Analog circuit-based real-time sparse signal reconstruction method

Abstract

The application relates to the fields of signal processing, image processing and communication engineering, and particularly relates to a real-time sparse signal reconstruction method based on an analog circuit, which comprises the following steps: acquiring an observation signal and an observation matrix; based on the observation signal and the observation matrix, an analog circuit is constructed; the numerical value of the observation signal is converted into a corresponding electric signal and applied to the input end of the analog circuit; the analog circuit is powered on and operated to a steady state, the steady-state voltage values of a plurality of predetermined nodes in the analog circuit are measured, and the measured steady-state voltage values are output as the reconstruction values of the sparse signal. The application adopts a technical path of a full-analog computing system architecture, and aims at a sparse signal reconstruction problem, converts a key mathematical model (specifically, an equation group represented by KKT conditions) in a solving process of the problem into a circuit physical structure, and outputs an optimal solution through a steady-state response of the circuit in one step.

Description

Technical Field

[0001] This application relates to fields such as signal processing, image processing, and communication engineering, and more specifically, to a real-time sparse signal reconstruction method based on analog circuits. Background Technology

[0002] With the deep penetration of signal processing technology into fields such as image processing, medical imaging, radar signal processing, and machine learning, "reconstruction and recovery of original high-dimensional signals based on limited observation data" has become one of the core requirements. Traditional sampling theories (such as Shannon's sampling theorem) have stringent requirements on the sampling rate, while practical scenarios often face limitations such as high sampling costs or incomplete measurement data. Therefore, exploring efficient reconstruction methods suitable for incomplete signals has urgent practical significance. It should be noted that sparse signal reconstruction, a typical representative of this type of problem, is essentially an NP-hard problem. This characteristic makes it difficult to achieve efficient solutions through conventional methods in practical engineering applications.

[0003] Existing technologies have provided a key breakthrough in solving this problem, demonstrating that, under certain conditions, convex relaxation methods can effectively solve it. This conclusion allows mature convex optimization algorithms to be reasonably introduced and applied to practical computational processes, providing a feasible path for the engineering implementation of this problem. In the field of sparse signal reconstruction, several classic algorithms with differentiated advantages have been developed for different application scenarios: Greedy algorithms iteratively select the atoms (corresponding to column vectors in the dictionary matrix) with the strongest correlation to the residual to gradually approximate the sparse solution, with low computational complexity, suitable for real-time signal processing scenarios with strict limitations on computing resources; Basis Pursuit transforms the non-convex L0 norm minimization problem into a convex L1 norm minimization problem, solved by linear programming, which can guarantee global optimality and has good noise robustness; Gradient Projection for Sparse Reconstruction handles sparse optimization problems based on the gradient projection idea and is widely used in large-scale data processing scenarios; Iterative Soft Thresholding Algorithm combines gradient descent and threshold shrinkage operations, balancing convergence speed and sparsity constraints, and is suitable for efficient reconstruction of large-scale signals; SL0 The algorithm uses a Gaussian function to approximate the L0 norm and solves the problem through gradient ascent, balancing reconstruction accuracy and computational complexity, making it suitable for high-precision sparse localization scenarios. Iterative decorrelation estimation (IDE) processes the observed signal iteratively, estimating the sparse structure of the signal step by step based on decorrelation operations, which can accurately recover the original high-dimensional sparse signal from limited observation data. The weighted least squares focusing algorithm (FOCUSS) first obtains a low-resolution initial estimate of the sparse signal, and then prunes the solution through multiple rounds of iteration to improve sparsity. Each round of iteration solves the corresponding optimization problem by correcting the pseudo-inverse of the weighting matrix, and finally obtains a more accurate sparse representation.

[0004] Although the traditional sparse signal reconstruction methods mentioned above have demonstrated good signal recovery performance in practice, there are still shortcomings that need to be improved: current solutions generally rely on iterative algorithms, resulting in slow convergence speed and high computation time, making it difficult to meet the needs of high real-time scenarios. Summary of the Invention

[0005] To address the aforementioned issues, this application provides a real-time sparse signal reconstruction method based on analog circuits. The method aims to transform the key mathematical model in the solution process of sparse signal reconstruction into a circuit physical structure, and output the optimal solution in a "one-step" manner through the steady-state response of the circuit.

