Waveform non-negative iterative optimization method for maintaining power spectrum characteristics and related device

Abstract

The invention provides a waveform non-negative iterative optimization method for maintaining power spectrum characteristics and a related device, and the method comprises the steps: setting system initial setting, and initializing the input; performing negative suppression operation and energy normalization processing on the initial time domain waveform in the time domain by using the suppression factor and the total waveform energy to obtain a first time domain waveform; performing power spectrum hybrid constraint and phase reservation processing on the first time domain waveform in a frequency domain by using the hybrid factor and a target power spectrum to obtain a first frequency domain waveform; performing time domain updating on the first frequency domain waveform to obtain a second time domain waveform; judging whether the current iteration meets a preset convergence condition or not; if it is determined that the current iteration does not meet the preset convergence condition, iteration optimization processing is returned; and if it is determined that the current iteration meets the preset convergence condition, outputting the second time domain waveform as a final time domain waveform. According to the method, the approximately optimal waveform which can be physically realized and can be used in engineering can be obtained.

Description

Technical Field

[0001] This application relates to the field of signal processing and waveform design technology, and in particular to a waveform nonnegativity iterative optimization method and related apparatus that preserves power spectrum characteristics. Background Technology

[0002] In many signal processing and waveform design applications, it is often necessary to design a time-domain waveform. to make its power spectrum Matching a preset ideal target power spectrum For example, in photoacoustic imaging, the power spectrum of the excitation laser needs to be optimized to maximize the accuracy of the estimation of absorber parameters; in radar systems, a transmitted signal with a specific power spectrum needs to be designed to obtain good resolution characteristics.

[0003] The conventional signal processing and waveform design process is as follows: first, obtain the target power spectrum through optimization theory. Then, the time-domain waveform is generated through inverse Fourier transform. A common approach is to take the square root of the target power spectrum as the Fourier amplitude and assume an initial phase (usually zero phase), which can be expressed by the following formula (1). Wherein, in formula (1) This represents the inverse Fourier transform.

[0004] (1)

[0005] However, the waveform directly generated by formula (1) It often contains significant negative components. In physical systems such as laser emitters and acoustic transducers, negative values ​​correspond to "absorbed energy," which is physically difficult to achieve or places unrealistic demands on the hardware. Therefore, the "optimal" waveform theoretically obtained from formula (1) is often unusable due to physical limitations.

[0006] Currently, phase retrieval algorithms have been extensively studied to address the problem of reconstructing signals from power spectra (or Fourier amplitudes), such as the Gerchberg-Saxton (GS) algorithm and its variants, as well as the Wirtinger Flow algorithm in recent years. However, these algorithms recover the phase of the signal by alternately applying constraints (such as time-domain support sets, real-valuedness, and frequency-domain amplitude) in the time and frequency domains, and typically do not treat the numerical sign (i.e., non-negativity) of the time-domain signal as a core constraint.

[0007] In addition, although there are algorithms that force nonnegativity in fields such as image processing (such as Richardson-Lucy deconvolution and fast positive signal recovery algorithm based on quadratic programming), their goal is image restoration, not waveform design, nor is it aimed at matching a specific power spectrum.

[0008] Furthermore, while there are studies on constant modulus signal design in radar waveform design, these methods also do not specifically address nonnegativity issues.

[0009] In summary, existing technologies lack a waveform design method that can simultaneously meet the following three key requirements: (1) The power spectrum of the generated waveform is highly consistent with the given target power spectrum; (2) The negative energy in the time domain of the generated waveform is suppressed to the greatest extent (ideally negligible) to meet the engineering requirements of physical implementation; (3) The total energy of the waveform is controllable or kept constant. Summary of the Invention

[0010] This application provides a waveform nonnegativity iterative optimization method and related apparatus that preserves power spectrum characteristics, in order to solve the problems existing in related technologies. The technical solution is as follows: In a first aspect, embodiments of this application provide a waveform nonnegativity iterative optimization method that preserves power spectral characteristics, including: Set the initial system settings and initialize the inputs. The initial system settings include the target power spectrum, total waveform energy, suppression factor for controlling the strength of nonnegativity constraints, mixing factor for controlling the strength of power spectrum matching, maximum number of iterations, and convergence threshold. The initial inputs include setting the initial time-domain waveform and setting the number of iterations to 1. Using the suppression factor and the total energy of the waveform, the initial time-domain waveform is subjected to negative suppression and energy normalization in the time domain to obtain the first time-domain waveform; Using the mixing factor and the target power spectrum, the first time-domain waveform is subjected to power spectrum mixing constraint and phase preservation processing in the frequency domain to obtain the first frequency-domain waveform; The first frequency domain waveform is updated in the time domain to obtain the second time domain waveform; Determine whether the current iteration meets the preset convergence condition, wherein the preset convergence condition is that the number of iterations reaches the maximum number of iterations, or the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold. If it is determined that the current iteration does not meet the preset convergence condition, the iteration number is incremented by 1, and the second time-domain waveform replaces the initial time-domain waveform. Then, the process is returned to perform negative suppression and energy normalization on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. If it is determined that the current iteration satisfies the preset convergence condition, then the second time-domain waveform is output as the final time-domain waveform.

[0011] In one embodiment, using the suppression factor and the total waveform energy, the initial time-domain waveform is subjected to negative suppression and energy normalization in the time domain to obtain a first time-domain waveform, including: The initial time-domain waveform is subjected to negative suppression using the suppression factor to obtain the third time-domain waveform. The first time-domain waveform is obtained by normalizing the energy of the third time-domain waveform using the total energy of the waveform.

