An LCA algorithm circuit for realizing compressed sensing restoration of matrices in positive and real number domains

Abstract

The present invention discloses an LCA algorithm circuit for realizing compressed sensing restoration of matrices in the positive number domain and the real number domain, and belongs to the field of integrated circuit technology. The present invention designs a matrix-matrix-vector multiplication circuit for matrices in the positive number domain and the real number domain based on the principle of conductance compensation, and based on the circuit, a feedback loop is formed by connecting with analog components such as a transimpedance amplifier (TIA) and a single-power-supply subtractor to construct a compressed sensing restoration circuit. The present invention realizes an analog computing system of a compressed sensing restoration algorithm in a continuous time domain, which can restore compressed sensing signals in one step, reduces the operation steps and power consumption, and reduces hardware overhead. It is a high-throughput, high-energy-efficiency compressed sensing hardware system, and has broad application prospects in the fields of image compression, magnetic resonance imaging, channel estimation, and target detection.

Description

Technical Field

[0001] The present invention belongs to the field of semiconductors, analog computing and integrated circuits, and relates to an analog matrix computing circuit for implementing a compressed sensing restoration algorithm, and specifically to an analog computing circuit design based on a variable resistor device (such as a resistive memory, a phase change memory, a magnetic memory, a ferroelectric memory, etc.). Background Art

[0002] Compressed sensing can break the Nyquist sampling theorem. If the original signal is sparse or sparse in a certain transform domain, a small amount of signal can be collected through the acquisition matrix and the original signal can be well reconstructed through the nonlinear restoration algorithm. Since it was proposed in 2004, the compressed sensing theory has been rapidly applied to magnetic resonance imaging, image classification, target detection, channel estimation, single-pixel cameras, electrocardiograms and other fields. The compressed sensing restoration algorithm is generally more complex. The time complexity of the algorithm based on convex function optimization is O(n 3 ), where n is the size of the matrix, and the large amount of matrix calculations involved will impose a huge burden on traditional digital computers in terms of data calculation, storage and transportation, thereby increasing computing time and power consumption.

[0003] Crossbar arrays based on variable resistor devices (such as resistive random access memory, phase change memory, magnetic random access memory, and ferroelectric memory) can be used to accelerate matrix-vector multiplication, providing a feasible method for accelerating compressed sensing restoration algorithms. However, this method is currently limited to using variable resistor arrays to accelerate matrix-vector multiplication operations in iterative algorithms, while other nonlinear operations, input / output data conversion and handling operations require interaction with digital systems to complete, which will bring additional operations and hardware overhead. In addition, there is no compact and efficient solution for the matrix-matrix-vector (MMVM) operations involved in the restoration algorithm. Therefore, it is necessary to study a circuit system for fast calculation of compressed sensing restoration. Compared with discrete iterative algorithms, analog circuits in the continuous time domain can reduce the number of operation steps and data handling, thereby achieving low-power, low-hardware-overhead compressed sensing restoration. Summary of the invention

[0004] The purpose of the present invention is to construct an analog matrix calculation circuit for realizing positive domain and real domain matrices based on a local competition algorithm (LCA), which is applied to compressed sensing signal restoration in different scenarios.

[0005] The technical solution provided by the present invention is as follows:

[0006] Two execution TThe analog matrix calculation circuit module of Ψa matrix-matrix-vector multiplication (MMVM) operation can realize MMVM operations of matrices in the positive number domain and real number domain respectively, and two LCA algorithm circuits based on the MMVM module can realize compressed sensing restoration of matrices in the positive number domain and real number domain respectively.

[0007] The principle of the present invention is described as follows:

[0008] Consider an underdetermined problem y=Φx, where Φ is an n×m (n<m) matrix, y and x are n×1 and m×1 vectors respectively. In compressed sensing, Φ is the detection matrix, x is the original signal, and y is the detected signal. If the original signal is sparse in a certain transform domain x=Aa, where A(m×m) is the sparse transform domain, and a is the sparse representation of x in A, then the underdetermined problem can be transformed into y=Φx=ΦAa=Ψa. Among them, Ψ=ΦA is the perception matrix, and the process of compressed sensing restoration is to use the detection signal y to restore the sparse representation a, and the original signal can be obtained through x=Aa. Since we need to take into account both the sparsity and correctness of the signal to be solved, the problem can be abstracted as: where ||a|| n L stands for a n norm, solving this minimization problem requires traversing the subspace of all solution vectors a with sparsity k, which is a very slow process and a typical NP-hard problem. The basis pursuit (BP) method can minimize L 0 The problem of minimizing L 1 Norm problem: This converts it into a convex function optimization problem. The LCA algorithm based on the soft threshold function (STF) solves a by minimizing this formula. The LCA algorithm can be described as follows:

[0009]

[0010] a(t)=T λ (μ(t))=max(μ(t)-λ,0)

[0011] Where T λ () is a soft threshold function with a threshold of λ, I is the identity matrix, and μ is an intermediate variable of a.

[0012] The LCA circuit of the present invention is composed of m TIAs, a subtractor, a voltage inverter and an MMVM circuit.

[0013] For the positive matrix MMVM circuit, if it is an n×m matrix, the MMVM circuit consists of a 2m×n variable resistor array and a 1×n compensation resistor. The matrix is ​​written into the upper and lower halves of the variable resistor array as the simulated conductance value, that is, the matrix Ψ T(m×n) are mapped to the analog conductance values ​​of the upper and lower parts of the array respectively, and then the conductance values ​​of the compensation resistors connected to the ground on the array column lines are programmed (a total of n compensation resistors), so that the sum of the conductance values ​​of all resistor devices on each column line is equal. If a voltage a is applied to half of the row lines, the voltage a can be obtained on the other half of the row lines connected to the ground. The output current is, where c is a constant. When the circuit is working, the voltage vector is input on the m row lines in the lower half, and the output current is obtained on the other m row lines connected to the ground, that is, the positive matrix MMVM operation result. The m TIAs, inverters, subtractors and positive matrix MMVM circuits in the LCA circuit form an analog circuit in the continuous time domain. The cΨ and the compensation resistor are mapped to the MMVM module in the LCA circuit. The detection signal y is input at the input end, and the sparse representation a of the signal in A is obtained at the output end of the subtractor, thereby realizing a compressed sensing restoration operation with low power consumption and low hardware overhead. The n compensation resistors can also be implemented using variable resistor devices.

[0014] For the real matrix MMVM circuit, if it is an n×m matrix containing negative elements, the MMVM circuit consists of two 2m×n variable resistor arrays, 1×n compensation resistors, m TIAs with series resistors at the output terminals, and m inverters. The two variable resistor arrays share column lines, and the row lines are connected together through m voltage inverters and m transimpedance amplifiers (TIAs) with series output resistors. The original matrix is ​​converted into two non-negative matrices, which are then written into the arrays as the analog conductance values ​​of the variable resistors, and two are mapped in the two arrays respectively. The matrix and two The m rows in the lower half are connected through inverters, and the m rows in the upper half are connected through TIAs with resistors in series at the output end. When the circuit is working, a voltage vector is input on the m rows in the lower half, and the output current is obtained on the other m rows connected to the ground, which is the result of the real-domain MMVM operation. The m TIAs, subtractors, and real-matrix MMVM circuits in the LCA circuit form an analog circuit in the continuous-time domain. cΨ1, cΨ2, and the compensation resistor are mapped to the MMVM module in the LCA circuit. The detection signal y is input at the input end, and the sparse representation a is obtained at the output end of the subtractor. It is worth noting that since the real-matrix MMVM circuit itself contains a voltage inverter, the corresponding LCA circuit no longer requires additional m voltage inverters.

[0015] In the circuit that uses a subtractor to implement a soft threshold function, the supply voltage of the m integrated operational amplifiers ranges from 0 to V DD , and the voltage λ is input to the reverse input of the subtractor as the threshold of STF, and the output of TIA is connected to the positive input of the subtractor as μ, thereby realizing a=T with good performance and adjustable threshold value. λ (μ) function.