[0006] The first aspect of this invention provides a real-time sparse signal reconstruction method based on analog circuits, comprising:

[0007] Acquire the observed signals and observation matrix;

[0008] Based on the observed signal and the observation matrix, an analog circuit is constructed:

[0009] Based on the observed signal and the observation matrix, a mathematical optimization model is established with the goal of minimizing the L1 norm; the KKT optimality condition corresponding to the mathematical optimization model is derived, generating a nonlinear equation set; based on the nonlinear equation set, the connection relationship and parameters of each functional module in the analog circuit are determined, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set;

[0010] The observed signal value is converted into a corresponding electrical signal and applied to the input terminal of the analog circuit;

[0011] The analog circuit is powered on and run to a steady state. The steady-state voltage values ​​of multiple predetermined nodes in the analog circuit are measured, and the measured steady-state voltage values ​​are output as the reconstructed values ​​of the sparse signal.

[0012] In one alternative implementation, the mathematical optimization model is in one of the following forms:

[0013] The linear programming model corresponding to the noiseless observation scenario is constructed with the goal of minimizing the L1 norm of the sparse signal, while satisfying the following equality constraints:

[0014]

[0015] in, For observing signals, For the observation matrix, It is a sparse signal;

[0016] The regularization model corresponding to noisy observation scenarios is constructed to minimize an objective function, the formula of which is:

[0017]

[0018] in, To minimize the function, This is the regularization function.

[0019] In one optional implementation, based on the nonlinear equations, the connection relationships and parameters of each functional module in the analog circuit are determined, specifically including the following mapping relationships:

[0020] The variables to be solved in the nonlinear equation system are mapped to circuit node voltages;

[0021] The linear operational relationships of the nonlinear equation system are mapped to basic operational modules composed of operational amplifiers and resistors;

[0022] The linear transformation relationship related to the observation matrix in the nonlinear equation system is mapped into a multi-port linear transformation module;

[0023] The complementary relaxation conditions in the nonlinear equations are mapped to an ideal diode unit consisting of a PN junction diode and an operational amplifier feedback circuit.

[0024] In one optional implementation, the basic operational module includes at least one of a voltage inverter, a voltage forward amplifier, a voltage adder, and a voltage subtractor.

[0025] In one alternative implementation, the transmission parameters of the multi-port linear transformation module are configured according to the values ​​of the observation matrix.

[0026] In one alternative implementation, the ideal diode unit is composed of a single PN junction diode connected to an operational amplifier, wherein the operational amplifier connection is in the form of negative feedback.

[0027] A second aspect of this invention provides a real-time sparse signal reconstruction system based on analog circuits, the system comprising:

[0028] The data acquisition module is used to acquire observation signals and observation matrices;

[0029] The circuit construction module is used to construct an analog circuit based on the observed signal and the observation matrix.

[0030] Based on the observed signal and the observation matrix, a mathematical optimization model is established with the goal of minimizing the L1 norm; the KKT optimality condition corresponding to the mathematical optimization model is derived, generating a nonlinear equation set; based on the nonlinear equation set, the connection relationship and parameters of each functional module in the analog circuit are determined, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set;

[0031] An electrical signal conversion module is used to convert the value of the observed signal into a corresponding electrical signal and apply it to the input terminal of the analog circuit;

[0032] The reconstructed value output module is used to power on the analog circuit until it reaches a steady state, measure the steady-state voltage values ​​of multiple predetermined nodes in the analog circuit, and output the measured steady-state voltage values ​​as the reconstructed values ​​of the sparse signal.

[0033] A third aspect of the present invention provides an electronic device, characterized in that it includes: a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a real-time sparse signal reconstruction method based on analog circuits.

[0034] A fourth aspect of the present invention provides a computer-readable storage medium, characterized in that a computer program is stored on the computer-readable storage medium, and the computer program, when executed by a processor, is a real-time sparse signal reconstruction method based on analog circuits.