[0012] In one embodiment, the method of using the inhibition factor to perform a negative value suppression operation on the initial time-domain waveform to obtain a third time-domain waveform includes: using the inhibition factor to perform a negative value suppression operation on the initial time-domain waveform based on the following formula (3) to obtain the third time-domain waveform; The process of normalizing the third time-domain waveform with the total energy of the waveform to obtain the first time-domain waveform includes: normalizing the third time-domain waveform with the total energy of the waveform based on the following formula (4) to obtain the first time-domain waveform; (3) In formula (3), Represented as the third time-domain waveform; Represented as an indicator function; The inhibitory factor is denoted as [insert inhibitory factor here], which controls the intensity of negative inhibition: For strong suppression (set to zero). To preserve attenuation, To decay and invert the sign; This is represented as the initial time-domain waveform; (4) In formula (4), Represented as the first time-domain waveform; E It is represented as the total energy of the waveform.

[0013] In one embodiment, the first time-domain waveform is subjected to power spectrum mixing constraint and phase preservation processing in the frequency domain using the mixing factor and the target power spectrum to obtain the first frequency-domain waveform, including: The first time-domain waveform is transformed in the frequency domain and its power spectrum is calculated to obtain the second frequency-domain waveform and the first power spectrum. By combining the target power spectrum and the first power spectrum with the mixing factor, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing to obtain the third frequency domain waveform. The first frequency domain waveform is obtained by applying Hermite symmetry constraints to the third frequency domain waveform.

[0014] In one embodiment, performing frequency domain transformation and power spectrum calculation on the first time domain waveform to obtain a second frequency domain waveform and a first power spectrum includes: performing frequency domain transformation on the first time domain waveform based on the following formula (5) to obtain a second frequency domain waveform, and then performing power spectrum calculation on the second time domain waveform based on the following formula (6) to obtain the first power spectrum; Using the mixing factor to combine the target power spectrum and the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing to obtain the third frequency domain waveform, including: using the mixing factor to combine the target power spectrum and the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing based on the following formula (7) to obtain the third frequency domain waveform; Applying Hermite symmetry constraints to the third frequency domain waveform to obtain the first frequency domain waveform includes: applying Hermite symmetry constraints to the third frequency domain waveform based on the following formula (8) to obtain the first frequency domain waveform; (5) In formula (5), Represented as the first time-domain waveform; Represented as a second frequency domain waveform; F This is represented as a Fourier transform; (6) In formula (6), This is represented as the first power spectrum; (7) In formula (7), The waveform in the third frequency domain is represented as arctan 2; arctan 2 is represented as the arctangent function in the fourth quadrant. i Represented as the imaginary unit; This is represented by taking the imaginary part. Represented as taking the real part; Represented as a mixing factor, it controls the tightness of the power spectral constraint: This indicates a strict requirement for the target power spectrum. A value closer to 1 indicates a more moderate update, relying more on the results of the current iteration; (8) In formula (8), Represented as a waveform in the first frequency domain; Indicated as taking Conjugate.

[0015] In one implementation, updating the first frequency domain waveform in the time domain to obtain a second time domain waveform includes: The first frequency domain waveform is updated in the time domain based on the following formula (9) to obtain the second time domain waveform; (9) in, Represented as a second time-domain waveform; Represented as the first frequency domain waveform; This is represented as the inverse Fourier transform.

[0016] In one implementation, determining whether the current iteration satisfies a preset convergence condition includes: Calculate the total negative energy of the second time-domain waveform in the current iteration and the total negative energy of the initial time-domain waveform, respectively. Then, based on the total negative energy of the second time-domain waveform and the total negative energy of the initial time-domain waveform, calculate the rate of change of the total negative energy in the current iteration. Calculate the initial power spectrum corresponding to the initial time-domain waveform; The mean square error of the first power spectrum and the mean square error of the initial power spectrum in the current iteration are calculated respectively. Then, based on the mean square error of the first power spectrum and the mean square error of the initial power spectrum, the rate of change of the mean square error of the power spectrum in the current iteration is calculated. The current iteration is judged to meet the preset convergence condition by determining whether the current iteration number has reached the maximum iteration number, and by determining that the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold.

[0017] Secondly, embodiments of this application also provide a waveform nonnegativity iterative optimization system that preserves power spectrum characteristics, comprising: An initial setting unit is used to set the initial settings of the system and initialize the inputs. The initial settings of the system include the target power spectrum, the total energy of the waveform, the suppression factor for controlling the strength of the non-negativity constraint and the mixing factor for controlling the strength of the power spectrum matching, the maximum number of iterations and the convergence threshold. The initial inputs include setting the initial time-domain waveform and setting the number of iterations to 1. The first processing unit is used to perform negative suppression operation and energy normalization processing on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. The second processing unit is used to perform power spectrum mixing constraint and phase preservation processing on the first time domain waveform in the frequency domain using the mixing factor and the target power spectrum to obtain the first frequency domain waveform. A time-domain update unit is used to update the first frequency-domain waveform in the time domain to obtain a second time-domain waveform. The result judgment unit is used to determine whether the current iteration meets the preset convergence condition, wherein the preset convergence condition is that the number of iterations reaches the maximum number of iterations, or the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold; if it is determined that the current iteration does not meet the preset convergence condition, the iteration number is incremented by 1, and the second time-domain waveform replaces the initial time-domain waveform, and the process is returned to the first processing unit to perform negative value suppression and energy normalization processing on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform; if it is determined that the current iteration meets the preset convergence condition, the second time-domain waveform is output as the final time-domain waveform.

[0018] Thirdly, embodiments of this application also provide an electronic device, which includes a memory and a processor, wherein the memory stores instructions, the instructions are loaded and executed by the processor to implement the methods in any of the above embodiments, wherein the memory and the processor communicate with each other through an internal connection path.

[0019] Fourthly, embodiments of this application also provide a computer-readable storage medium storing a computer program that, when run on a computer, implements the methods in any of the above-described embodiments.

[0020] The advantages or beneficial effects of the above technical solutions include at least the following: (a) High physical realizability: Through optimization, the total negative energy of the waveform ( TNE The residual negative values ​​are reduced to extremely low levels (e.g., below 0.1% of the total energy). In engineering, such residual negative values ​​can be completely eliminated through simple post-processing, resulting in a strictly non-negative transmit waveform, thus solving the fundamental problem that the theoretically optimal waveform is physically unrealizable.

