A calcium ion imaging signal spike inference method and system based on deep learning

Abstract

This invention relates to the field of biomedical signal processing technology, and discloses a method and system for inferring peaks in calcium ion imaging signals based on deep learning. The method includes the following steps: generating a recovered sequence by segmenting the original noisy calcium ion signal time series through interval sampling, and training a one-dimensional U-Net neural network model; processing historical noisy calcium ion signal time series using the one-dimensional U-Net neural network model to obtain historical denoised signals, and training a one-dimensional convolutional neural network model using the historical denoised signals; inputting the denoised original noisy calcium ion signal time series to be processed into the one-dimensional convolutional neural network model to infer the absolute peak rate sequence of neurons. This invention suppresses noise without external ground truth data through self-supervised denoising, improves the signal-to-noise ratio using a two-stage framework, and accurately calculates discrete firing events of neurons, solving the problems of existing technologies that rely on ground truth databases and have low inference accuracy under low signal-to-noise ratios.

Description

Technical Field

[0001] This invention relates to the field of biomedical signal processing technology, specifically to a method and system for inferring calcium ion imaging signal spikes based on deep learning. Background Technology

[0002] Calcium ion imaging is an important tool in neuroscience research. It indirectly reflects neuronal activity potentials by detecting changes in calcium ion concentration within neurons. Calcium ion imaging signals have high spatial resolution and can simultaneously record the activity of a large number of neurons, making them widely used in research related to neural activity perception and functional connectivity analysis.

[0003] However, the raw calcium ion signals obtained in actual data acquisition are often affected by photon noise and readout noise, and there are signal coupling problems. Traditional computational inference methods based on denoising and biological simulation require the pre-setting of complex parameters and models. These methods are not robust to noise and are difficult to adapt to individual differences in neuronal activity.

[0004] Currently, there are peak inference techniques based on supervised deep networks, such as using large-scale databases for model training. However, existing supervised deep network techniques typically rely on matching with large-scale ground truth databases to optimize the model. The matching mechanism of large-scale ground truth databases is based on simple statistical features, which are difficult to effectively handle background fluorescence fluctuations and complex non-Gaussian noise such as motion artifacts present in real-world data. When the noise characteristics of the target data differ from those of the database samples, the denoising ability and peak inference accuracy of existing supervised deep network techniques decrease.

[0005] Furthermore, under conditions of low signal-to-noise ratio, low activity frequency, or complex calcium dynamics, existing supervised deep network technologies do not achieve ideal accuracy and temporal resolution in identifying single or continuous spikes, especially when inferring the absolute spike rate of low-activity-frequency neurons, where quantization accuracy needs to be improved.

[0006] Meanwhile, traditional supervised learning methods require a large number of noisy and noiseless data pairs for training when performing denoising. However, it is difficult to obtain high-quality noiseless calcium ion signal ground truth in practice. The difficulty in obtaining high-quality noiseless calcium ion signal ground truth limits the training effect and generalization ability of traditional supervised learning methods.

[0007] Therefore, this invention proposes a method and system for inferring calcium ion imaging signal spikes based on deep learning to address the shortcomings of existing technologies. Summary of the Invention

[0008] To address the shortcomings of existing technologies, this invention provides a deep learning-based method and system for inferring peaks in calcium ion imaging signals. This method solves the problems of existing calcium ion imaging signal peak inference techniques, which rely on a large amount of external noise-free ground truth data for model training, lack robustness in the face of complex non-Gaussian noise such as background fluorescence fluctuations and motion artifacts, and have low peak inference accuracy and limited temporal resolution under low signal-to-noise ratio conditions.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] The first aspect of this invention provides a method for inferring calcium ion imaging signal spikes based on deep learning. The method for inferring calcium ion imaging signal spikes based on deep learning includes the following steps:

[0011] The processor segments the original noisy calcium ion signal time series into subsequences and generates a recovered sequence through interval sampling. The processor then uses the recovered sequence to construct a self-supervised learning task. This task trains a one-dimensional U-Net neural network model. The self-supervised learning task uses supervisory signals mined from the noisy data itself to drive model parameter updates.

[0012] The processor acquires the training dataset. The training dataset contains historical noisy calcium ion signal time series. The training dataset also contains corresponding real action potential sequences. The processor uses a trained one-dimensional U-Net neural network model to denoise the historical noisy calcium ion signal time series. The processor obtains the historical denoised signal.

[0013] The processor uses historical denoised signals as input data. The processor uses real action potential sequences as the output target. The processor trains a one-dimensional convolutional neural network model. The one-dimensional convolutional neural network model establishes a mapping relationship between changes in calcium ion concentration and neuronal firing activity.

[0014] The processor acquires the original noisy calcium ion signal time series to be processed. The processor uses a trained one-dimensional U-Net neural network model to denoise the original noisy calcium ion signal time series. The processor obtains the denoised calcium ion time series to be inferred. The processor inputs the denoised calcium ion time series to be inferred into the trained one-dimensional convolutional neural network model. The processor uses the one-dimensional convolutional neural network model to infer the absolute peak rate sequence of neurons.

[0015] Furthermore, the processor divides the original noisy calcium ion signal time series into subsequences and generates a recovered sequence through interval sampling as follows:

[0016] The processor segments the original noisy calcium ion signal time series with an initial length into multiple non-overlapping subsequences. These non-overlapping subsequences share the same underlying ground truth signal. Each non-overlapping subsequence contains independent noise samples.

[0017] The processor performs a Discrete Fourier Transform on the sampled subsequence of a first length. The processor obtains multiple frequency coefficients. The processor embeds these frequency coefficients into a new array of a second length, which is greater than the first length. The processor extends the frequency coefficients to the second length by padding the high-frequency regions with zeros. The processor then obtains zero-padded frequency coefficients.