[0035] This application has at least the following advantages or beneficial effects:

[0036] This invention constructs a dedicated analog computing architecture that transforms the 'solution process' of the mathematical optimization problem of sparse signal reconstruction into a 'steady-state search process of a physical system'. This architecture achieves a paradigm shift of 'computation is physics' by systematically mapping each mathematical relationship in the KKT conditions to the physical behavior of a specific circuit module, demonstrating that, theoretically, this invention possesses complete solution capabilities for both noiseless and noisy sparse signal reconstruction problems. Furthermore, this is fundamentally different from running optimization algorithms on general-purpose processors, bypassing the iterative convergence process and achieving instantaneous solutions. Attached Figure Description

[0037] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0038] Figure 1 This is a flowchart of a real-time sparse signal reconstruction method based on analog circuits proposed in an embodiment of this application;

[0039] Figure 2 This is a schematic diagram of an ideal diode structure proposed in an embodiment of this application;

[0040] Figure 3 This is a structural diagram of an ideal current source proposed in an embodiment of this application;

[0041] Figure 4 This is a structural diagram of a voltage inverter according to an embodiment of this application;

[0042] Figure 5 This is a structural diagram of a voltage forward amplifier according to an embodiment of this application;

[0043] Figure 6 This is a structural diagram of a voltage adder according to an embodiment of this application;

[0044] Figure 7 This is a structural diagram of a voltage subtractor proposed in one embodiment of this application;

[0045] Figure 8This is a structural diagram of a (1+q) port converter proposed in an embodiment of this application;

[0046] Figure 9 This is a four-channel oscilloscope-based voltage test plot proposed in one embodiment of this application;

[0047] Figure 10 This is a dual-channel oscilloscope based on LP voltage test plot proposed in one embodiment of this application;

[0048] Figure 11 This is a voltage test plot of a four-channel oscilloscope based on QP, as proposed in one embodiment of this application;

[0049] Figure 12 This is a dual-channel oscilloscope-based voltage test plot proposed in one embodiment of this application;

[0050] Figure 13 This is a comparison chart of reconstruction results of various LP-based methods proposed in an embodiment of this application;

[0051] Figure 14 This is a comparison chart of the time consumption of various LP-based methods proposed in an embodiment of this application;

[0052] Figure 15 This is a comparison chart of reconstruction results of various QP-based methods proposed in an embodiment of this application;

[0053] Figure 16 This is a comparison chart of the time consumption of various QP-based methods proposed in an embodiment of this application;

[0054] Figure 17 This is a structural diagram of a real-time sparse signal reconstruction system based on analog circuits proposed in an embodiment of this application;

[0055] Figure 18 This is a schematic diagram of an electronic device according to this application. Detailed Implementation

[0056] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0057] Example 1, please refer to Figure 1 , Figure 1 This is a flowchart of a real-time sparse signal reconstruction method based on analog circuits proposed in an embodiment of this application. Figure 1As shown, a real-time sparse signal reconstruction method based on analog circuits includes:

[0058] S100: Acquire observation signals and observation matrix;

[0059] S200: Based on the observed signal and the observation matrix, construct an analog circuit;

[0060] In this embodiment, an analog circuit is constructed based on the observed signal and the observation matrix. The specific steps are as follows:

[0061] S210: Based on the observed signals and the observation matrix, establish a mathematical optimization model with the objective of minimizing the L1 norm;

[0062] For linear programming models corresponding to noise-free observation scenarios, the sparse signal reconstruction problem is transformed into a convex optimization problem of minimizing the L1 norm:

[0063]

[0064] Here, matrix A is discussed in Example 1 when no noise term is included:

[0065] ;

[0066] To eliminate the non-smoothness of the L1 norm and improve the solvability of the problem, we introduce the following variable decomposition transformation:

[0067]

[0068] Where u and fraction v Instead of the nonnegative decomposition of the absolute values ​​of the positive and negative components of the original signal, the remaining elements are padded with zeros to maintain dimensionality consistency. Through this transformation, the original problem can be converted into the following easily solvable linear programming problem:

[0069]

[0070] As shown in List 1 below, a one-to-one correspondence can be established between the variables of the problem before and after the transformation:

[0071] Table 1

[0072]

[0073] in, Representative by indivual The column vector formed by these.