[0021] (ii) Excellent spectral fidelity and controllable negative value suppression: By independently adjusting the suppression factor and mixing factor, users can achieve excellent power spectral fidelity (…). MSE ) and negative suppression intensity ( TNE It makes a fine and predictable trade-off between these factors, flexibly adapting to the tolerance requirements of different applications.

[0022] (iii) Strong robustness: It is not sensitive to the choice of initial time-domain waveform. Using an initial time-domain waveform close to the optimal solution can accelerate convergence. Even if it starts with a positive definite waveform with large differences (such as a Gaussian pulse), it can still converge stably to a satisfactory solution.

[0023] (iv) Clear convergence: Provides a method based on TNE rate of change and MSEAn objective convergence criterion for the rate of change makes the iterative process controllable and predictable.

[0024] (v) High versatility: It does not depend on a specific physical model and is applicable to any field that needs to generate low negative values ​​or even non-negative waveforms from the power spectrum, thus having good universality.

[0025] The above overview is for illustrative purposes only and is not intended to be limiting in any way. In addition to the illustrative aspects, embodiments, and features described above, further aspects, embodiments, and features of this application will become readily apparent from the accompanying drawings and the following detailed description. Attached Figure Description

[0026] In the accompanying drawings, unless otherwise specified, the same reference numerals throughout the various drawings denote the same or similar parts or elements. These drawings are not necessarily drawn to scale. It should be understood that these drawings depict only some embodiments disclosed in this application and should not be construed as limiting the scope of this application.

[0027] Figure 1 A flowchart illustrating an iterative optimization method for maintaining the non-negativity of the waveform while preserving power spectrum characteristics, provided in an embodiment of this application; Figure 2 This application provides an embodiment that uses an optimal waveform as the initial time-domain waveform, and takes... =0.1、 Example graph of the convergence curve when = 0.9; Figure 3 A corresponding embodiment provided in this application Figure 2 The final time-domain waveform Example diagram; Figure 4 This application provides an embodiment that uses a Gaussian pulse as the initial time-domain waveform, and takes... =0.1、 Example graph of the convergence curve when = 0.9; Figure 5 This application provides a structural block diagram of a waveform nonnegativity iterative optimization system that preserves power spectrum characteristics, as provided in an embodiment of the present application. Figure 6 This is a structural block diagram of an electronic device provided in an embodiment of this application. Detailed Implementation

[0028] In the following description, only certain exemplary embodiments are briefly described. As those skilled in the art will recognize, the described embodiments can be modified in various ways without departing from the spirit or scope of this application. Therefore, the drawings and description are considered to be exemplary in nature and not restrictive.

[0029] Figure 1 A flowchart illustrating an iterative optimization method for preserving the nonnegativity of the waveform according to an embodiment of this application is shown. Figure 1 As shown, the method may include the following steps: S110. Set the initial system settings and initialize the input.

[0030] In one implementation, the initial settings of the system may include, but are not limited to: target power spectrum, total waveform energy, suppression factor and mixing factor, maximum number of iterations, and convergence threshold. The suppression factor and mixing factor are tuning parameters, meaning they can be adjusted by the user / system. In this paper, the target power spectrum is... This indicates that the total waveform energy is expressed using... E This indicates that the inhibitory factor is used This indicates that the mixing factor is adopted. This indicates that the maximum number of iterations is K. max This indicates that the convergence threshold is adopted. express.

[0031] It should be understood that inhibitory factors Used to control the strength of nonnegativity constraints, where, The smaller the value, the stronger the constraint on nonnegativity. Mixture factor Used to control the power spectrum matching intensity, where The smaller the value, the stronger the constraint on the power spectrum. By adjusting these two parameters, a flexible trade-off can be struck between power spectrum fidelity and nonnegativity to suit different application requirements.

[0032] For example, an inhibitory factor can be set. The range of values ​​is A mixing factor can be set. The range of values ​​is .

[0033] In practical implementation, the maximum number of iterations and convergence threshold The value can be selected according to actual needs, and the embodiments in this application are not specifically limited here.

[0034] In one implementation, the initialization input may include, but is not limited to: setting an initial time-domain waveform and setting the number of iterations to 1.

[0035] As an example, the initial time-domain waveform It can be expressed using the following formula (2).

[0036] (2) In formula (2), kThis represents the number of iterations. It should be understood that during the initialization of input operations, k =1.

[0037] In practical applications, the initial time-domain waveform can be other waveforms besides those in the examples above, such as other positive definite initial waveforms (e.g., Gaussian pulses), etc. This application does not limit this.

[0038] S120. Using the suppression factor and the total energy of the waveform, the initial time-domain waveform is subjected to negative suppression operation and energy normalization in the time domain to obtain the first time-domain waveform.

[0039] In one implementation, the process of step S120 may include the following sub-steps: S121, Utilizing inhibitory factors The initial time-domain waveform is subjected to negative value suppression to obtain the third time-domain waveform.

[0040] As an example, inhibitory factors can be utilized. The initial time-domain waveform is subjected to negative value suppression operation based on the following formula (3) to obtain the third time-domain waveform.

[0041] (3) In formula (3), Represented as a third time-domain waveform; Represented as an indicator function; inhibition factor Controlling the intensity of negative value suppression: For strong suppression (set to zero). To preserve attenuation, This is a decay and inverted sign.

[0042] In this embodiment of the application, by executing sub-step S121, a soft positive constraint can be enforced, that is, by utilizing an inhibition factor. The negative values ​​of the initial time-domain waveform were suppressed. This can be understood as sub-step S121 being a key step in the iterative process, which uses a suppression factor... Controlling the attenuation of negative values ​​is a necessary condition for ensuring that optimized waveforms can be physically achieved in fields such as optical imaging, photoacoustic imaging, and lidar, which require non-negativity of waveforms.

[0043] S122, Utilizing the total energy of the waveform E The third time-domain waveform is subjected to energy normalization to obtain the first time-domain waveform.

[0044] As an example, the total energy of the waveform can be utilized. E The third time-domain waveform is normalized by the following formula (4) to obtain the first time-domain waveform.