[0016] The beneficial effects of the present invention are as follows:

[0017] The present invention uses an integrated operational amplifier and a variable resistor device (resistive random access memory, phase change memory, magnetic random access memory and ferroelectric memory) array to realize an analog circuit that completes the compressed sensing restoration function in one step. It is a continuous time domain computing system. A DC voltage is input at the input end of the circuit, and a corresponding sparse signal can be obtained at the output end of the circuit. Compared with other hardware systems that realize similar functions, it does not require an iterative process, nor does it require data conversion and transportation, thereby reducing additional digital system hardware overhead, simplifying the operation process and improving the computing speed. At the same time, due to the sparse characteristics of the output signal, the power consumption of the variable resistor array is also reduced.

[0018] The present invention also provides a compensation resistor technology suitable for MMVM operation, which can realize MMVM operation in positive number domain and real number domain in one step without using other integrated devices, thereby reducing hardware overhead and lowering power consumption of operation.

[0019] In addition, the present invention also provides a method for realizing a soft threshold function with an adjustable threshold by using an integrated operational amplifier. A subtractor constructed by a single-power-supply operational amplifier can realize a soft threshold function with good performance, adjustable threshold, and meeting the requirements of the LCA algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 is the positive matrix MMVM circuit of the present invention;

[0021] Figure 2 is the real matrix MMVM circuit of the present invention;

[0022] Figure 3 It is a LCA circuit for positive number matrix of the present invention;

[0023] Figure 4 is a real number matrix-oriented LCA circuit of the present invention;

[0024] Figure 5 This is an example of the effect of the present invention applied to picture restoration. DETAILED DESCRIPTION

[0025] In order to more clearly illustrate the purpose, technical solutions and advantages of the present invention, the following is a further detailed description in conjunction with the accompanying drawings. The description herein is only used to explain the present invention and is not intended to limit the present invention.

[0026] The present invention provides a one-step solution for realizing compressed sensing restoration based on the LCA algorithm, including an analog matrix calculation circuit for executing the LCA algorithm for positive number matrices and real number matrices. The circuit combines a variable resistor array with an integrated operational amplifier, and can calculate the sparse signal a in one step by writing the sensing matrix Ψ and the input voltage vector y. Since the problem to be solved is the same, the circuit can also be applied to sparse coding. In addition, the invention also provides two MMVM circuits based on the principle of conductance compensation and a soft threshold function implementation method based on a subtractor.

[0027] Figure 1 It is a positive matrix MMVM circuit, which is composed of a 2m×n variable resistor array and a 1×n compensation resistor, and realizes the MMVM operation of the positive matrix in one step. In the present invention, the unit conductance g0=1 is agreed, and i in the description represents the i-th row and j represents the j-th column. T The elements in are mapped to the simulated conductance values ​​of the variable resistor devices in the array, represents the conductance value of the i-th row and j-th column of the upper array or the lower array, and the conductance of the j-th column ground compensation resistor is expressed as g c，j , the input voltage of the i-th row is represented by a i , let the jth column line voltage be V BL，j According to Kirchhoff's current law, the current flowing into the jth column line is equal to the current flowing out of the jth column line, which can be expressed as Writing the expression in matrix form, we can get Ψa=U1V BL , where the U1 matrix is ​​a positive diagonal matrix with diagonal elements If we make all diagonal elements in U1 equal: That is, adjust the conductance value of the compensation resistor on the column line to satisfy Then we can get Figure 1 Formula (1):

[0028]

[0029] According to Kirchhoff's current law and Ohm's law, the output current can be obtained on the m grounded lines, which is Figure 1 (2) in the figure, which implements the operation of MMVM.

[0030]

[0031] Figure 2 It is a real matrix MMVM circuit, which contains two variable resistor arrays of size 2m×n, m voltage inverters and m TIAs connected in series with resistors. The circuit can implement real domain MMVM operation. First, the matrix Ψ containing negative elements is decomposed into Ψ=Ψ1-Ψ2, where the matrix The elements in are all non-negative numbers. The matrix maps to the conductance values ​​of the upper and lower halves of the left array, respectively. The matrix is ​​mapped to the conductance values ​​of the upper and lower halves of the array on the right. According to Kirchhoff's current law, the current flowing into the jth column is equal to the current flowing out of the jth column. At the same time, according to the "virtual short and virtual open" characteristics of the operational amplifier working in the linear amplification region, the current flowing into the input of the op amp is approximately 0, and the voltage of the positive input and reverse input of the op amp is approximately equal. Here, the positive input is virtual ground, that is, the potential is approximately 0, so the expression can be listed, Write this expression in matrix form, Ψa=U2V BL , where the diagonal elements of the U2 matrix are The diagonal matrix of the compensation resistor is adjusted to make the diagonal elements equal, that is, Then we can get Figure 2 Formula (3) in

[0032]

[0033] According to Kirchhoff's current law and the "virtual short and virtual disconnection" of the op amp, we can get Figure 2 The output voltage of the TIA is Therefore, the output current on the grounded row line can be calculated as Figure 2 (4) in .

