Optical fiber logging data compression and transmission method based on distributed acoustic sensing

Abstract

The invention discloses an optical fiber logging data compression and transmission method based on distributed acoustic sensing. The method comprises the following steps: firstly, deploying an encoder and a decoder of a DPDCR network; in the well logging process, down-sampling compression and nonlinear mapping are carried out on well logging data through a convolutional layer and an activation function of an encoder, and compressed floating point type well logging data are obtained; then converting the floating point type data into a binary bit stream through a quantization algorithm; and converting the binary bit stream into floating point data, recovering the size dimension of an original signal through transposition convolution in a decoder, and further performing reconstruction and quality improvement on the original signal through an attention mechanism so as to obtain a final high-fidelity DAS logging signal.

Description

Technical Field

[0001] This invention belongs to the field of well logging technology, and more specifically, relates to a method for compressing and transmitting fiber optic well logging data based on distributed acoustic sensing. Background Technology

[0002] Distributed Acoustic Sensing (DAS) logging has significant application value in the field of dynamic monitoring of oil and gas well production. Distributed optical fibers themselves serve as both sensing media and sensors. Fibers are fixed to the downhole casing or production pipeline. When an event occurs downhole, vibration waves act on the fiber, altering the backscattering characteristics of the light. Using heterodyne phase detection technology, instantaneous vibration information at each location along the fiber can be acquired, enabling real-time monitoring of events such as temperature, pressure, fluid flow, and fracturing within the wellbore. DAS technology offers advantages such as distributed operation, long distance, high sampling density, and real-time monitoring, acquiring signals that simultaneously contain multiple dimensions of information, including depth, time, frequency, and amplitude. However, this also results in daily data volumes reaching TB or even PB levels, posing significant challenges to signal storage and transmission. Furthermore, DAS signals are highly sensitive to complex events in the well, often resulting from a mixture of downhole events producing complex, non-steady-state signals, making signal compression and reconstruction even more difficult. Existing data storage methods typically rely on hard drives at the well logging site. Due to the massive data volume and limited storage resources, terabyte-level data volumes cannot support wireless transmission at well logging sites in the field or at sea. The data storage hard drives must be brought back from the well logging site to the production monitoring department. This storage method severely limits the timeliness of wellbore monitoring. Therefore, exploring efficient methods for compressing and reconstructing DAS logging signals is of great significance.

[0003] In signal compression, distributed fiber optic sensing data compression methods based on implicit neural networks utilize convolutional kernels to map signals to a low-dimensional space, and then use techniques such as transposed convolution to reconstruct the compressed signal. In the encoder-decoder framework, the encoder is responsible for signal compression, and the decoder is responsible for signal reconstruction. However, most current research only considers the reconstruction of signals in the time domain, which is not applicable to the DAS logging signals studied in this paper. DAS signals in production logging are affected by the combined effects of wellbore and formation events, exhibiting characteristics such as non-stationarity, large amplitude fluctuations, and strong randomness in the time domain. The sampling points in the time domain are the result of the superposition of multiple frequency components, making it difficult to recover such multi-frequency component signals in the time domain. While traditional compressed sensing methods perform well with sparse signals, using a fixed-structure measurement matrix to compress high-dimensional signals into low-dimensional measurement vectors, and then selecting the most relevant atoms from the dictionary to recover the signal, these greedy strategy-based algorithms are inefficient, requiring multiple iterations to find the correct signal estimate. Furthermore, DAS logging signals lack sparsity in both the time and frequency domains, making random subsampling impossible. Random subsampling essentially seeks a suitable measurement matrix that can well preserve the structure of the signal, making it difficult to design a suitable measurement matrix to capture information in the signal.

[0004] Deep learning-based compressed sensing networks have been proposed, and their structure, from the encoder to the decoder, focuses on signal compression and reconstruction based on learnable measurement matrices. The signal compression at the decoder follows the same principle as compressed sensing, using the measurement matrix to compress the original signal. However, at the decoder, the deep learning-based compressed sensing network updates the measurement matrix using gradient descent during backpropagation—a self-learning process that addresses the design challenges of the measurement matrix in traditional compressed sensing to some extent. This also introduces new challenges: relying on a single learnable measurement matrix for the entire decoder is detrimental to signal reconstruction. In sparse signals, no matter how the measurement matrix is ​​updated and optimized, accurate signal estimates cannot be obtained. Therefore, signal feature extraction needs to be incorporated into the network, utilizing multiple network parameters to restore the continuity between signal feature sampling points. Low bit rates, or even 1-bit quantization, can theoretically reduce storage requirements, but they severely lose amplitude information, significantly increasing the difficulty of signal reconstruction, especially noticeable in noisy and rapidly changing DAS logging signals. Summary of the Invention