[0045] (4) In formula (4), This is represented as the first time-domain waveform.

[0046] In practical applications, such as optical imaging, photoacoustic imaging, and lidar, devices have strict limitations on waveform energy. Therefore, this embodiment of the application can enforce energy limitations by executing sub-step S122, which normalizes the total waveform energy variation introduced in sub-step S121 to maintain a constant total signal energy, thus meeting the device's energy requirements.

[0047] S130. Using the mixing factor and the target power spectrum, the first time-domain waveform is subjected to power spectrum mixing constraint and phase preservation processing in the frequency domain to obtain the first frequency-domain waveform.

[0048] In one implementation, the process of step S130 may include the following sub-steps: S131. Perform frequency domain transformation and power spectrum calculation on the first time domain waveform to obtain the second frequency domain waveform and the first power spectrum.

[0049] As an example, the first time-domain waveform can be frequency-domain transformed based on the following formula (5) to obtain the second frequency-domain waveform, and then the power spectrum of the second time-domain waveform can be calculated based on the following formula (6) to obtain the first power spectrum.

[0050] (5) In formula (5), Represented as a second frequency domain waveform; F This is represented as a Fourier transform.

[0051] (6) In formula (6), This is represented as the first power spectrum.

[0052] In this embodiment of the application, by executing sub-step S131, the first time-domain waveform in step S120 can be transformed to the frequency domain for subsequent processing. Sub-step S131 can be understood as an intermediate step in the iterative process.

[0053] S132. Using a mixing factor to combine the target power spectrum and the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing to obtain the third frequency domain waveform.

[0054] As an example, a mixing factor can be used. Combined with target power spectrum Based on the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing according to the following formula (7) to obtain the third frequency domain waveform.

[0055] (7) In formula (7), Represented as a waveform in the third frequency domain; arctan 2 represents the arctangent function in the fourth quadrant; i Represented as the imaginary unit; This is represented by taking the imaginary part; Represented as taking the real part; mixing factor Controlling the tightness of power spectral constraints: This indicates a strict requirement to use the target power spectrum; A value close to 1 indicates a more moderate update, relying more on the results of the current iteration.

[0056] In this embodiment of the application, by executing sub-step S132, soft amplitude constraints can be implemented during the update, i.e., by utilizing a hybrid factor. Soft constraints are applied to the power spectrum. This can be understood as sub-step S132 being a key step in the iterative process, which utilizes a mixing factor. Smooth adjustment of the spectral amplitude can meet the requirements for waveform power spectrum distribution in fields such as optical imaging, photoacoustic imaging, and lidar.

[0057] S133. Apply Hermitian symmetry constraints to the third frequency domain waveform to obtain the first frequency domain waveform.

[0058] As an example, the first frequency domain waveform can be obtained by applying Hermite symmetry constraints to the third frequency domain waveform based on the following formula (8).

[0059] (8) In formula (8), Represented as a waveform in the first frequency domain; Indicated as taking Conjugate.

[0060] In this embodiment, by executing sub-step S133, Helmet symmetry can be forcibly introduced to ensure that the waveform is real in the time domain. Sub-step S133 can be understood as a key step in the iteration process that generates a physically realizable waveform, guaranteeing that the time-domain signal is real.

[0061] In this embodiment, a soft-constraint iterative framework is proposed by executing steps S120 and S130. This framework, combining projection and feedback mechanisms, innovatively constructs a dual soft-constraint mechanism. Specifically, it applies a parameterized negative suppression operation in the time domain (e.g., using a suppression factor in the time domain). Handling the negative value portion, including scaling, attenuation, and sign inversion, and applying parameterized power spectral mixing constraints in the frequency domain (such as using a mixing factor in the frequency domain). This soft-constraint iterative framework involves a weighted mixing of the current and target power spectra, with energy normalization and phase preservation alternately performed during iteration. This allows for the systematic and controllable minimization of negative energy in the time-domain waveform while strictly ensuring high-fidelity power spectrum and total energy constraints, resulting in a physically realizable and engineering-usable near-optimal waveform. In other words, this framework extends traditional Gerchberg-Saxton methods, for the first time integrating nonnegativity and power spectrum constraints simultaneously into the iterative projection process.

[0062] S140. Update the first frequency domain waveform in the time domain to obtain the second time domain waveform.

[0063] As an example, the second time-domain waveform can be obtained by updating the first frequency domain waveform based on the following formula (9).

[0064] (9) In formula (9), Represented as a second time-domain waveform; This is represented as the inverse Fourier transform.

[0065] In this embodiment of the application, a new generation of time-domain waveforms can be generated by executing step S140. When the preset convergence condition is met in the subsequent determination, it becomes the final time-domain waveform.

[0066] S150. Determine whether the current iteration meets the preset convergence condition. If not, proceed to step S160; or if it does, proceed to step S170.

[0067] In one implementation, the preset convergence condition is that the number of iterations k reaches the maximum number of iterations K. max Or, the rate of change of the total negative energy of the waveform and the rate of change of the mean square error of the power spectrum are both less than the convergence threshold. .

[0068] In one implementation, the total negative energy of the second time-domain waveform in the current iteration can be calculated separately. TNE k+1 The total negative energy of the initial time-domain waveform TNE k Based on the total negative energy of the second time-domain waveform TNE k+1 The total negative energy of the initial time-domain waveform TNE k The total negative energy change rate of the current iteration is calculated.

[0069] As an example, the total negative energy of the second time-domain waveform can be calculated according to the following formula (10). TNE k+1The total negative energy of the initial time-domain waveform TNE k Based on the total negative energy of the second time-domain waveform TNE k+1 The total negative energy of the initial time-domain waveform TNE k The total negative energy change rate of the current iteration is calculated using the following formula (11).