[0018] The processor performs an inverse discrete Fourier transform on the zero-padded frequency coefficients of the second length. The processor obtains a recovered sequence of the second length. Through frequency domain zero-padded and inverse transform, the processor achieves lossless recovery from the low-frequency subsequence to the original length sequence.

[0019] Furthermore, the processor utilizes the recovery sequence to construct a self-supervised learning task to train a one-dimensional U-Net neural network model. The specific operations are as follows:

[0020] The processor performs a selection operation on each set of restored sequences. The processor selects one restored sequence as the network input. The processor then sums the remaining restored sequences pixel-by-pixel. The processor uses the result of this pixel-by-pixel summation as the target. The input restored sequences correspond to a single sampled signal. The target pixel-by-pixel summation result corresponds to a superimposed signal from multiple samples.

[0021] Because noise is independent and uncorrelated across different subsequences, the signal-to-noise ratio (SNR) of a superimposed signal from multiple samples is higher than that of a single sample. The processor trains a one-dimensional U-Net neural network model using the input and target. The processor defines a loss function to quantify the difference between the network's predicted output and the target. The processor updates the network parameters using backpropagation to minimize the loss function.

[0022] The processor forces the one-dimensional U-Net neural network model to learn to extract shared low-level signals from the input. The processor also forces the one-dimensional U-Net neural network model to suppress independent noise in the input.

[0023] Furthermore, the loss function used is L2 loss. L2 loss calculates the sum of squared errors between the network prediction output and the target of the one-dimensional U-Net neural network model.

[0024] Furthermore, the processor utilizes the trained one-dimensional U-Net neural network model to perform denoising on the historical noisy calcium ion signal time series as follows:

[0025] The processor inputs the historical noisy calcium ion signal time series into a one-dimensional U-Net neural network model. The one-dimensional U-Net neural network model performs forward propagation computation. Based on the network parameters, the one-dimensional U-Net neural network model identifies and suppresses high-noise components in the historical noisy calcium ion signal time series as non-shared random perturbations. The one-dimensional U-Net neural network model preserves the underlying shared signal that conforms to the characteristics of calcium ion dynamics. The one-dimensional U-Net neural network model outputs the historical denoised signal.

[0026] Furthermore, the specific operation of the processor in training a one-dimensional convolutional neural network model using historical denoised signals as input data and real action potential sequences as output targets is as follows:

[0027] The processor defines the design goal of the one-dimensional convolutional neural network model. The design goal is to map the input historical denoised signal to the actual action potential sequence at the corresponding time point. The actual action potential sequence is numerically represented by the absolute peak rate. The processor adjusts the network parameters of the one-dimensional convolutional neural network model through optimization algorithms.

[0028] The goal of the optimization algorithm is to minimize the difference between the predicted output and the true peak rate of a one-dimensional convolutional neural network (CNN) model. The processor calculates the norm distance between the predicted output and the true peak rate of the CNN model. The processor then calculates the gradient based on the norm distance. Finally, the processor updates the network parameters using the gradient.

[0029] Furthermore, the specific operation of the processor to acquire the raw noisy calcium ion signal time series to be processed is as follows: The processor acquires one-dimensional fluorescence intensity data through a two-photon microscope imaging system. The processor obtains the raw noisy calcium ion signal time series to be processed. The raw noisy calcium ion signal time series to be processed contains photon noise. The raw noisy calcium ion signal time series to be processed contains readout noise.

[0030] Furthermore, the specific operation by which the processor infers the absolute peak rate sequence of neurons is as follows: the one-dimensional convolutional neural network model uses multiple convolutional kernels to process the denoised calcium ion time series to be inferred. The multiple convolutional kernels perform a sliding operation in the time dimension.

[0031] One-dimensional convolutional neural network (CNN) models automatically identify key features associated with spike occurrence through multiple layers of convolutional kernels. Key features include the steepness of the rising edge of the calcium signal, peak amplitude, and decay rate. The CNN model performs a nonlinear deconvolution mapping. Finally, it transforms the extracted key features into a sequence of absolute spike rates.

[0032] Furthermore, the denoised calcium ion time series output by the one-dimensional U-Net neural network model is aligned on the time axis with the original noisy calcium ion signal time series to be processed. No phase delay is introduced into the denoised calcium ion time series to be inferred.

[0033] A second aspect of the present invention provides a deep learning-based calcium ion imaging signal spike inference system, the deep learning-based calcium ion imaging signal spike inference system comprising:

[0034] Memory is used to store computer-executable instructions. Memory is used to store the parameters of a trained self-supervised denoising model. Memory is used to store the parameters of a trained supervised spike mapping network.

[0035] A processor is used to read and execute computer-executable instructions stored in memory. When executing the computer-executable instructions, the processor implements the deep learning-based calcium ion imaging signal spike inference method described in the first aspect above.

[0036] The input / output interface establishes a physical connection between the deep learning-based calcium ion imaging signal spike inference system and an external data source. It receives the raw, noisy calcium ion signal time series from a two-photon microscope imaging system and outputs the absolute spike rate sequence of neurons calculated by the processor.

[0037] The communication bus is used to physically connect to the processor. It is also used to physically connect to memory and input / output interfaces. The communication bus establishes a data transmission channel between the processor, memory, and input / output interfaces.

[0038] This invention provides a method and system for inferring calcium ion imaging signal spikes based on deep learning. It has the following beneficial effects:

[0039] 1. This invention segments the original noisy calcium ion signal time series into subsequences that share the underlying ground truth signal but contain independent noise samples by interval sampling. The subsequences are used to construct input data and target data for self-supervised training of a one-dimensional U-Net neural network model. This can suppress photon noise and readout noise without the need for external noise-free ground truth data, while fully preserving the biological characteristics of the rising edge and decay rate of calcium transient events, thus solving the problem of model training relying on a large-scale, high-quality ground truth database.