[0074] S220: Derive the KKT optimality conditions corresponding to the mathematical optimization model to generate a nonlinear system of equations;

[0075] Specifically, for convex problems in linear programming models corresponding to noise-free observation scenarios, the Karush-Kuhn-Tucker (KKT) conditions can be used for solving. The corresponding system of equations can be expressed as follows:

[0076]

[0077] in, These are the Lagrange multipliers corresponding to the equality constraints. These are the Lagrange multipliers corresponding to the inequality constraints.

[0078] S230: Based on the nonlinear equation set, determine the connection relationship and parameters of each functional module in the analog circuit, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set.

[0079] In this embodiment, based on the nonlinear equation set, the connection relationships and parameters of each functional module in the analog circuit are determined, specifically including the following mapping relationships:

[0080] S231: Map the variables to be solved in the nonlinear equation system to circuit node voltages;

[0081] S232: Map the linear operational relationships of the nonlinear equation system into a basic operational module composed of operational amplifiers and resistors;

[0082] S233: Map the linear transformation relationship related to the observation matrix in the nonlinear equation system to a multi-port linear transformation module;

[0083] S234: Map the complementary relaxation conditions in the nonlinear equation system to an ideal diode unit composed of a PN junction diode and an operational amplifier feedback circuit.

[0084] Specifically, the analog circuit includes: an ideal diode, an ideal current source, a voltage inverter, a voltage forward amplifier, a voltage adder, and a voltage subtractor. Port converter;

[0085] Among them, such as Figure 2 (a) and Figure 2 As shown in (b), the ideal diode unit is connected by... This circuit is implemented using a topology consisting of a junction diode and an operational amplifier feedback circuit. To distinguish it from an ideal diode, a circle is added around the symbol for an ideal diode. The drive-point characteristics of this circuit are highly similar to those of an ideal diode.

[0086] Based on the constructed ideal diode and Figure 2 (c) The physical characteristics of this diode can be characterized by the following mathematical expression:

[0087] .

[0088] like Figure 3 As shown, the ideal current source is realized by a feedback circuit consisting of a DC voltage source, resistors, transistors, and an operational amplifier, which can stably output current. DC current.

[0089] like Figure 4 As shown, the voltage inverter is implemented by a circuit consisting of resistors and operational amplifiers. Compared to a conventional voltage inverter, this module adds a voltage follower, whose function is to extract only the node voltage without injecting current into that node; when a voltage is input to this module... At that time, the output voltage can be stabilized. .

[0090] like Figure 5 As shown, the forward voltage amplifier is implemented by a circuit consisting of resistors and an operational amplifier. The purpose of adding a voltage follower to this circuit is to extract only the node voltage without injecting current into that node. When the input voltage is... At that time, it can output stably. The voltage. It should be noted that the parameters in the diagram... The value of is non-negative.

[0091] like Figure 6 As shown, the voltage adder is implemented by a circuit consisting of resistors and an operational amplifier. The purpose of adding a voltage follower to this circuit is to extract only the node voltage without injecting current into that node. When the input voltage is... and At that time, the module will output stably. The voltage.

[0092] like Figure 7 As shown, the voltage subtractor is implemented by a circuit consisting of resistors and an operational amplifier. The purpose of adding a voltage follower to this circuit is to extract only the node voltage without injecting current into that node. When the input voltage is... and At that time, the module will output stably. The voltage.

[0093] like Figure 8 As shown, A port converter is implemented by a circuit consisting of resistors and operational amplifiers, and its function can be characterized by the following matrix form:

[0094]

[0095] in, This represents the weight of each voltage, and also determines the weight of the current.

[0096] The voltage input at the right end of this module undergoes a specific linear transformation and the transformation result is output from the left end; at the same time, the current generated by the voltage will also follow the corresponding linear transformation rules, thereby realizing the function described by the above matrix equation.

[0097] To ensure that all signals are within the dynamic range of the operational amplifier, the following normalization value is selected:

[0098]

[0099] For all circuit models involved in this invention, all voltage, current and resistance values ​​must be normalized relative to the above values.

[0100] By organically integrating the basic circuit models proposed above and introducing several basic resistive elements, the physical simulation circuit mapped by the mathematical expression can be constructed.

[0101] Finally, we only need to map each node voltage to its corresponding variable, and sum each reverse diode current to the Lagrange multipliers constrained by the inequality. Correspondingly, the current flowing out of the DC voltage source is simultaneously compared with the Lagrange multipliers constrained by the equation. correspond.