[0070] (10) In formula (10), TNE It is represented as the total negative energy of the time-domain waveform. Represented as a time-domain waveform; it should be understood that when calculating the total negative energy of the second time-domain waveform, the second time-domain waveform... Can replace The total negative energy of the second time-domain waveform TNE k+1 Can replace TNE When calculating the total negative energy of the initial time-domain waveform, the initial time-domain waveform... Can replace The total negative energy of the initial time-domain waveform TNE k Can replace TNE .

[0071] (11) In formula (11) This represents the rate of change of total negative energy in the current iteration.

[0072] In one implementation, the initial power spectrum corresponding to the initial time-domain waveform can be calculated. Then, the mean square error of the first power spectrum in the current iteration can be calculated. MSE k+1 and initial power spectrum mean square error MSE k Then, based on the mean square error of the first power spectrum MSE k+1 and initial power spectrum mean square error MSE k The mean square error rate of the power spectrum in the current iteration is calculated.

[0073] As an example, the initial power spectrum corresponding to the initial time-domain waveform can be calculated by referring to the above formulas (5) and (6). Then, the mean square error of the first power spectrum in the current iteration can be calculated according to the following formula (12). MSEk+1 and initial power spectrum mean square error MSE k Then, based on the mean square error of the first power spectrum MSE k+1 and initial power spectrum mean square error MSE k The mean square error rate of the power spectrum in the current iteration is calculated using the following formula (13).

[0074] (12) In formula (12), MSE This is expressed as the mean square error of the power spectrum; W Represented as The bandwidth; it should be understood that when calculating the mean square error of the first power spectrum, the first power spectrum Can replace The mean square error of the first power spectrum MSE k+1 Can replace MSE ; Calculate the initial power spectrum When the mean square error is , the initial power spectrum Can replace Initial power spectrum mean square error MSE k Can replace MSE .

[0075] (13) In formula (13). This represents the rate of change of the mean square error of the power spectrum in the current iteration.

[0076] It should be understood that total negative energy TNE It can be used to quantify the energy of the negative portion of a time-domain waveform. (Power spectral density mean square error) MSE It can be used to quantify the difference between the generated waveform and the target power spectrum.

[0077] In one implementation, the current iteration number can be determined. k Has the maximum number of iterations K been reached? max And determine whether the rate of change of total negative energy in the current iteration and the rate of change of the mean square error of the power spectrum in the current iteration are both less than the convergence threshold. This is used to determine whether the current iteration meets the preset convergence condition. For example, the current iteration only needs to satisfy the current iteration number. k Reaching the maximum number of iterations K max The rate of change of total negative energy and the rate of change of mean square error of power spectrum in the current iteration are both less than the convergence threshold. If either of these two conditions is met, the current iteration can be determined to satisfy the preset convergence condition. If neither of these two conditions is met, the current iteration cannot be determined to satisfy the preset convergence condition.

[0078] In this embodiment of the application, by performing step S150, two quantitative evaluation indicators (i.e., total negative energy) can be introduced. TNE and power spectrum mean square error MSE This allows the performance of the iterative algorithm to be quantified and compared. For example, based on a given target power spectrum and total waveform energy, it can find the real-valued time-domain waveform and minimize the total negative energy, while minimizing the mean square error of the power spectrum, which facilitates parameter tuning and convergence judgment.

[0079] S160, record the iteration count +1, replace the initial time domain waveform with the second time domain waveform, and return to step S120.

[0080] S170, Output the second time-domain waveform as the final time-domain waveform.

[0081] As an example, one could adopt This is represented as the final time-domain waveform.

[0082] In the embodiments of this application, by executing steps S150-S170, under a given target power spectrum and energy constraints, the time-domain waveform generated by iterative optimization can simultaneously converge to two objectives: power spectrum matching and minimizing negative energy. This allows for the systematic and controllable minimization of negative energy in the time-domain waveform, thereby obtaining a physically realizable and engineering-usable near-optimal waveform that minimizes negative energy in the time domain and highly matches the target power spectrum.

[0083] It should be understood that by executing steps S120-S170, the embodiments of this application can construct a specific iterative loop logic chain containing energy constraints, namely "time-domain negative value suppression → energy normalization → frequency-domain spectrum constraint (preserving phase) → time-domain update". This chain can minimize the total negative energy of the time-domain waveform while maintaining a strictly real value as one of the optimization objectives. At the same time, it constrains the power spectrum to approximate a given target power spectrum for iterative optimization, ultimately generating a time-domain waveform with minimal negative energy. This solves the problem of difficulty in balancing non-negativity and spectral fidelity in the prior art.

[0084] To facilitate a further understanding of the waveform nonnegativity iterative optimization method for preserving power spectral characteristics provided in the embodiments of this application, MATLAB R2019b is used as the simulation platform below, combined with... Figures 2-4 The following is a description of three embodiments.

[0085] Example 1: Optimization of photoacoustic imaging waveform (preferred parameters) 1. Problem Definition: The power spectrum required for photoacoustic imaging is obtained by maximizing mutual information, as described in the literature (Z. Sun and N. Baddour, “Photoacoustic Waveform Design for Optimal Parameter Estimation Based on Maximum Mutual Information,” Symmetry, vol. 16, no. 10, p.1402, 2024). For the target power spectrum, the waveform non-negativity iterative optimization method provided in the embodiments of this application, which preserves the characteristics of the power spectrum, is used to obtain the waveform with the time-domain minimum negative value. The total energy is set. E = 1 (normalization, convergence threshold) = 0.001 (0.1%).

[0086] 2. Initialization: The optimal waveform is used as the initial time-domain waveform, i.e. , k =1.

[0087] 3. Parameter settings: Select the inhibition factor =0.1 (negative values ​​are moderately attenuated and retained), mixing factor = 0.9 (strongly enforces the target power spectrum).

[0088] 4. Iteration Process and Results: Execute steps S120-S170 above. For example... Figure 2 As shown, in the initial stage of iteration TNE Rapidly declining, MSE It increases slightly due to the application of a nonnegativity constraint. Subsequently, the algorithm adjusts the phase to... MSE It also began to decline. Finally, it converged after approximately 160 iterations. TNE and MSE The rate of change is less than 0.1%. Final time-domain waveform ( Figure 3 (a) has a strictly zero imaginary part and a non-negative real part. TNE <10⁻⁶), its power spectrum ( Figure 3 (c) The blue line is highly consistent with the target power spectrum (black line).