[0040] 2. This invention adopts a two-stage processing framework. First, the trained one-dimensional U-Net neural network model is used to denoise the original noisy calcium ion signal time series to obtain a high signal-to-noise ratio historical denoised signal. Then, the historical denoised signal is used to train a one-dimensional convolutional neural network model. This cascaded approach improves the signal-to-noise ratio of the input data, enabling the one-dimensional convolutional neural network model to accurately identify low-amplitude calcium transient events from complex background fluorescence fluctuations, reduce the false negative rate of real action potentials, and improve the inference accuracy under low signal-to-noise ratio conditions.

[0041] 3. This invention utilizes a one-dimensional convolutional neural network model to automatically extract key features of the rising edge steepness and peak amplitude of calcium ion signals. Through nonlinear deconvolution mapping, the key features are transformed into a sequence of absolute peak rates of neurons. This end-to-end supervised learning mechanism directly learns noise patterns from the data distribution. Compared with traditional methods that rely on simple statistical matching, this invention has stronger robustness to motion artifacts and complex non-Gaussian noise such as background fluorescence fluctuations, ensuring generalization ability under different neuronal activity patterns. Attached Figure Description

[0042] Figure 1 This is a flowchart of the method of the present invention;

[0043] Figure 2 This is a system block diagram of the present invention;

[0044] Figure 3 This is one of the comparison images of the original noisy calcium ion signal and the denoised calcium ion signal;

[0045] Figure 4 This is one of the comparison images of the original noisy calcium ion signal and the denoised calcium ion signal;

[0046] Figure 5 This is one of the comparison images of the original noisy calcium ion signal and the denoised calcium ion signal;

[0047] Figure 6 This is one of the comparison images of the original noisy calcium ion signal and the denoised calcium ion signal;

[0048] Figure 7 This is one of the comparison images of the original noisy calcium ion signal and the denoised calcium ion signal;

[0049] Figure 8 This is the time-domain waveform of the original noisy calcium ion signal in this invention;

[0050] Figure 9 This is the time-domain waveform of the denoised calcium ion signal in this invention;

[0051] Figure 10 This is a schematic diagram of the actual neuronal peak firing rate sequence in this invention;

[0052] Figure 11 This is a schematic diagram of the absolute peak rate sequence of neurons inferred in this invention.

[0053] Legend

[0054] 1. Memory; 2. Processor; 3. Input / output interface; 4. Communication bus. Detailed Implementation

[0055] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] See attached document Figure 1 and attached Figure 2 This invention provides a method and system for inferring peaks in calcium ion imaging signals based on deep learning. The technical solution provided by this invention employs a two-stage processing framework: the first stage is self-supervised denoising, which preprocesses the original calcium ion signal for denoising without requiring an external noise-free ground truth; the second stage is supervised peak mapping, which uses the denoised high signal-to-noise ratio signal to train a deep network model, achieving a high-precision mapping from the calcium ion signal to the peak rate of neurons.

[0057] See attached document Figure 2 This invention provides a deep learning-based method for inferring calcium ion imaging signal spikes, applied to a deep learning-based calcium ion imaging signal spike inference system. The deep learning-based calcium ion imaging signal spike inference system includes:

[0058] Memory 1 is used to store computer-executable instructions, parameters of the trained self-supervised denoising model, and parameters of the trained supervised spike mapping network.

[0059] Processor 2 is used to read and execute computer-executable instructions stored in memory 1, and to execute a deep learning-based calcium ion imaging signal spike inference method;

[0060] Input / output interface 3 is used to establish a physical connection between the computing device and an external data source, receive the original noisy calcium ion signal time series from the two-photon microscope imaging system, and output the absolute peak rate sequence of neurons calculated by processor 2.

[0061] Communication bus 4 is used to physically connect processor 2, memory 1 and input / output interface 3, and to build a data transmission channel between processor 2, memory 1 and input / output interface 3.

[0062] Processor 2, memory 1, communication bus 4, and input / output interface 3 all belong to the computing device. The computing device is physically configured to execute the various steps in the deep learning-based calcium ion imaging signal spike inference method.

[0063] Communication bus 4 is used for physical connection to processor 2. Communication bus 4 is used for physical connection to memory 1. Communication bus 4 is used for physical connection to input / output interface 3. Communication bus 4 establishes a data transmission channel between processor 2, memory 1, and input / output interface 3.

[0064] Memory 1 is used to store computer-executable instructions. Memory 1 is used to store the parameters of the trained self-supervised denoising model. Memory 1 is used to store the parameters of the trained supervised spike mapping network. Memory 1 is also used to store the training dataset containing historical data. Memory 1 includes high-speed random access memory 1. Memory 1 includes non-volatile memory 1. Non-volatile memory 1 ensures that the parameters of the self-supervised denoising model and the supervised spike mapping network are not lost after power failure.

[0065] Processor 2 is connected to memory 1. Processor 2 is used to read and execute computer-executable instructions stored in memory 1. When processor 2 executes computer-executable instructions, it implements step S1. Step S1 divides the raw data into multiple raw noisy calcium ion signal time series. When processor 2 executes computer-executable instructions, it implements step S2. Step S2 generates multiple subsequences containing the same underlying signal but with independent noise samples. When processor 2 executes computer-executable instructions, it implements step S3. Step S3 implements a pre-trained model for self-supervised denoising. When processor 2 executes computer-executable instructions, it implements step S4. Step S4 denoises the raw calcium ion signals. When processor 2 executes computer-executable instructions, it implements step S5. Step S5 constructs a supervised deep network model for learning and training. When processor 2 executes computer-executable instructions, it implements step S6. Step S6 maps calcium ion signals to neuronal spike potentials.

