initial characteristic and the size of the low-resolution sub-image by adopting two-dimensional fftshift operation, cutting the processing result, and carrying out inverse Fourier transformation on the cut image to obtain an emergent wave of the low-resolution sub-image; the intensity of the low resolution sub-image is calculated from the exit wave.
The specific process for training the artificial neural network comprises the following steps:
S1: acquiring original image data, and obtaining a plurality of low-resolution sub-images (25 application examples) by adopting interval sampling, wherein the image size of the low-resolution sub-images is recorded as (Nx, ny), the common number is 225 (15 x 15), 289 (17 x 17), 441 (21 x 21), and the images are used as the input of an artificial neural network;
S2: establishing an artificial neural network, wherein variables to be solved of the network are amplitude and phase information of an object to be recovered;
V= Aexp (j θ), the image size of which is denoted (NX, NY), typically nx= aNx, ny= aNY, a being the scale factor, typically 3,4 or 5, depending on the fourier stack imaging physical parameters. Initial values are given to an a matrix, which may be given a random number or use the center LED image as the initial value, and a θ matrix, which is generally set to an initial value of 0, v representing the input low resolution sub-image.
S3: the fourier ptychographic forward process is described using an artificial neural network forward model. Taking an LED incidence angle of (beta x,βy) as an example, the inclined monochromatic light incidence sample is equivalent to the shift of the center origin of a frequency domain, namely (k x,ky), and the formed emergent wave is
Wherein the method comprises the steps ofAndRepresenting the two-dimensional fourier and inverse transforms respectively,Is a two-dimensional fftshift operation. Crop is an image cropping operation, which crops a sub-region image of (Nx, ny) size centered on (kx, ky). The intensity formula of the simulation generated image is:
Wherein, Representing convolution operation, LF representing lens transfer function.
S4: establishing a system loss function
Where J i is the measured image, TV is the full variation function, and λ is the balance data item and constraint item weight coefficients. n is the number of low-resolution images used for training the artificial neural network, and the value of n can be 1,3,5,7 and other numerical values. Different from the traditional optimization function target, the system cost function data constraint term provided by the invention is the minimum absolute deviation, and the system cost function data constraint term can be solved by adopting a least square method, namely solving the loss function is equivalent to solving the least square problem with sparse constraint, and is different from a common least square solving method.
S5: optimizing the loss function by adopting a random gradient descent optimization method;
Wherein the method comprises the steps of And alpha is the learning rate for solving partial derivatives by utilizing neural network error reverse conduction.
S6, inputting all data into the model for iteration, and obtaining amplitude and phase information of the reconstructed high-resolution image after the iteration is completed, so as to complete training of the model.
The acquired original data is obtained by generating 441 low-resolution sub-images of 128×128 in total using two images of 640×640 in resolution, that is, fig. 1 (a 1) and (a 2) as amplitude and phase images, respectively, and then acquiring 25 low-resolution sub-images in total at equal intervals by sparse sampling to constitute a sparse sample dataset. The high-resolution amplitude image and the phase image reconstructed by the proposed least-squares-based sparse sampling Fourier stacked image artificial neural network reconstruction method are shown in fig. 1 (c 1) and (c 2).
In order to measure the performance of the model, the sparse sampling Fourier laminated imaging image reconstruction method based on the neural network is compared with a classical GS reconstruction method to obtain reconstruction results shown in fig. 1 (b 1) and (b 2), when the same 25 sparse sampling data sets are used, the GS algorithm cannot effectively reconstruct super-resolution images, and the method can efficiently reconstruct clear images when a very low number of input sub-images are used. Meanwhile, compared with experimental acquisition data, the method uses 25 low-resolution images of 128 x 128, the size of the reconstructed images is 384 x 384, fig. 2 (a 1) and (a 2) are full-sampling 441-picture reconstruction results, fig. 2 (b 1) and (b 2) are conventional GS methods, and fig. 2 (c 1) and (b 2) are reconstruction methods of the invention. From the results, it can be observed that the central part of the GS method image (the area below the numerals 8, 9) is not correctly reconstructed, the numerals "5,6" and the areas beside the numerals "8" are not resolved, the central area of the invention is correctly reconstructed, the numerals "5,6" are clearly visible, only the areas beside the numerals "5,6" are slightly blurred, and the numerals "8" are clearly visible.
While the foregoing is directed to embodiments, aspects and advantages of the present invention, other and further details of the invention may be had by the foregoing description, it will be understood that the foregoing embodiments are merely exemplary of the invention, and that any changes, substitutions, alterations, etc. which may be made herein without departing from the spirit and principles of the invention.
Claims (1)
1. The least square based sparse sampling Fourier stacked imaging artificial neural network reconstruction method is characterized by comprising the following steps of: acquiring a sparse image to be reconstructed, and sampling the acquired sparse image to be reconstructed to obtain a low-resolution sub-image; inputting all the obtained low-resolution sub-images into a trained artificial neural network to obtain reconstructed super-resolution images;
the training process of the artificial neural network comprises the following steps:
S1: acquiring an original image data set, and performing interval sampling on each image data in the original image data set to obtain a low-resolution sub-image; dividing the obtained low-resolution sub-images to obtain a training set and a testing set;
S2: constructing an artificial neural network; processing the low-resolution sub-images in the training set by adopting an artificial neural network model to obtain the intensity of the images; the method comprises the following steps: acquiring the size of a low-resolution sub-image, extracting initial features of the low-resolution sub-image, and performing Fourier forward transformation on the acquired initial features; acquiring a frequency domain center origin of a low-resolution sub-image; processing the frequency domain center origin, the Fourier positive transformation of the initial characteristic and the size of the low-resolution sub-image by adopting two-dimensional fftshift operation, cutting the processing result, and carrying out inverse Fourier transformation on the cut image to obtain an emergent wave of the low-resolution sub-image; calculating the intensity of the low-resolution sub-image according to the emergent wave;
The formula of the outgoing wave of the low resolution sub-image is:
where V denotes the input low resolution sub-image, AndRepresenting the two-dimensional fourier and inverse transforms respectively,For two-dimensional fftshift operations, crop is an image cropping operation, (k x,ky) represents the frequency domain center origin coordinates of the low-resolution sub-image, and (Nx, ny) represents the size of the low-resolution sub-image;
The formula for the intensity of the low resolution sub-image is:
wherein, ψ exit represents the outgoing wave of the low resolution sub-image, Representing convolution operation, LF representing lens transfer function;
S3: constructing a model loss function according to the intensity of the reconstructed Fourier laminated image; solving a loss function of the model to obtain a loss function value; wherein solving the loss function is equivalent to solving a least squares problem with sparse constraints; wherein the loss function of the model is:
Wherein J i is a measured image, TV is a total variation function, lambda is a weight coefficient of a balance data item and a constraint item, and n is the number of low-resolution images used for training an artificial neural network;
S4: optimizing the loss function by adopting a random gradient descent optimization method; the optimization formula is as follows:
where V denotes the input low resolution sub-image, For partial derivatives solved by utilizing neural network error reverse conduction, alpha is the learning rate;
S5: and inputting all data in the training set into the model for iteration, and obtaining the amplitude and phase information of the reconstructed high-resolution image after the iteration is completed, thereby completing the training of the model.
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