[0102] for The output voltage at the left end of the port converter, for The input current at the right end of the port converter; in fact, The value of and Consistent. In this circuit, the left-hand side is used to satisfy the equality constraint: through The port converter performs a linear transformation on the input voltage on the right to obtain... It is then coupled to the corresponding DC voltage source, indicating that the two are equal; the current flowing out of the DC voltage source This can be understood as the Lagrange multipliers corresponding to equality constraints. This current also serves as The port converter receives input at the left end and outputs the corresponding current at the right end. , respectively constitute and Part of the corresponding KKT equations, namely On the right side of the circuit, based on the aforementioned analysis, the physical characteristics of an ideal diode fully satisfy the complementary relaxation condition in the KKT conditions. Specifically, and The non-negativity of the diode can be effectively guaranteed; at the same time, under the specified current direction, the current output by the diode is... and Neither of them are positive, but and Lagrange multipliers corresponding to inequality constraints Just by and This is reflected in the diagram. Simultaneously, the ideal current source constructed in the diagram can be used as the DC bias in the equation, i.e., the matrix. According to Ohm's law and Kirchhoff's current law, at each voltage... and The current equation for the corresponding node is written, which is that the sum of all currents flowing out of the node is zero, thus successfully characterizing the equation with zero gradient in the KKT condition.

[0103] S300: Convert the value of the observed signal into a corresponding electrical signal and apply it to the input terminal of the analog circuit;

[0104] In this embodiment, and Corresponding to the node voltage of each branch, the diode reverse current and With inequality constraints, the pre-Lagrange operator Corresponding to.

[0105] S400: Power on the analog circuit to a steady state, measure the steady-state voltage values ​​of multiple predetermined nodes in the analog circuit, and output the measured steady-state voltage values ​​as the reconstruction values ​​of the sparse signal.

[0106] In this embodiment, combining the above table data and the system of equations, we can directly obtain:

[0107]

[0108] in, For variables The corresponding Lagrange multipliers, For variables The corresponding Lagrange multipliers.

[0109] To present this system of equations more concretely, let Meanwhile, for the matrix The following regulations are made: Represented by matrix No. A row vector is formed by maintaining the relative positions of its row elements. Based on the above stipulations, we can obtain the system of equations:

[0110]

[0111] To facilitate the subsequent construction of analog circuits, after some adjustments and transformations, we can obtain:

[0112]

[0113] By combining this system of equations with the aforementioned analog circuit diagram, a one-step solution can be achieved. Among these, Represented by a DC current source, The current flowing out of the reverse diode is used to represent the current, and the remaining terms are represented by the current generated by applying the corresponding node voltage across the resistor. Finally, according to Kirchhoff's Current Law (that is, the sum of all currents flowing out of any node is zero), all the above currents are summed and set to zero. Thus, the mathematical expression for zero gradient in the KKT conditions can be perfectly mapped to the physical circuit.

[0114] Based on the above analysis, all the mathematical expressions in the KKT conditions are fully interpreted in the constructed analog circuit. Ultimately, the optimal solution, i.e., the required sparse signal, can be obtained simply by measuring the node voltages using specialized measuring tools.

[0115] To verify the performance of the proposed method in terms of accuracy and timeliness, this study compares it with the interior-point method and the orthogonal matching pursuit (OMP) algorithm. The results are shown in Tables 2 and 3. Table 2 shows the optimal solutions for the noiseless model problem by different methods, and Table 3 shows the time required by different methods to solve the noiseless model problem. Figure 13 , 14 It is a visual representation of tabular data;

[0116] Table 2

[0117]

[0118] Table 3

[0119]

[0120] Regarding the circuit method, there is no time consumption in solving the problem because it can be completed in a single step. As can be seen from the results in the two tables above, the circuit method performs exceptionally well in terms of solution accuracy. Furthermore, since it does not require a convergence process, it has a significant advantage in time efficiency.

[0121] Furthermore, the basic operation module includes at least one of a voltage inverter, a voltage forward amplifier, a voltage adder, and a voltage subtractor.

[0122] Furthermore, the transmission parameters of the multi-port linear transformation module are configured according to the values ​​of the observation matrix.