[0066] Processor 2 includes a central processing unit. Processor 2 also includes a graphics processing unit. The graphics processing unit is configured with a parallel computing architecture. The parallel computing architecture is used to accelerate the backpropagation gradient update calculation of the one-dimensional U-Net model in step S32. The parallel computing architecture is used to accelerate the convolution operation of the one-dimensional convolutional neural network in step S5.

[0067] Input / output interface 3 is used to establish a physical connection between the computing device and an external data source. The external data source includes a two-photon microscope imaging system. Input / output interface 3 receives the raw, noisy calcium ion signal time series from the two-photon microscope imaging system. Input / output interface 3 transmits the raw, noisy calcium ion signal time series to memory 1. Input / output interface 3 outputs the absolute spike rate sequence of neurons calculated by processor 2 to an external display terminal. The deep learning-based calcium ion imaging signal spike inference system utilizes the hardware collaboration of processor 2, memory 1, and input / output interface 3 to complete the signal conversion and inference from the noisy calcium ion signal to the neuronal spike potential.

[0068] See attached document Figure 1 This invention provides a method for inferring calcium ion imaging signal spikes based on deep learning, comprising the following steps:

[0069] The original noisy calcium ion signal time series was segmented into subsequences and a recovery sequence was generated by interval sampling. The recovery sequence was then used to construct a self-supervised learning task to train a one-dimensional U-Net neural network model.

[0070] A training dataset containing historical noisy calcium ion signal time series and corresponding real action potential sequences is obtained. The trained one-dimensional U-Net neural network model is used to denoise the historical noisy calcium ion signal time series to obtain the historical denoised signal.

[0071] A one-dimensional convolutional neural network model is trained by using historical denoised signals as input data and real action potential sequences as output targets.

[0072] The original noisy calcium ion signal time series to be processed is obtained, and the trained one-dimensional U-Net neural network model is used to denoise the original noisy calcium ion signal time series to be processed, so as to obtain the denoised calcium ion time series to be inferred.

[0073] The denoised calcium ion time series to be inferred is input into the trained one-dimensional convolutional neural network model to infer the absolute peak rate sequence of neurons.

[0074] After establishing the operating environment for the aforementioned deep learning-based calcium ion imaging signal spike inference system, processor 2 begins executing step S1. Step S1 performs interval sampling segmentation of the raw data. Processor 2 first acquires data of length... The original noisy calcium ion signal time series (i.e., the original noisy calcium ion signal time series with an initial length). The original noisy calcium ion signal time series is one-dimensional fluorescence intensity data acquired by equipment such as two-photon microscopes.

[0075] Processor 2 uses an interval sampling method to sample data of length 10 ... The original noisy calcium ion signal time series was segmented into Non-overlapping subsequences. The non-overlapping subsequences are labeled as follows: The length of each subsequence is defined as (i.e., the first length). The interval sampling operation ensures that each data point in the original noisy calcium ion signal time series is assigned to only one subsequence.

[0076] The physical basis for performing interval sampling in step S1 lies in the temporal redundancy characteristics of calcium ion signals. The original noisy calcium ion signal time series contains both ground truth and noise signals. The ground truth signal reflects changes in intracellular calcium concentration. The ground truth signal is a slow signal; its rate of change is slower than the firing rate of neuronal spikes. Therefore, in the original noisy calcium ion signal time series, the ground truth signals between adjacent frames or adjacent sampling points are highly correlated. The ground truth signals between adjacent frames or adjacent sampling points are considered to share the same biological state.

[0077] On the other hand, the noise signals appear independent and uncorrelated across different frames of the original noisy calcium ion signal time series. The noise signals mainly consist of photon noise from the acquisition process and readout noise. The noise signals conform to the statistical characteristics of independent and identically distributed signals.

[0078] Processor 2 utilizes the above characteristics to generate [the desired result] through interval sampling in step S1. Subsequences Specific conditions must be met. These specific conditions are: Each subsequence shares the same underlying truth signal, but Each subsequence contains independent noise samples. This data structure enables processor 2 to construct the training data pairs required for self-supervised learning by utilizing the cross-correlation between subsequences without requiring external real noise-free data. Step S1 provides an independent and aligned data foundation for the frequency domain transformation and interpolation recovery in the subsequent step S2.

[0079] See attached document Figure 1 After processor 2 divides the original data into multiple subsequences in step S1, it then executes step S2. Step S2 generates multiple subsequences containing the same underlying signal but with independent noise sampling. Step S2 specifically includes steps S21, S22, and S23. Processor 2 executes steps S21, S22, and S23 sequentially to achieve lossless recovery from the low-frequency subsequences to the original length sequence.

[0080] Processor 2 first executes step S21. Processor 2 processes the sampled data with a first length... subsequence of Perform a Discrete Fourier Transform (DFT). The DFT will transform the subsequence... Transform from the time domain to the frequency domain to obtain Each frequency coefficient represents a subsequence. Energy distribution at different frequency components. Frequency coefficient. Specifically, it is calculated using the following formula:

[0081] ;

[0082] in, Indicates the first One frequency coefficient; Indicates the length after sampling is The subsequence at time The value; Indicates the length of the subsequence. Indicates time-domain index, Indicates frequency domain index, It represents the imaginary unit.

[0083] Processor 2 then executes step S22. Processor 2 uses the frequency coefficients calculated in step S21. Embedded into a new array In the middle. New array The length is set to (That is, the second length). Second length Greater than the first length Processor 2 embeds the frequency coefficients into this new array of second length, extending the frequency coefficients to the length by padding the high-frequency regions with zeros. Zero-filling increases the number of sampling points in the frequency domain without introducing additional high-frequency noise. Zero-filling corresponds to interpolation in the time domain, yielding zero-fill frequency coefficients. The specific calculation formula for zero-filling is as follows:

[0084] ;

[0085] in, Indicates length is The zero-fill frequency coefficient; This represents the frequency coefficients calculated in step S21; Indicates the new array length; This indicates the frequency domain index.