[0005] The purpose of this invention is to overcome the shortcomings of the prior art and provide a fiber optic logging data compression and transmission method based on distributed acoustic sensing. In the logging field, data compression and quantization are used to achieve real-time transmission of low data volume. On the ground server, the compressed data is reconstructed to improve the reconstruction quality of high compression ratio data.

[0006] To achieve the above-mentioned objectives, the present invention provides a method for compressing and transmitting fiber optic logging data based on distributed acoustic sensing, characterized by comprising the following steps:

[0007] (1) The distributed acoustic sensing system receives the signal data to be reconstructed;

[0008] (1.1) During fiber optic logging, the DAS fiber optic logging data received by the distributed acoustic sensing system is denoted as... ;

[0009] (1.2) Based on the preset time truncation window, process the DAS fiber optic logging data. Slicing was performed to obtain the DAS fiber optic logging data sequence, denoted as... ,in, Indicates the first Each signal slice data, express The number of slices;

[0010] (2) Deploy a dual-path deep compression and reconstruction network DPDCR-Net;

[0011] The encoder in the trained DPDCR-Net network is deployed on the inference device at the well logging site, and the decoder is deployed on the land server. When powered on, the network parameters of the encoder and decoder are initialized and loaded first.

[0012] (3) Compress the slice data using the encoder in the fully trained DPDCR-Net network;

[0013] (3.1) Iterate through each slice of data in sequence. The data is then input into the encoder of the DPDCR-Net network, where compressed data is obtained through two consecutive convolutional downsampling operations. ;

[0014]

[0015]

[0016] in, , , , These represent convolution operations with kernel sizes of 1×1, 5×5, 3×3, and 3×3, respectively. This indicates that the individual slice signals are spliced ​​together. This represents the compressed data after concatenation;

[0017] (3.2) Compressed data by applying the LeakyReLU activation function. By performing a linear mapping, the observations of the fully compressed DAS logging data are obtained. ;

[0018]

[0019] in, express The slope of the activation function when it is negative;

[0020] (4) Convert DAS logging observations into a bit stream;

[0021] Quantify observations using 3-bit binary numbers. The integer part uses 8 bits to quantize the observation. The decimal part is quantified using 1 bit of binary. The sign bit determines the quantized result as the bit stream to be transmitted. ;

[0022] (5) Convert the binary bit stream Transmitted to the land server, and then the binary bit stream is processed on the land server. Convert to decimal data to obtain floating-point data. ;

[0023] (6) Utilize the decoder in the fully trained dual-path deep compression reconstruction network DPDCR-Net to... Perform real-time decoding and reconstruction;

[0024] (6.1) Transfer floating-point data As input to the decoder, the data is fed into the frequency domain reconstruction network and the time domain reconstruction network, respectively. Before being fed into the frequency domain reconstruction network, the floating-point data needs to be processed. Perform a discrete Fourier transform;

[0025]

[0026] Where DFT stands for Discrete Fourier Transform. Represents the spectrum after DFT transformation. Represents the real part of the complex number of the spectrum. Represents the imaginary part of the complex number of the spectrum;

[0027] (6.2) Transfer floating-point data The signal is fed into the temporal reconstruction network and passes through three layers of upsampling modules and three layers of multi-scale joint attention modules in sequence to obtain the decoding output of the temporal reconstruction network.