[0123] In this embodiment, the multi-port linear transformation module is: Port converter.

[0124] Furthermore, the ideal diode unit is composed of a single PN junction diode connected to an operational amplifier, wherein the operational amplifier connection is in the form of negative feedback.

[0125] Experimental results are as follows Figure 9 , 10 As shown, based on the above technical solution, the optimal solution for the experiment can be obtained through simulation in professional software. Measurements show that the node... and The voltage measurements are respectively , , , and The theoretical optimal solution to this problem is:

[0126]

[0127] Clearly, the error obtained using this method is negligible. Therefore, the effectiveness of this method under a noise-free model is verified.

[0128] Example 2, corresponding to the regularization model for noisy observation scenarios, requires modification of the original model. This modification mainly involves the equality constraint part, that is, introducing a perturbation term related to the noise vector on the basis of the original constraints:

[0129]

[0130] in, For the noise term in the system (when (When, corresponding to a noise-free model).

[0131] When the system contains noise At that time, it can be used for To approximate satisfaction, the common practice is to relax the constraints as follows:

[0132]

[0133] in, Since it is the Euclidean norm (L2 norm), the problem can be transformed into:

[0134]

[0135] In machine learning or statistics, the following form is preferred:

[0136]

[0137] Here, matrix A is discussed in Example 2 when noise terms are included, and the parameters selected are different from those in Example 1:

[0138]

[0139] Among them, the first item Used to measure fitting error; second term It belongs to the L1 regularization term, which can make the solution sparse; is the regularization coefficient, used to balance good fit and sparsity. When As the value increases, the algorithm focuses more on the "sparse" property, and will include more... Compressed to zero; while when The smaller the value, the more the algorithm focuses on reducing it. The value of . Therefore, it is necessary to . The value is adjusted to balance the relationship between noise magnitude and sparsity.

[0140] To effectively solve the above problems, it is necessary to transform its form. It is basically consistent with the Lagrange form of problems with equality constraints (where the Lagrange multipliers corresponding to the equality constraints are defined as follows): The difference between the two is that current research only focuses on variables. without involving Therefore, only when Only when the value is appropriate will the solution to this problem be consistent with the solution to the problems discussed above.

[0141] Following the same processing logic as described above, The positive and negative elements in the equation need to be processed separately, that is, let:

[0142]

[0143] Assuming all vectors and matrices belong to the real number field, it can be proved that the minimum point of the following cost function is equal to... The local minimum point corresponds exactly to the cost function. The mathematical expression is:

[0144]

[0145] As shown in List 4 below, the various quantities in the problem before and after the transformation can be mapped to each other:

[0146] Table 4

[0147]

[0148] For the quadratic programming problem corresponding to the regularized model in a noisy observation scenario, the KKT conditions are used to solve it. The KKT equations are as follows:

[0149]

[0150] in, For the Lagrange multipliers corresponding to the inequality constraints.

[0151] Based on the nonlinear equations determined by the KKT conditions, a method for designing specific analog circuits is still used to ensure that the physical steady state of the circuit exactly satisfies the solution of the equations, thereby achieving a one-step solution.

[0152] Experimental results are as follows Figure 11 , 12 As shown, based on the technical solution described above, experiments were conducted using professional simulation software, and the output results can be presented on an oscilloscope. Measurements showed that the nodes... and The voltage measurements are respectively , , , and The theoretical optimal solution to this problem is:

[0153]

[0154] The comparison shows that the error generated by this method is extremely small. This demonstrates that the effectiveness of this method in noise-free model scenarios has been fully verified.

[0155] To verify the performance of the proposed method in terms of accuracy and timeliness, this study compares it with the Alternating Direction Multiplier Method (ADMM) and the Fast Iterative Shrinking Threshold Algorithm (FISTA). The results are shown in Tables 5 and 6. Table 5 shows the optimal solutions for noisy model problems by different methods, and Table 6 shows the time required for different methods to solve noiseless model problems. Figure 15 , 16 It is a visualization of the corresponding tabular data.

[0156] Table 5

[0157]

[0158] Table 6

[0159]

[0160] Similarly, the circuit method directly outputs the result through a "one-step" solution, eliminating the "solution time" consumed by traditional iterative algorithms. The data from the two charts above verify that the circuit method not only demonstrates superior performance in solution accuracy but also possesses a significant advantage in time efficiency due to its "no convergence time" characteristic.