[0086] Processor 2 finally executes step S23. Processor 2 then processes the second length... Zero-fill frequency coefficient Perform the inverse discrete Fourier transform. The inverse discrete Fourier transform fills in the zero-filled frequency coefficients. Transform from the frequency domain back to the time domain to obtain a value with a second length. recovery sequence Recovery sequence The length is .because Zeros were filled in the high-frequency region to recover the sequence. In the time domain, it exhibits a smooth interpolation result. (Recovering the sequence) The original subsequence was preserved. The low-frequency physical characteristics. The specific calculation formula for the inverse discrete Fourier transform is as follows:

[0087] ;

[0088] in, Indicates length is The recovery sequence; Indicates length is The zero-fill frequency coefficient; Indicates the new array length; Indicates a time-domain index; Indicates frequency domain index; It represents the imaginary unit.

[0089] Processor 2 for each subsequence Repeat steps S21 to S23. Processor 2 eventually obtains... A length of The recovery sequence. The recovery sequences will be used in subsequent steps to construct the input and target data required for self-supervised training.

[0090] See attached document Figure 1 After obtaining the recovered sequence in step S2, processor 2 then executes step S3. Step S3 is used to implement the pre-trained model for self-supervised denoising. Step S3 specifically includes steps S31, S32, and S33. Processor 2 uses the recovered sequence to construct a self-supervised learning task and trains the denoising model by mining supervision signals from the noisy data itself.

[0091] Processor 2 first executes step S31. For each set of recovery sequences, processor 2 selects one recovery sequence as the input to the network. Processor 2 marks the selected single recovery sequence as... Processor 2 will use the remaining Each of the recovered sequences is summed pixel-by-pixel (i.e., the remaining recovered sequences are summed pixel-by-pixel). Processor 2 uses the summation result as the target. The remaining The recovery sequences are labeled as .enter For a single sampled signal, the input It has a low signal-to-noise ratio. Target This corresponds to the superposition of multiple sampled signals. Since the noise is independent and has zero mean in different recovered sequences, the superposition of multiple independent noise samples leads to a reduction in noise variance. Target The signal-to-noise ratio is higher than the input. The signal-to-noise ratio. Target Used as a pseudo-real value for network learning. Input and target The construction follows the formula below:

[0092] ;

[0093] ;

[0094] in, Indicates the network input; Indicates the selected single sampled image; Indicate the goal; Indicates the remainder One image; This indicates the number of subsequences into which the segment is divided.

[0095] Processor 2 then executes step S32. Processor 2 constructs a one-dimensional U-Net neural network model. The one-dimensional U-Net neural network model is used to fit the input. To the target The mapping relationship. Processor 2 defines a loss function to quantify the mapping relationship between the network's predicted output and the target. The differences between them. The loss function uses mean squared error loss (based on...). Norm construction). Mean squared error loss calculation: Network prediction output and target of a one-dimensional U-Net neural network model. The sum of squared errors between them. The optimization process aims to minimize... Loss. In minimizing During the loss process, the one-dimensional U-Net neural network model is forced to learn to extract the input. Shared underlying signals, while suppressing input. Independent noise in the middle. The specific formula for calculating the loss is as follows:

[0096] ;

[0097] in, express loss; Indicates the number of samples; Indicates the first The sum of squared errors of each sample; Indicates the sequence length; This represents the network prediction output of a one-dimensional U-Net neural network model; Indicates the target is in the first place. The value at each position.

[0098] Processor 2 then executes step S33. Processor 2 uses the constructed input. and target The dataset is used for self-supervised training of a one-dimensional U-Net neural network model. Processor 2 updates the network parameters using the backpropagation algorithm to minimize... Loss. Processor 2 saves the trained network parameters. The training method described in step S33 solves the problem of not being able to obtain noiseless ground truth data during training. Step S33 only requires a large amount of noisy raw data for training. Due to the target encountered during the training process... It still contains weak noise, and the one-dimensional U-Net neural network model shows stronger generalization ability for noise in real data.

[0099] See attached document Figure 1 After processor 2 completes self-supervised training and saves the model parameters in step S3, processor 2 then executes step S4. Step S4 is used to denoise the original calcium ion signal. Step S4 utilizes the trained self-supervised model to directly process the noisy observation data without requiring real, noise-free data as a reference.

[0100] Processor 2 first acquires the raw, noisy calcium ion signal sequence to be processed. This raw, noisy calcium ion signal sequence is the target data for peak inference in subsequent steps. Processor 2 uses the raw, noisy calcium ion signal sequence as input. Processor 2 will input The data is then transferred to the one-dimensional U-Net neural network model trained in step S3.

[0101] The one-dimensional U-Net neural network model receives input The one-dimensional U-Net neural network model for input Perform forward propagation computation. The forward propagation computation utilizes the network parameters optimized through self-supervised learning in step S3. The one-dimensional U-Net neural network model, based on the network parameters, performs input... High-noise components in the input are identified as non-shared random perturbations and suppressed. Meanwhile, the one-dimensional U-Net neural network model preserves the input... The underlying shared signal conforms to the characteristics of calcium ion dynamics.

[0102] The one-dimensional U-Net neural network model outputs a denoised signal. The denoised signal is labeled as follows: The denoised signal Compared to input It has a higher signal-to-noise ratio. The denoised signal The waveform morphology of the calcium transient event was restored. The network's inference process is specifically expressed by the following formula:

[0103] ;

[0104] in, This represents the signal after denoising. The parameter is Neural network model; This represents the input high-noise sequence.