[0028]

[0029]

[0030] Wherein, USB represents the upsampling module, and MSJAB represents the multi-scale joint attention module. , These represent average pooling and max pooling, respectively. This represents a multilayer perceptron. Indicates sigmoid nonlinear activation, subscript This indicates that the module is executed three times. This represents the output of the time-domain reconstruction network;

[0031] (6.3) Spectrum The data is fed into the frequency domain reconstruction network, whereby... The data is fed into a real-branch reconstruction network, and then sequentially passes through a three-layer upsampling module and a three-layer multi-scale joint attention module to obtain the decoded output of the real-branch reconstruction network. ;Will The signal is fed into the virtual branch reconstruction network, and then sequentially passes through a three-layer upsampling module and a three-layer multi-scale joint attention module to obtain the decoded output of the virtual branch reconstruction network. ;

[0032] The outputs of the real-branch reconstruction network and the virtual-branch reconstruction network are combined to obtain the complex spectrum. Then, for the complex number of the spectrum Perform an inverse Fourier transform to obtain the time-domain signal. ;

[0033]

[0034]

[0035] in, Indicates the inverse Fourier transform;

[0036] (6.4) Output of the time-domain reconstruction network With time domain signal The signals are concatenated along the channel dimension, then convolved to output the final reconstructed signal. ;

[0037]

[0038] in, This indicates a splicing operation. This represents a 1×1 convolution operation.

[0039] The objective of this invention is achieved as follows:

[0040] This invention relates to a fiber optic logging data compression and transmission method based on distributed acoustic sensing. First, an encoder and decoder of a DPDCR network are deployed. During the logging process, the logging data is downsampled, compressed, and nonlinearly mapped using the encoder's convolutional layer and activation function to obtain compressed floating-point logging data. Then, the floating-point data is converted into a binary bitstream using a quantization algorithm. Next, the binary bitstream is converted back to floating-point data, and the original signal size is restored using transpose convolution in the decoder. Furthermore, an attention mechanism is used to reconstruct and improve the quality of the original signal, thereby obtaining the final high-fidelity DAS logging signal.

[0041] Meanwhile, the fiber optic logging data compression and transmission method based on distributed acoustic sensing of this invention also has the following beneficial effects:

[0042] (1) Deploying lightweight encoders and data quantization algorithms at the logging site enables real-time compression of massive DAS logging data, achieving a compression ratio of 0.05, which means the signal is compressed by 20 times, thus improving the wireless transmission speed.

[0043] (2) The decoder structure innovatively uses a multi-branch interactive network, in which the intermediate output layers of different branch networks flow to other network branches, making up for the insufficient reconstruction capability of a single domain network.

[0044] (3) The attention mechanism module involved in this invention uses a dynamic weighting mechanism to enrich the signal feature changes and improve the signal reconstruction quality. Attached Figure Description

[0045] Figure 1 This is a flowchart of the fiber optic logging data compression and transmission method based on distributed acoustic sensing according to the present invention.

[0046] Figure 2 This is a structural diagram of a dual-path deep compression and reconstruction network;

[0047] Figure 3 This is a comparison chart of the reconstruction effects of dual-path deep compression and reconstruction networks. Detailed Implementation

[0048] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0049] Example

[0050] In this embodiment, as Figure 1 As shown, the present invention discloses a method for compressing and transmitting fiber optic logging data based on distributed acoustic sensing, comprising the following steps:

[0051] (1) Construct a dual-path deep compression and reconstruction network DPDCR-Net;

[0052] In this embodiment, as Figure 2 As shown, the dual-path deep compression and reconstruction network DPDCR-Net consists of two parts: an encoder and a decoder. The encoder contains four convolutional modules, each of which contains a convolutional layer, a batch normalization layer, and a LeakyReLU activation function layer.

[0053] The decoder consists of two parts: a frequency domain reconstruction network and a time domain reconstruction network. The frequency domain reconstruction network includes a real branch reconstruction network and a virtual branch reconstruction network. Each real branch reconstruction network and virtual branch reconstruction network consists of a three-layer upsampling module (USB) and a three-layer multi-scale joint attention module (MSJA).

[0054] The temporal reconstruction network has the same structure as the real-branch reconstruction network and the virtual-branch reconstruction network, and is also composed of a three-layer upsampling module USB and a three-layer multi-scale joint attention module MSJA.

[0055] (2) Train the DPDCR-Net network;

[0056] (2.1) During fiber optic logging, multiple sets of DAS fiber optic logging data are received using a distributed acoustic sensing system, denoted as... , This indicates the number of groups of DAS fiber optic logging data, with K set to 100.