[0161] Please refer to Figure 17 , Figure 17This is a structural diagram of a real-time sparse signal reconstruction system based on analog circuits, as proposed in an embodiment of this application. Figure 17 As shown in the embodiments of this disclosure, a real-time sparse signal reconstruction system based on analog circuits is also provided, the system comprising:

[0162] The data acquisition module is used to acquire observation signals and observation matrices;

[0163] The circuit construction module is used to construct an analog circuit based on the observed signal and the observation matrix.

[0164] Based on the observed signal and the observation matrix, a mathematical optimization model is established with the goal of minimizing the L1 norm; the KKT optimality condition corresponding to the mathematical optimization model is derived, generating a nonlinear equation set; based on the nonlinear equation set, the connection relationship and parameters of each functional module in the analog circuit are determined, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set;

[0165] An electrical signal conversion module is used to convert the value of the observed signal into a corresponding electrical signal and apply it to the input terminal of the analog circuit;

[0166] The reconstructed value output module is used to power on the analog circuit until it reaches a steady state, measure the steady-state voltage values ​​of multiple predetermined nodes in the analog circuit, and output the measured steady-state voltage values ​​as the reconstructed values ​​of the sparse signal.

[0167] This disclosure also provides an electronic device, please refer to... Figure 18 , Figure 18 This is a schematic diagram of an electronic device illustrated in an embodiment of this disclosure. For example... Figure 18 As shown, the electronic device 100 includes a memory 110 and a processor 120. The memory 110 and the processor 120 are connected via a bus for communication. The memory 110 stores a computer program that can run on the processor 120 to implement the steps in the real-time sparse signal reconstruction method based on analog circuits disclosed in this embodiment.

[0168] The disclosed embodiments also provide a computer-readable storage medium that, when the instructions in the computer-readable storage medium are executed by a processor of a computer device, enables the computer device to perform steps as described in the real-time sparse signal reconstruction method based on analog circuits of the present disclosure embodiments.

[0169] In summary, the effectiveness of this invention has been systematically verified in sparse signal reconstruction tasks. The theoretical derivation and experimental results are consistent, demonstrating its robustness and reliability. The underlying support for this effectiveness lies precisely in the innovative integration of mathematical optimization theory (KKT conditions) with analog circuit design, constructing a synergistic system of "constraint mapping - circuit module - signal output." The current-voltage characteristics of an ideal diode naturally satisfy the complementary relaxation condition, and the linear amplification characteristics of an operational amplifier accurately realize matrix transformation. The modules are not simply superimposed, but rather the mathematical optimality conditions are strictly reproduced through the current and voltage relationships of the physical circuit. Ultimately, a novel "one-step solution" technical effect is achieved, which far surpasses traditional iterative algorithms in terms of time efficiency, fully demonstrating the creativity of this solution.

[0170] This application describes embodiments with reference to flowchart illustrations and / or block diagrams of methods, systems, electronic devices, and computer program products according to embodiments of this application. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A system that specifies functions in one or more boxes.

[0171] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including an instruction set implemented in a process. Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0172] These computer program instructions can also be loaded onto a computer or other programmable data processing terminal equipment, causing a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0173] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The same or similar parts between the various embodiments can be referred to each other.

[0174] Although preferred embodiments of the present application have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the present application.