[0105] Processor 2 outputs a high signal-to-noise ratio (SNR) calcium ion time series in step S4. This high SNR calcium ion time series not only removes background noise but also avoids introducing artificial phase delays or waveform distortions. The high SNR calcium ion time series provides a high-quality data foundation for subsequent steps. It is important to note that step S4 plays a dual role in the processing flow: in the training phase, it processes historical training data to build the dataset; in the inference phase, it processes the raw, noisy data to be inferred to generate model input.

[0106] See attached document Figure 1 After obtaining the denoised signal in step S4, processor 2 then executes step S5. Step S5 is used to construct a supervised deep network model for learning and training. Step S5 aims to establish a precise mapping relationship between changes in calcium ion concentration and neuronal firing activity using the denoised, high-quality signal.

[0107] Processor 2 first constructs a one-dimensional convolutional neural network model. This model is configured as a supervised learning architecture. The design goal of the one-dimensional convolutional neural network model is to map the calcium signal sequence within an input time window to the action potential sequence at the corresponding time point. The action potential sequence is numerically represented as the absolute peak rate. The unit of absolute peak rate is the number of peaks per second.

[0108] To supervise the training of the one-dimensional convolutional neural network model, processor 2 first acquires a training dataset containing historical data. Specifically, the training dataset includes historical noisy calcium ion signal time series and corresponding true action potential sequences. To ensure the consistency of the input distribution, processor 2 uses the one-dimensional U-Net neural network model trained in step S3 to denoise the historical noisy calcium ion signal time series in the training dataset, obtaining denoised historical signals. The historical noisy calcium ion signal time series refers to sample data collected and stored before the current inference task for model training; the true action potential sequence refers to ground truth data obtained through high-precision methods such as electrophysiological recordings, corresponding to the historical noisy calcium ion signal time series in time.

[0109] To ensure the consistency of the input distribution, processor 2 uses the one-dimensional U-Net neural network model trained in step S3 to denoise the historical noisy calcium ion signal time series in the training dataset. The processing procedure is consistent with the forward inference calculation in step S4. Processor 2 obtains the processed historical denoised signal.

[0110] Processor 2 defines the input data for the one-dimensional convolutional neural network model. The input data is the historical denoised signal obtained above. Processor 2 defines the output target of the one-dimensional convolutional neural network model. The output target is the true action potential sequence corresponding to the historical noisy calcium ion signal time series. During the training phase, the true action potential sequence is obtained through electrophysiological recording and other means, serving as the baseline ground truth for training.

[0111] Processor 2 constructs the training dataset. The training dataset consists of a large number of paired data samples. Each data sample contains a historical denoised signal and a corresponding sequence of true peak rates. Processor 2 uses the training dataset to perform supervised training on the one-dimensional convolutional neural network model.

[0112] During training, processor 2 adjusts the network parameters of the one-dimensional convolutional neural network model using an optimization algorithm. The goal of the optimization algorithm is to minimize the difference between the predicted output and the actual peak rate of the one-dimensional convolutional neural network model. The specific formula for calculating the optimization objective is as follows:

[0113] ;

[0114] in, Indicates network parameters; Represents the loss function; This represents the predicted output of a one-dimensional convolutional neural network model. Represents the actual action potential sequence or absolute peak rate; Indicates the number of samples; Indicates the norm type; Indicates the first One calcium signal sequence sample; Indicates the first The true peak rate corresponding to each sample.

[0115] Processor 2 performs the above optimization process. Processor 2 calculates the predicted output of the one-dimensional convolutional neural network model. Compared with the true peak rate The norm distance between them is calculated. Processor 2 calculates the gradient based on the norm distance. Processor 2 uses the gradient to update the network parameters. Through repeated iterations, the one-dimensional convolutional neural network model gradually converges, ultimately yielding network parameters capable of accurately predicting neuronal spike activity. Processor 2 stores the trained supervised deep network model.

[0116] See attached document Figure 1 After processor 2 completes the construction and training of the supervised deep network model in step S5, it then executes step S6. Step S6 is used to map calcium ion signals to neuronal spike potentials. Step S6 applies the one-dimensional convolutional neural network model trained in step S5 to infer new observation data.

[0117] Processor 2 acquires the denoised calcium ion time series to be inferred. The denoised calcium ion time series to be inferred originates from the processing result of the newly input original noisy calcium ion signal time series (i.e., the original data to be processed acquired in step S1) in step S4. Processor 2 inputs the denoised calcium ion time series to be inferred into a trained one-dimensional convolutional neural network. The trained one-dimensional convolutional neural network is in inference mode.

[0118] A one-dimensional convolutional neural network (CNN) receives a denoised calcium ion time series. The CNN processes the denoised calcium ion time series using multiple layers of convolutional kernels. These kernels slide along the time dimension. This sliding operation allows the CNN to scan the entire denoised calcium ion time series.

[0119] One-dimensional convolutional neural networks automatically identify key features related to spike occurrence through multiple layers of convolutional kernels. These key features specifically include the steepness of the rising edge of the calcium signal, the peak amplitude, and the decay rate. Based on these key features, the one-dimensional convolutional neural network determines the probability and intensity of neuron firing.

[0120] One-dimensional convolutional neural networks perform complex nonlinear deconvolution mapping. This nonlinear deconvolution mapping transforms the extracted biophysical features into a target output. The target output is a sequence of absolute peak rates of neurons. This absolute peak rate sequence visually reflects the firing frequency of neurons at different times.

[0121] In step S6, processor 2 completes the end-to-end inference process. This process utilizes a supervised learning mechanism to capture the causal relationship between calcium signals and neuronal firing. The end-to-end inference process maps slow, ambiguous calcium signals to fast, discrete action potentials. Processor 2 stores the generated absolute peak rate sequence in memory 1, or outputs the absolute peak rate sequence through input / output interface 3.