[0057] (2.2) For each DAS fiber optic logging data Slicing is performed to obtain the DAS fiber optic logging data sequence for each channel, denoted as... ,in, Indicates the first DAS fiber optic logging data sequence No. Each signal slice data;

[0058] (2.3) Traverse each DAS fiber optic logging data sequence and extract from it. =128 slices of data As a batch of training data, then a batch of sliced ​​data The DAS logging data observations are obtained through encoder encoding processing. ;

[0059] (2.4) DAS logging observations Input decoder, through decoder Real-time decoding and reconstruction are performed to obtain the reconstructed signal. ;

[0060] (2.5) Calculate the total loss function value after this round of training. ;

[0061]

[0062]

[0063]

[0064]

[0065]

[0066]

[0067]

[0068]

[0069] in, For time-domain reconstruction loss, To cover the actual losses incurred in rebuilding, For the reconstruction loss of the virtual branch, For temporal structural similarity loss, For the real branch structure similarity loss, For the virtual branch structure similarity loss, Indicates the decoder for the first slice data The reconstructed signal, , They represent The magnitude of the complex real part of the spectrum and the magnitude of the complex real part of the spectrum of the corresponding reconstructed signal. , They represent The magnitude of the complex imaginary part of the spectrum and the magnitude of the complex imaginary part of the spectrum of the reconstructed signal. , They represent The real part of the spectrum and the real part of the reconstructed spectrum, , They represent The imaginary part of the spectrum and the imaginary part of the reconstructed spectrum, express The reconstructed signal, , They represent and The mean, , express and variance express and covariance, , It should be a constant to prevent the denominator from being zero; , These represent weighting factors, set to 1 and 0.5 respectively;

[0070] (2.6) Update the network parameters using gradient descent based on the total loss function value, and then return to step (2.3) for the next round of training until the DPDCR-Net network converges.

[0071] (3) Signal data to be reconstructed received by the distributed acoustic sensing system;

[0072] (3.1) During fiber optic logging, the DAS fiber optic logging data received by the distributed acoustic sensing system is denoted as... ;

[0073] (3.2) Based on the preset time truncation window, process the DAS fiber optic logging data. Slicing was performed to obtain the DAS fiber optic logging data sequence, denoted as... ,in, Indicates the first Each signal slice data, express The number of slices;

[0074] (4) Deploy a dual-path deep compression and reconstruction network DPDCR-Net;

[0075] The encoder in the trained DPDCR-Net network is deployed on the inference device at the well logging site, and the decoder is deployed on the land server. When powered on, the network parameters of the encoder and decoder are initialized and loaded first.

[0076] (5) Compress the slice data using the encoder in the fully trained DPDCR-Net network;

[0077] (5.1) Iterate through each slice of data in sequence. The data is then input into the encoder of the DPDCR-Net network, where compressed data is obtained through two consecutive convolutional downsampling operations. ;

[0078]

[0079]

[0080] in, , , , These represent convolution operations with kernel sizes of 1×1, 5×5, 3×3, and 3×3, respectively. This indicates that the individual slice signals are spliced ​​together. This represents the compressed data after concatenation;

[0081] (5.2) Compressed data by applying the LeakyReLU activation function. By performing a linear mapping, the observations of the fully compressed DAS logging data are obtained. ;

[0082]

[0083] in, express The slope of the activation function when it is negative;

[0084] (6) Convert DAS logging observations into bit streams;

[0085] Quantify observations using 3-bit binary numbers. The integer part uses 8 bits to quantize the observation. The decimal part is quantified using 1 bit of binary. The sign bit determines the quantized result as the bit stream to be transmitted. ;

[0086] (7) Convert the binary bit stream Transmitted to the land server, and then the binary bit stream is processed on the land server. Convert to decimal data to obtain floating-point data. ;

[0087] (8) Utilize the decoder in the fully trained dual-path deep compression reconstruction network DPDCR-Net to... Perform real-time decoding and reconstruction;

[0088] (8.1) Transfer floating-point data As input to the decoder, the data is fed into the frequency domain reconstruction network and the time domain reconstruction network, respectively. Before being fed into the frequency domain reconstruction network, the floating-point data needs to be processed. Perform a discrete Fourier transform;

[0089]

[0090] Where DFT stands for Discrete Fourier Transform. Represents the spectrum after DFT transformation. Represents the real part of the complex number of the spectrum. Represents the imaginary part of the complex number of the spectrum;

[0091] (8.2) Transfer floating-point data The signal is fed into the temporal reconstruction network and passes through three layers of upsampling modules and three layers of multi-scale joint attention modules in sequence to obtain the decoding output of the temporal reconstruction network.