[0089] Example 2: The Influence of Initial Values ​​on Convergence Rate 1. Initialization: A Gaussian pulse is used as the initial time-domain waveform, i.e. , k =1.

[0090] 2. Parameters and objectives: Same as in Example 1 (i.e., take...) =0.1、 = 0.9).

[0091] 3. Iteration process and results: such as Figure 4 As shown, since the initial time-domain waveform itself is non-negative, TNE The index almost immediately met the convergence condition, but because its power spectrum differed significantly from the target, MSE It took more than 270 iterations to converge. The power spectral fidelity of the final time-domain waveform was comparable to that of Example 1, but the number of iterations required for convergence increased significantly. This confirms the importance of choosing an initial waveform close to the theoretical optimal solution for improving algorithm efficiency.

[0092] Example 3: Analysis of the Impact of Parameter Adjustment 1. Strong negative value suppression mode ( , = 0.9): More negative This means that the negative value portion is attenuated and its sign is reversed, which can more quickly guide the overall waveform towards the positive value region, thereby accelerating the process. TNE The decline, but possibly with a slight increase in the final value. MSE At the cost.

[0093] 2. Strong Spectral Constraint Mode ( = 0.1、 = 0.1): smaller This allows the algorithm to be more strictly forced to conform to the target power spectrum in the frequency domain, which can greatly speed up the process. MSE The convergence speed may be faster, but the suppression of negative values ​​may be weakened, leading to a final convergence rate of [missing information]. TNE Slightly higher than the strong negative value suppression mode.

[0094] The above three embodiments verify the effectiveness and practicality of the waveform non-negativity iterative optimization method for preserving power spectrum characteristics provided in this application in physically constrained systems (such as photoacoustic imaging). Furthermore, the above three embodiments also demonstrate that the waveform non-negativity iterative optimization method for preserving power spectrum characteristics provided in this application proposes a novel iterative optimization scheme for waveform design problems, providing a solution to waveform design while simultaneously satisfying multiple constraints such as non-negativity, power spectrum preservation, Hermite symmetry, and total energy constraints. Simultaneously, adjustable tuning parameters (i.e., suppression factors) are also provided. and mixing factors It provides users with clear control methods, allowing them to select the optimal parameter combination based on the different emphases on spectral accuracy and signal non-negativity in specific applications.

[0095] As described above, the waveform nonnegativity iterative optimization method for maintaining power spectrum characteristics provided in this application is the first to systematically introduce time-domain nonnegativity constraints into power spectrum optimization. It clarifies that time-domain nonnegativity is introduced as a hard constraint into the iteration process, filling the gap between power spectrum matching and time-domain nonnegativity. It breaks the limitation that traditional waveform design methods (such as the Gerchberg-Saxton algorithm) usually do not enforce the nonnegativity of time-domain signals. Under a given target power spectrum constraint, by introducing a negative value suppression operation with an adjustable suppression factor in the time domain and a power spectrum soft constraint with an adjustable mixing factor in the frequency domain, and alternately performing energy normalization and phase preservation, the waveform is guided to converge to both the power spectrum matching and the goal of minimizing negative energy. This allows the algorithm to systematically and controllably suppress negative energy in the waveform while maintaining high power spectrum fidelity, thereby generating a time-domain waveform with minimal negative energy in the time domain.

[0096] In summary, the waveform non-negativity iterative optimization method for preserving power spectrum characteristics provided in this application addresses the physical constraint that laser energy cannot be negative in photoacoustic imaging. It proposes a waveform generation scheme that can be directly applied to practical systems, and is particularly suitable for scenarios in physical systems such as photoacoustic imaging and radar where negative signals must be avoided. In other words, the waveform non-negativity iterative optimization method for preserving power spectrum characteristics provided in this application can be applied in fields such as optical imaging, photoacoustic imaging, and lidar that require non-negative or extremely low negative excitation signals.

[0097] In summary, compared with the prior art, the waveform nonnegativity iterative optimization method for preserving power spectrum characteristics provided in this application embodiment has the following advantages: (a) High physical realizability: Through optimization, the total negative energy of the waveform ( TNE The residual negative values ​​are reduced to extremely low levels (e.g., below 0.1% of the total energy). In engineering, such residual negative values ​​can be completely eliminated through simple post-processing, resulting in a strictly non-negative transmit waveform, thus solving the fundamental problem that the theoretically optimal waveform is physically unrealizable.

[0098] (ii) Excellent spectral fidelity and controllable negative value suppression: By independently adjusting the suppression factor and mixing factor, users can achieve excellent power spectral fidelity (…). MSE ) and negative suppression intensity ( TNE It makes a fine and predictable trade-off between these factors, flexibly adapting to the tolerance requirements of different applications.

[0099] (iii) Strong robustness: It is not sensitive to the choice of initial time-domain waveform. Using an initial time-domain waveform close to the optimal solution can accelerate convergence. Even if it starts with a positive definite waveform with large differences (such as a Gaussian pulse), it can still converge stably to a satisfactory solution.

[0100] (iv) Clear convergence: Provides a method based on TNE rate of change and MSE An objective convergence criterion for the rate of change makes the iterative process controllable and predictable.

[0101] (v) High versatility: It does not depend on a specific physical model and is applicable to any field that needs to generate low negative values ​​or even non-negative waveforms from the power spectrum, thus having good universality.