[0122] See attached document Figure 3 Appendix Figure 4 Appendix Figure 5 Appendix Figure 6 and attached Figure 7 This invention verifies the technical effectiveness of the first-stage self-supervised denoising preprocessing using experimental data. To verify the effectiveness of the signal denoising inference in step S4, processor 2 selects a typical original noisy calcium ion signal as the test object. The original noisy calcium ion signal was acquired using a two-photon microscope.

[0123] The original noisy calcium ion signal contains photon noise. The original noisy calcium ion signal contains readout noise. The baseline portion of the original noisy calcium ion signal exhibits violent random fluctuations. These random fluctuations mask small, weak calcium transient events.

[0124] Processor 2 inputs the raw, noisy calcium ion signal into the one-dimensional U-Net neural network model trained in step S3. The one-dimensional U-Net neural network model performs forward inference computation. The one-dimensional U-Net neural network model outputs the denoised calcium ion signal. (Appendix) Figure 3 Appendix Figure 4 Appendix Figure 5 Appendix Figure 6 and attached Figure 7 The time-domain waveforms of the original noisy calcium ion signal and the denoised calcium ion signal are shown.

[0125] Observation Appendix Figure 3 Appendix Figure 4 Appendix Figure 5 Appendix Figure 6 and attached Figure 7 The waveform comparison results show that the denoised calcium ion signal suppresses high-frequency noise components in the background. The baseline of the denoised calcium ion signal exhibits a smooth curve. The signal-to-noise ratio (SNR) of the denoised calcium ion signal is higher than that of the original noisy calcium ion signal. The high SNR indicates that the one-dimensional U-Net neural network model successfully separated the underlying signal from random noise.

[0126] Further comparison of the morphological characteristics of the original noisy calcium ion signal and the denoised calcium ion signal revealed that the denoised calcium ion signal fully preserved the rising edge steepness of the calcium transient event. The denoised calcium ion signal also fully preserved the exponential decay rate of the calcium transient event. Rising edge steepness and exponential decay rate are key biophysical features for subsequent inference of neuronal spikes.

[0127] The denoised calcium ion signal is strictly aligned with the original noisy calcium ion signal on the time axis. No phase delay is introduced into the denoised calcium ion signal. The peak occurrence time of the denoised calcium ion signal coincides with the peak occurrence time of the original noisy calcium ion signal. This zero phase delay characteristic makes the self-supervised denoising method of this invention superior to traditional linear filters or low-pass filters. Zero phase delay ensures the accuracy of neuronal action potential timing. The denoised calcium ion signal provides a high-quality, high-fidelity input data foundation for the second-stage supervised spike mapping.

[0128] See attached document Figure 8 Appendix Figure 9 Appendix Figure 10 and attached Figure 11 This invention further verifies the technical effectiveness of the second-stage supervised spike mapping using experimental data. After processor 2 completes the signal denoising inference in step S4 and obtains a high-quality denoised calcium ion signal, processor 2 continues to execute the end-to-end nonlinear mapping inference in step S6. Processor 2 inputs the denoised calcium ion signal into the trained one-dimensional convolutional neural network model.

[0129] The one-dimensional convolutional neural network model outputs an inferred sequence of absolute neuronal peak rates. To verify the accuracy of the inferred sequence, extracellular electrophysiological signals recorded simultaneously with calcium imaging were introduced. These signals were processed and converted into a true sequence of neuronal peak firing rates. This true sequence served as the ground truth for verifying the accuracy of the inference.

[0130] Appendix Figure 8 Appendix Figure 9 Appendix Figure 10 and attached Figure 11 This demonstrates the complete process from raw input to final inference, and compares the inferred absolute peak rate sequence of neurons with the actual peak firing rate sequence of neurons on the same time axis, i.e., the inferred frequency. Figure 8 The waveform in the image represents the time-domain waveform of the original noisy calcium ion signal input. (See attached image.) Figure 9 The waveform in the image represents the time-domain waveform of the denoised calcium ion signal after step S4. (See attached image.) Figure 10 The waveforms in the image represent the actual spike firing rate sequence of neurons. (See attached image.) Figure 11 The waveform in the figure represents the inferred absolute spike rate sequence of neurons.

[0131] Observation Appendix Figure 10 and attached Figure 11 It can be seen that the inferred absolute peak rate sequence of neurons is consistent with the actual peak firing rate sequence of neurons in terms of time phase. During the time window when the actual peak firing rate sequence of neurons exhibits dense firing, the inferred absolute peak rate sequence of neurons synchronously shows a high-amplitude response peak. During the resting period without firing activity, the inferred absolute peak rate sequence of neurons remains at a baseline level close to zero.

[0132] Processor 2 uses the Pearson correlation coefficient as a quantitative indicator to objectively evaluate the prediction accuracy. Processor 2 calculates the degree of linear correlation between the inferred absolute peak rate sequence of neurons and the actual peak firing rate sequence of neurons.

[0133] The Pearson correlation coefficient is calculated using the following formula:

[0134] ;

[0135] in, This represents the Pearson correlation coefficient; This represents the total number of time points in the sequence. Indicates the first The predicted absolute peak rate value at each time point; This represents the average value of the predicted absolute peak rate sequence; Indicates the first The actual peak distribution rate at each point in time; This represents the average value of the true peak release rate sequence.

[0136] The Pearson correlation coefficient calculated using the above formula reaches above 0.85. A Pearson correlation coefficient above 0.85 indicates that the one-dimensional convolutional neural network model successfully established a strong correlation mapping between calcium fluorescence signals and neuronal electrical activity. Experimental results confirm that the deep learning-based calcium ion imaging signal spike inference system proposed in this invention can accurately calculate discrete firing events of neurons from complex calcium dynamic changes. Experimental results also confirm that the deep learning-based calcium ion imaging signal spike inference system recovers the intensity information of neuronal activity while preserving temporal accuracy.