[0092]

[0093]

[0094] Wherein, USB represents the upsampling module, and MSJAB represents the multi-scale joint attention module. , These represent average pooling and max pooling, respectively. This represents a multilayer perceptron. Indicates sigmoid nonlinear activation, subscript This indicates that the module is executed three times. This represents the output of the time-domain reconstruction network;

[0095] (8.3) Spectrum The data is fed into the frequency domain reconstruction network, whereby... The data is fed into a real-branch reconstruction network, and then sequentially passes through a three-layer upsampling module and a three-layer multi-scale joint attention module to obtain the decoded output of the real-branch reconstruction network. ;Will The signal is fed into the virtual branch reconstruction network, and then sequentially passes through a three-layer upsampling module and a three-layer multi-scale joint attention module to obtain the decoded output of the virtual branch reconstruction network. ;

[0096] The outputs of the real-branch reconstruction network and the virtual-branch reconstruction network are combined to obtain the complex spectrum. Then, for the complex number of the spectrum Perform an inverse Fourier transform to obtain the time-domain signal. ;

[0097]

[0098]

[0099] in, Indicates the inverse Fourier transform;

[0100] (8.4) Output of the time-domain reconstruction network With time domain signal The signals are concatenated along the channel dimension, then convolved to output the final reconstructed signal. ;

[0101]

[0102] in, This indicates a splicing operation. This represents a 1×1 convolution operation.

[0103] In this embodiment, Figure 3 A comparison of the reconstruction results of DPDCR-Net, in which, Figure 3 (a) represents the original DAS logging time-domain signal, which is a mid-to-low frequency broadband signal. Figure 3 (b) Yes Figure 3 (a) The result of compression and reconstruction of the DAS logging time domain signal. The amplitude of the reconstructed signal is highly consistent with the amplitude of the corresponding sampling point of the original signal. Figure 3 (c) represents the original DAS logging time-domain signal, which is a low-frequency narrowband signal with strong periodicity. Figure 3 (d) is Figure 3 (c) The result of compression and reconstruction of the DAS logging time-domain signal shows that the amplitude of the reconstructed signal is highly consistent with the amplitude of the corresponding sampling points of the original signal. This confirms that the proposed dual-path depth compression and reconstruction network DPDCR-Net has strong applicability in the field of DAS logging data compression and reconstruction.

[0104] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for distributed acoustic sensing based fiber optic well logging data compression and transmission, characterized in that, Comprise the following steps: (1) The distributed acoustic sensing system receives the signal data to be reconstructed; (1.1) In the process of optical fiber logging, the DAS optical fiber logging data received by the distributed acoustic sensing system is denoted as ; (1.2), according to the preset time truncation window, the DAS optical fiber logging data is sliced to obtain a DAS optical fiber logging data sequence, denoted as , wherein, represents the first signal slice data, represents the number of slices.​ (2) Deploy a two-way deep compression reconstruction network DPDCR-Net; The trained DPDCR-Net network is deployed in the inference device on the well site, and the decoder is deployed on the land server side; When powered on, first initialize and load the network parameters of the encoder and the decoder; (3) Use the trained DPDCR-Net network to compress the slice data; (3.1), traversing each slice data in turn and input to the encoder in the DPDCR-Net network, and obtain compressed data through twice continuous convolution downsampling operations in the encoder ; ； ； wherein, , , , respectively represent a convolution operation with a kernel size of 1x1, 5x5, 3x3, 3x3, represents splicing of each slice signal, represents compressed data after splicing. (3.2), compressing data by an activation function LeakyRelu linear mapping to obtain the observation value of the compressed complete DAS logging data ; ； wherein represents activation function slope when the value is negative; (4) Convert the DAS logging observation value into a bit stream; The integer part of the observation value is quantized using 3-bit binary quantization The decimal part of the observation value is quantized using 8-bit binary quantization The sign bit of the observation value is quantized using 1-bit binary quantization The quantized result is taken as the bit stream to be transmitted ; (5) the binary bit stream is transmitted to the land server end, and then the binary bit stream is converted into decimal data at the land server end to obtain floating point type data ;​​ (6) using the decoder in the trained two-path deep compression reconstruction network DPDCR-Net to perform real-time decoding and reconstruction; performing real-time decoding and reconstruction; (6.1), the floating point type data As the input of the decoder, it is sent into the frequency domain reconstruction network and the time domain reconstruction network respectively, and it is needed to do the discrete Fourier transform before being sent into the frequency domain reconstruction network floating point type data ； wherein DFT denotes a discrete Fourier transform, denotes the frequency spectrum after DFT transform, denotes the real part of the frequency spectrum complex number, denotes the imaginary part of the frequency spectrum complex number; (6.2), the floating point type data is sent into the time domain reconstruction network, and sequentially passes through three layers of up-sampling modules and three layers of multi-scale joint attention modules to obtain a decoding output of the time domain reconstruction network. ； ； wherein, USB denotes an up-sampling module, MSJAB denotes a multi-scale joint attention module, , denote average pooling and max pooling, respectively, denotes a multi-layer perceptron, denotes a sigmoid non-linear activation, the subscript denotes that the module is executed three times, denotes the output of the temporal reconstruction network; (6.3), the spectrum is sent into a frequency domain reconstruction network, wherein is sent into a real part branch reconstruction network, and sequentially passes through three layers of up-sampling modules and three layers of multi-scale joint attention modules to obtain a decoding output of the real part branch reconstruction network ; the imaginary part is sent into an imaginary part branch reconstruction network, and also sequentially passes through three layers of up-sampling modules and three layers of multi-scale joint attention modules to obtain a decoding output of the imaginary part branch reconstruction network ; combining the outputs of the real partial reconstruction network and the imaginary partial reconstruction network to obtain a spectral complex number performing inverse Fourier transform on the spectral complex number to obtain a time-domain signal ; ； ； wherein denotes the inverse Fourier transform; (6.4), output of the time-domain reconstruction network with the time-domain signal The final reconstructed signal is output after splicing in the channel dimension and convolution operation ; ； wherein, denotes a concatenation operation, denotes a 1 x 1 convolution operation.