[0102] Figure 5 A block diagram of a waveform nonnegativity iterative optimization system that preserves power spectral characteristics according to an embodiment of this application is shown. Figure 5 As shown, the system may include: The initial setting unit 210 is used to set the initial settings of the system and initialize the inputs. The initial settings of the system include the target power spectrum, the total energy of the waveform, the suppression factor for controlling the strength of the non-negativity constraint and the mixing factor for controlling the strength of the power spectrum matching, the maximum number of iterations and the convergence threshold. The initial inputs include setting the initial time-domain waveform and setting the number of iterations to 1. The first processing unit 220 is used to perform negative suppression operation and energy normalization on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. The second processing unit 230 is used to perform power spectrum mixing constraint and phase preservation processing on the first time domain waveform in the frequency domain using the mixing factor and the target power spectrum to obtain the first frequency domain waveform. The time-domain update unit 240 is used to update the first frequency-domain waveform in the time domain to obtain the second time-domain waveform. The result judgment unit 250 is used to determine whether the current iteration meets the preset convergence condition. The preset convergence condition is that the number of iterations reaches the maximum number of iterations, or the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold. If it is determined that the current iteration does not meet the preset convergence condition, the iteration number is incremented by 1, and the second time-domain waveform replaces the initial time-domain waveform. The process is then returned to the first processing unit 220 to perform negative value suppression and energy normalization on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. If it is determined that the current iteration meets the preset convergence condition, the second time-domain waveform is output as the final time-domain waveform.

[0103] The functions of each unit in the waveform nonnegativity iterative optimization system that preserves power spectrum characteristics in this application embodiment can be found in the corresponding descriptions in the above methods, and will not be repeated here.

[0104] Figure 6 A structural block diagram of an electronic device according to an embodiment of this application is shown. Figure 6As shown, the electronic device includes a memory 310 and a processor 320. The memory 310 stores instructions, which are loaded and executed by the processor 320 to implement the waveform nonnegativity iterative optimization method for maintaining power spectrum characteristics in the above embodiment. The number of memories 310 and processors 320 can be one or more.

[0105] The electronic device also includes: The communication interface 330 is used to communicate with external devices and perform data exchange and transmission.

[0106] If the memory 310, processor 320, and communication interface 330 are implemented independently, they can be interconnected via a bus to communicate with each other. This bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. This bus can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 6 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0107] Optionally, in a specific implementation, if the memory 310, processor 320 and communication interface 330 are integrated on a single chip, the memory 310, processor 320 and communication interface 330 can communicate with each other through an internal interface.

[0108] This application provides a computer-readable storage medium storing a computer program. When the computer program is run on a computer, it implements the method provided in this application.

[0109] This application also provides a chip, which includes a processor for calling and executing instructions stored in a memory, causing a communication device with the chip installed to perform the method provided in this application.

[0110] This application also provides a chip, including: an input interface, an output interface, a processor, and a memory. The input interface, output interface, processor, and memory are connected through an internal connection path. The processor is used to execute code in the memory. When the code is executed, the processor is used to execute the method provided in the application embodiment.

[0111] It should be understood that the aforementioned processor can be a Central Processing Unit (CPU), or other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. General-purpose processors can be microprocessors or any conventional processor. It is worth noting that the processor can be a processor supporting Advanced Reduced Instruction Set Machines (ARM) architecture.

[0112] Further, optionally, the aforementioned memory may include read-only memory and random access memory, and may also include non-volatile random access memory. The memory may be volatile or non-volatile, or may include both. Non-volatile memory may include read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. Volatile memory may include random access memory (RAM), which serves as an external cache. Many forms of RAM are available by way of example, but not limitation. Examples include static random access memory (SRAM), dynamic random access memory (DRAM), synchronous dynamic random access memory (SDRAM), double data rate synchronous dynamic random access memory (DDR SDRAM), enhanced synchronous dynamic random access memory (ESDRAM), synchronous linked dynamic random access memory (SLDRAM), and direct rambus RAM (DR RAM).

[0113] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transferred from one computer-readable storage medium to another.

[0114] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0115] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "a plurality of" means two or more, unless otherwise explicitly specified.

[0116] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or more executable instructions for implementing a particular logical function or process. Furthermore, the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functionality involved.

[0117] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0118] It should be understood that various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. All or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware, the program being stored in a computer-readable storage medium, which, when executed, includes one or a combination of the steps of the method embodiments.

[0119] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium. This storage medium can be a read-only memory, a disk, or an optical disk, etc.

[0120] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any person skilled in the art can easily conceive of various variations or substitutions within the technical scope disclosed in this application, and these should all be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A waveform nonnegativity iterative optimization method that preserves power spectrum characteristics, characterized in that, include: Set the initial system settings and initialize the inputs. The initial system settings include the target power spectrum, total waveform energy, suppression factor for controlling the strength of nonnegativity constraints, mixing factor for controlling the strength of power spectrum matching, maximum number of iterations, and convergence threshold. The initial inputs include setting the initial time-domain waveform and setting the number of iterations to 1. Using the suppression factor and the total energy of the waveform, the initial time-domain waveform is subjected to negative suppression and energy normalization in the time domain to obtain the first time-domain waveform; Using the mixing factor and the target power spectrum, the first time-domain waveform is subjected to power spectrum mixing constraint and phase preservation processing in the frequency domain to obtain the first frequency-domain waveform; The first frequency domain waveform is updated in the time domain to obtain the second time domain waveform; Determine whether the current iteration meets the preset convergence condition, wherein the preset convergence condition is that the number of iterations reaches the maximum number of iterations, or the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold. If it is determined that the current iteration does not meet the preset convergence condition, the iteration number is incremented by 1, and the second time-domain waveform replaces the initial time-domain waveform. Then, the process is returned to perform negative suppression and energy normalization on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. If it is determined that the current iteration satisfies the preset convergence condition, then the second time-domain waveform is output as the final time-domain waveform.

2. The method according to claim 1, characterized in that, Using the suppression factor and the total energy of the waveform, negative suppression and energy normalization are performed on the initial time-domain waveform in the time domain to obtain the first time-domain waveform, which includes: The initial time-domain waveform is subjected to negative suppression using the suppression factor to obtain the third time-domain waveform. The first time-domain waveform is obtained by normalizing the energy of the third time-domain waveform using the total energy of the waveform.