Claims

1. A method for inferring calcium ion imaging signal spikes based on deep learning, characterized in that, Includes the following steps: The original noisy calcium ion signal time series was segmented into subsequences and a recovered sequence was generated by interval sampling. The method of constructing a self-supervised learning task using the recovered sequences to train a one-dimensional U-Net neural network model includes: for each set of recovered sequences, selecting one of the recovered sequences as the network input, and summing the remaining recovered sequences pixel by pixel as the target; the input corresponds to a single-sampled signal, the target corresponds to a superimposed signal of multiple samples, and the signal-to-noise ratio of the target is higher than that of the input; training the one-dimensional U-Net neural network model using the input and the target, defining a loss function to quantify the difference between the network's predicted output and the target, updating the network parameters through a backpropagation algorithm to minimize the loss function, and forcing the one-dimensional U-Net neural network model to learn to extract the shared low-level signals in the input and suppress independent noise in the input; A training dataset containing historical noisy calcium ion signal time series and corresponding real action potential sequences is obtained. The trained one-dimensional U-Net neural network model is used to denoise the historical noisy calcium ion signal time series to obtain the historical denoised signal. A one-dimensional convolutional neural network model is trained using the historical denoised signal as input data and the real action potential sequence as output target. The original noisy calcium ion signal time series to be processed is obtained, and the trained one-dimensional U-Net neural network model is used to denoise the original noisy calcium ion signal time series to be processed, so as to obtain the denoised calcium ion time series to be inferred. The denoised calcium ion time series to be inferred is input into the trained one-dimensional convolutional neural network model to infer the absolute peak rate sequence of neurons.

2. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The specific steps for segmenting the original noisy calcium ion signal time series into sub-sequences and generating a recovered sequence by interval sampling include: The original noisy calcium ion signal time series with an initial length is divided into multiple non-overlapping subsequences, which share the same underlying ground truth signal and each contains independent noise samples. Perform a discrete Fourier transform on the sampled subsequence of the first length to obtain multiple frequency coefficients; The frequency coefficients are embedded into a new array with a second length, which is greater than the first length. The frequency coefficients are extended to the second length by filling the high-frequency region with zeros to obtain zero-filled frequency coefficients. Perform an inverse discrete Fourier transform on the zero-filled frequency coefficients having the second length to obtain the recovered sequence having the second length.

3. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The loss function uses mean squared error loss, which calculates the sum of squared errors between the network prediction output of the one-dimensional U-Net neural network model and the target.

4. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The step of denoising the historical noisy calcium ion signal time series using the trained one-dimensional U-Net neural network model specifically includes: The historical noisy calcium ion signal time series is input into the one-dimensional U-Net neural network model; The one-dimensional U-Net neural network model performs forward propagation calculations, identifies high-noise components in the historical noisy calcium ion signal time series as non-shared random perturbations based on network parameters and suppresses them, while retaining the underlying shared signals that conform to the characteristics of calcium ion dynamics, and outputs the historical denoised signal.

5. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The specific steps for training a one-dimensional convolutional neural network model using the historical denoised signal as input data and the real action potential sequence as output target include: The design goal of the one-dimensional convolutional neural network model is to map the input historical denoised signal to the real action potential sequence at the corresponding time point, wherein the real action potential sequence is numerically represented as the absolute peak rate. The network parameters of the one-dimensional convolutional neural network model are adjusted by an optimization algorithm. The goal of the optimization algorithm is to minimize the difference between the predicted output and the actual peak rate of the one-dimensional convolutional neural network model. Calculate the norm distance between the predicted output of the one-dimensional convolutional neural network model and the true peak rate, calculate the gradient based on the norm distance, and update the network parameters using the gradient.

6. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The specific steps for obtaining the original noisy calcium ion signal time series to be processed include: One-dimensional fluorescence intensity data was acquired using a two-photon microscope imaging system to obtain the original noisy calcium ion signal time series to be processed. The original noisy calcium ion signal time series to be processed contains photon noise and readout noise.

7. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The specific steps for inferring the absolute peak rate sequence of neurons include: The one-dimensional convolutional neural network model uses multi-layer convolutional kernels to process the denoised calcium ion time series to be inferred, and the multi-layer convolutional kernels perform sliding operations in the time dimension. The one-dimensional convolutional neural network model automatically identifies key features related to peak occurrence through the multi-layer convolutional kernels. These key features include the steepness of the rising edge of the calcium signal, the peak amplitude, and the decay rate. The one-dimensional convolutional neural network model performs nonlinear deconvolution mapping to transform the extracted biophysical features into the absolute peak rate sequence.

8. The method for inferring calcium ion imaging signal spikes based on deep learning according to claim 1, characterized in that, The denoised calcium ion time series output by the one-dimensional U-Net neural network model is aligned with the original noisy calcium ion signal time series on the time axis without introducing phase delay.

9. A deep learning-based calcium ion imaging signal spike inference system, characterized in that, A method for performing the deep learning-based calcium ion imaging signal spike inference method according to any one of claims 1-8 includes: The memory (1) is used to store computer-executable instructions, parameters of the trained self-supervised denoising model, and parameters of the trained supervised spike mapping network. The processor (2) is used to read and execute the computer-executable instructions stored in the memory (1) and execute the deep learning-based calcium ion imaging signal spike inference method; Input / output interface (3) is used to establish a physical connection between the computing device and an external data source, receive the original noisy calcium ion signal time series from the two-photon microscope imaging system, and output the neuron absolute peak rate sequence calculated by the processor (2); A communication bus (4) is used to physically connect the processor (2), the memory (1) and the input / output interface (3) and to establish a data transmission channel between the processor (2), the memory (1) and the input / output interface (3).

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