2. The method of claim 1, wherein, The structure of the two-way deep compression reconstruction network DPDCR-Net is: The two-way deep compression reconstruction network DPDCR-Net includes an encoder and a decoder, wherein the encoder includes four convolution modules, each of which includes a convolution layer, a batch normalization layer and a LeakyRelu activation function layer; The decoder includes a frequency domain reconstruction network and a time domain reconstruction network, wherein the frequency domain reconstruction network includes a real branch reconstruction network and an imaginary branch reconstruction network, and each of the real branch reconstruction network and the imaginary branch reconstruction network is composed of three up-sampling modules USB and three multi-scale joint attention modules MSJA; The time domain reconstruction network has the same structure as the real branch reconstruction network and the imaginary branch reconstruction network, and is also composed of three up-sampling modules USB and three multi-scale joint attention modules MSJA.

3. The method of claim 1, wherein, The training process of the two-way deep compression reconstruction network DPDCR-Net is: (S3.1), in the process of optical fiber logging, a plurality of groups of DAS optical fiber logging data are received by using a distributed acoustic sensing system, denoted as , , wherein n represents the number of groups of DAS optical fiber logging data. (S3.2), for each DAS optical fiber logging data slices to obtain each DAS optical fiber logging data sequence, denoted as wherein, represents the first DAS optical fiber logging data sequence of the first signal slice data; (S3.3), traversing each DAS optical fiber logging data sequence, and intercepting a slice data as a batch of training data, then a batch of slice data through the encoder coding processing, the observation value of the DAS logging data is obtained ; (S3.4), the DAS well logging observation values input decoder, decoding the signal by the decoder real-time decoding and reconstruction, obtaining the reconstructed signal ​ (S3.5), calculating the total loss function value after the current round of training ; ； ； ； ； ； ； ； ； wherein is a temporal reconstruction loss, is a real sub-branch reconstruction loss, is an imaginary sub-branch reconstruction loss, is a temporal structural similarity loss, is a real sub-branch structural similarity loss, is an imaginary sub-branch structural similarity loss, denotes a reconstructed signal of the decoder for the th slice data , , denote the spectral complex real part magnitude of the th slice data , denote the spectral complex imaginary part magnitude of the th slice data , denote the spectral real part of the th slice data , denote the spectral imaginary part of the th slice data denotes the reconstructed signal of the th slice data , denote the mean of the th slice data , , denote the variance of the th slice data , denote the covariance of the th slice data , , is a constant, , denotes a weight factor; (S3.6) According to the total loss function value, the network parameters are updated by using the gradient descent method, and then step (S3.3) is returned for the next round of training until the DPDCR-Net network converges.

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