[0175] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0176] The above provides a detailed description of a real-time sparse signal reconstruction method based on analog circuits provided in this application. Specific examples have been used to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the method and its core ideas. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A real-time sparse signal reconstruction method based on analog circuits, characterized in that, include: Acquire the observation signal and observation matrix; Based on the observed signal and the observation matrix, an analog circuit is constructed: Based on the observed signal and the observation matrix, a mathematical optimization model is established with the goal of minimizing the L1 norm; the KKT optimality condition corresponding to the mathematical optimization model is derived, generating a nonlinear equation set; based on the nonlinear equation set, the connection relationship and parameters of each functional module in the analog circuit are determined, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set; The mathematical optimization model is in one of the following forms: The linear programming model corresponding to the noiseless observation scenario is constructed with the goal of minimizing the L1 norm of the sparse signal, while satisfying the following equality constraints: in, For observing signals, For the observation matrix, It is a sparse signal; The regularization model corresponding to noisy observation scenarios is constructed to minimize an objective function, the formula of which is: in, To minimize the function, For regularization functions; Based on the aforementioned set of nonlinear equations, the connection relationships and parameters of each functional module in the analog circuit are determined, specifically including the following mapping relationships: The variables to be solved in the nonlinear equation system are mapped to circuit node voltages; The linear operational relationships of the nonlinear equation system are mapped to basic operational modules composed of operational amplifiers and resistors; The linear transformation relationship related to the observation matrix in the nonlinear equation system is mapped into a multi-port linear transformation module; The complementary relaxation conditions in the nonlinear equation system are mapped to an ideal diode unit composed of a PN junction diode and an operational amplifier feedback circuit. The observed signal value is converted into a corresponding electrical signal and applied to the input terminal of the analog circuit; The analog circuit is powered on and run to a steady state. The steady-state voltage values ​​of multiple predetermined nodes in the analog circuit are measured, and the measured steady-state voltage values ​​are output as the reconstructed values ​​of the sparse signal.

2. The real-time sparse signal reconstruction method based on analog circuits according to claim 1, characterized in that, The basic operation module includes at least one of a voltage inverter, a voltage forward amplifier, a voltage adder, and a voltage subtractor.

3. The real-time sparse signal reconstruction method based on analog circuits according to claim 1, characterized in that, The transmission parameters of the multi-port linear transformation module are configured according to the values ​​of the observation matrix.

4. The real-time sparse signal reconstruction method based on analog circuits according to claim 1, characterized in that, The ideal diode unit consists of a single PN junction diode connected to an operational amplifier, wherein the operational amplifier connection is in the form of negative feedback.

5. A real-time sparse signal reconstruction system based on analog circuits, characterized in that, The system includes: The data acquisition module is used to acquire observation signals and observation matrices; The circuit construction module is used to construct an analog circuit based on the observed signal and the observation matrix. Based on the observed signal and the observation matrix, a mathematical optimization model is established with the goal of minimizing the L1 norm; the KKT optimality condition corresponding to the mathematical optimization model is derived, generating a nonlinear equation set; based on the nonlinear equation set, the connection relationship and parameters of each functional module in the analog circuit are determined, so that the steady-state voltage value of each node in the analog circuit is equivalent to the solution of the nonlinear equation set; An electrical signal conversion module is used to convert the value of the observed signal into a corresponding electrical signal and apply it to the input terminal of the analog circuit; The reconstructed value output module is used to power on the analog circuit until it reaches a steady state, measure the steady-state voltage values ​​of multiple predetermined nodes in the analog circuit, and output the measured steady-state voltage values ​​as the reconstructed values ​​of the sparse signal. The mathematical optimization model is in one of the following forms: The linear programming model corresponding to the noiseless observation scenario is constructed with the goal of minimizing the L1 norm of the sparse signal, while satisfying the following equality constraints: in, For observing signals, For the observation matrix, It is a sparse signal; The regularization model corresponding to noisy observation scenarios is constructed to minimize an objective function, the formula of which is: in, To minimize the function, For regularization functions; Based on the aforementioned set of nonlinear equations, the connection relationships and parameters of each functional module in the analog circuit are determined, specifically including the following mapping relationships: The variables to be solved in the nonlinear equation system are mapped to circuit node voltages; The linear operational relationships of the nonlinear equation system are mapped to basic operational modules composed of operational amplifiers and resistors; The linear transformation relationship related to the observation matrix in the nonlinear equation system is mapped into a multi-port linear transformation module; The complementary relaxation conditions in the nonlinear equations are mapped to an ideal diode unit consisting of a PN junction diode and an operational amplifier feedback circuit.

6. An electronic device, characterized in that, include: A processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the real-time sparse signal reconstruction method based on analog circuits as described in any one of claims 1 to 4.

7. A computer-readable storage medium, characterized in that, A computer program is stored on the computer-readable storage medium, which, when executed by a processor, implements the real-time sparse signal reconstruction method based on analog circuits as described in any one of claims 1 to 4.

Images