3. The method according to claim 2, characterized in that, The process of using the suppression factor to perform negative value suppression on the initial time-domain waveform to obtain the third time-domain waveform includes: using the suppression factor to perform negative value suppression on the initial time-domain waveform based on the following formula (3) to obtain the third time-domain waveform; The process of normalizing the third time-domain waveform with the total energy of the waveform to obtain the first time-domain waveform includes: normalizing the third time-domain waveform with the total energy of the waveform based on the following formula (4) to obtain the first time-domain waveform; （3） In formula (3), Represented as the third time-domain waveform; Represented as an indicator function; The inhibitory factor is denoted as [insert inhibitory factor here], which controls the intensity of negative inhibition: For strong suppression (set to zero). To preserve attenuation, To decay and invert the sign; This is represented as the initial time-domain waveform; （4） In formula (4), Represented as the first time-domain waveform; E It is represented as the total energy of the waveform.

4. The method according to claim 1, characterized in that, Using the mixing factor and the target power spectrum, the first time-domain waveform is subjected to power spectrum mixing constraint and phase preservation processing in the frequency domain to obtain the first frequency-domain waveform, which includes: The first time-domain waveform is transformed in the frequency domain and its power spectrum is calculated to obtain the second frequency-domain waveform and the first power spectrum. By combining the target power spectrum and the first power spectrum with the mixing factor, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing to obtain the third frequency domain waveform. The first frequency domain waveform is obtained by applying Hermite symmetry constraints to the third frequency domain waveform.

5. The method according to claim 4, characterized in that, The process of performing frequency domain transformation and power spectrum calculation on the first time domain waveform to obtain the second frequency domain waveform and the first power spectrum includes: performing frequency domain transformation on the first time domain waveform based on the following formula (5) to obtain the second frequency domain waveform, and then performing power spectrum calculation on the second time domain waveform based on the following formula (6) to obtain the first power spectrum; Using the mixing factor to combine the target power spectrum and the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing to obtain the third frequency domain waveform, including: using the mixing factor to combine the target power spectrum and the first power spectrum, the second frequency domain waveform is subjected to power spectrum soft constraint and phase preservation processing based on the following formula (7) to obtain the third frequency domain waveform; Applying Hermite symmetry constraints to the third frequency domain waveform to obtain the first frequency domain waveform includes: applying Hermite symmetry constraints to the third frequency domain waveform based on the following formula (8) to obtain the first frequency domain waveform; （5） In formula (5), Represented as the first time-domain waveform; Represented as a second frequency domain waveform; F This is represented as a Fourier transform; （6） In formula (6), This is represented as the first power spectrum; （7） In formula (7), The waveform in the third frequency domain is represented as arctan 2; arctan 2 is represented as the arctangent function in the fourth quadrant. i Represented as the imaginary unit; This is represented by taking the imaginary part. Represented as taking the real part; Represented as a mixing factor, it controls the tightness of the power spectral constraint: This indicates a strict requirement for the target power spectrum. A value closer to 1 indicates a more moderate update, relying more on the results of the current iteration; （8） In formula (8), Represented as a waveform in the first frequency domain; Indicated as taking Conjugate.

6. The method according to any one of claims 1-5, characterized in that, The second time-domain waveform is obtained by updating the first frequency-domain waveform in the time domain, including: The first frequency domain waveform is updated in the time domain based on the following formula (9) to obtain the second time domain waveform; （9） in, Represented as a second time-domain waveform; Represented as the first frequency domain waveform; This is represented as the inverse Fourier transform.

7. The method according to claim 4, characterized in that, Determining whether the current iteration satisfies the preset convergence condition includes: Calculate the total negative energy of the second time-domain waveform in the current iteration and the total negative energy of the initial time-domain waveform, respectively. Then, based on the total negative energy of the second time-domain waveform and the total negative energy of the initial time-domain waveform, calculate the rate of change of the total negative energy in the current iteration. Calculate the initial power spectrum corresponding to the initial time-domain waveform; The mean square error of the first power spectrum and the mean square error of the initial power spectrum in the current iteration are calculated respectively. Then, based on the mean square error of the first power spectrum and the mean square error of the initial power spectrum, the rate of change of the mean square error of the power spectrum in the current iteration is calculated. The current iteration is judged to meet the preset convergence condition by determining whether the current iteration number has reached the maximum iteration number, and by determining that the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold.

8. A waveform nonnegativity iterative optimization system that preserves power spectrum characteristics, characterized in that, include: An initial setting unit is used to set the initial settings of the system and initialize the inputs. The initial settings of the system include the target power spectrum, the total energy of the waveform, the suppression factor for controlling the strength of the non-negativity constraint and the mixing factor for controlling the strength of the power spectrum matching, the maximum number of iterations and the convergence threshold. The initial inputs include setting the initial time-domain waveform and setting the number of iterations to 1. The first processing unit is used to perform negative suppression operation and energy normalization processing on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform. The second processing unit is used to perform power spectrum mixing constraint and phase preservation processing on the first time domain waveform in the frequency domain using the mixing factor and the target power spectrum to obtain the first frequency domain waveform. A time-domain update unit is used to update the first frequency-domain waveform in the time domain to obtain a second time-domain waveform. The result judgment unit is used to determine whether the current iteration meets the preset convergence condition, wherein the preset convergence condition is that the number of iterations reaches the maximum number of iterations, or the total negative energy change rate and the power spectrum mean square error change rate of the current iteration are both less than the convergence threshold; if it is determined that the current iteration does not meet the preset convergence condition, the iteration number is incremented by 1, and the second time-domain waveform replaces the initial time-domain waveform, and the process is returned to the first processing unit to perform negative value suppression and energy normalization processing on the initial time-domain waveform in the time domain using the suppression factor and the total energy of the waveform to obtain the first time-domain waveform; if it is determined that the current iteration meets the preset convergence condition, the second time-domain waveform is output as the final time-domain waveform.

9. An electronic device, characterized in that, include: A memory and a processor, wherein the memory stores instructions which are loaded and executed by the processor to implement the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when run on a computer, implements the method as described in any one of claims 1-7.

Images