[0034]

[0035] Figure 3 It is an LCA circuit for positive matrix. m TIAs, inverters, subtractors and positive matrix MMVM circuits form a continuous time domain analog circuit system, which can implement the LCA algorithm in one step. Among them, a 1×n MMVM circuit with input conductance of size cg0=c can be connected in series to realize -Ψ T Ψa+Ψ T y operation, the inverter realizes the -a operation, and the subtractor powered by a single power supply can realize the soft threshold function a=T λ (μ) operation, TIA realizes the core differential function and addition operation. When the circuit reaches a stable state, the static equation of the circuit can be obtained by using the "virtual short and virtual open" characteristics of the operational amplifier, which is Figure 3 (5) in it.

[0036] μ=Ψ T y-(Ψ T Ψ-I)a (5)

[0037] a=T λ (μ)

[0038] The static equation is the equation for the time first-order differential equation in LCA to reach stability, where μ is the output voltage of the TIA and the input voltage of the subtractor, and a is the output voltage of the subtractor and the sparse representation obtained by the circuit. The dynamic response of the circuit is analyzed with TIA as the core. Before the circuit reaches stability, the op amp cannot be considered to be a virtual short, that is, the voltages of the positive and negative input ports cannot be considered to be consistent. Set the reverse input voltage of the TIA to V I , the voltage at the reverse input of the inverter is set to V II , the output voltage of the inverter is set to V III , then using Kirchhoff's current law, we can list the expression: The first term on the left side of the equal sign in the formula is the current provided by the MMVM circuit to the TIA, the second term is the current provided by the inverter to the TIA, and the right side of the equal sign is the current flowing through the TIA feedback conductance. In the dynamic case, the column line voltage of the MMVM circuit with a series input resistor can be expressed as The dynamic equation of the inverter can be expressed as, V III =2V II -a, so Kirchhoff's current equation with TIA as the core can be rewritten as, Ψ T y+Ψ T Ψa-Ψ T ΨV I -cU3V I +V III =2V I -μ, where the U3 matrix is ​​a matrix with diagonal elements ∑ j Ψ i，j The diagonal matrix of the operational amplifier is combined with the open-loop transfer function. V III , Where L0 is the open-loop DC gain multiple of the op amp, and ω0 is the 3-dB bandwidth of the op amp, then we can get, Since the L0 value in the formula is very large, it is usually around 10 5 So by omitting the relevant small terms, we can get the dynamic equation of the circuit in the frequency domain, (2I+cU3+Ψ T Ψ)su-2sa=L0ω0[-μ+Ψ T y-(Ψ T Ψ-I)a], and then use the Laplace inverse transform to get the time domain equation of the circuit Since the input signal μ of the subtractor is the output voltage of the TIA, it is not a step signal, but an analog voltage signal that evolves over time with the time constant of the operational amplifier. Therefore, it is assumed that the output a of the subtractor is a signal that changes closely with its input μ, that is, And a(t) = T λ (μ(t)), so we can get the dynamic equation of the entire circuit, which is Figure 3 In formula (6),

[0039]

[0040] This is also the LCA time first-order differential equation mentioned above.

[0041] Figure 4 It is an LCA circuit for real number matrices. m TIAs, subtractors, and real number matrix MMVM circuits realize a continuous time analog circuit system for solving real number domain LCA. The more common detection matrix Φ and sparse basis matrix A in compressed sensing both contain negative elements, so the perception matrix Ψ generally also contains negative elements. Ψ is decomposed into two matrices Ψ=Ψ1-Ψ2 containing only non-negative elements, and then cΨ1 and cΨ2 are mapped to the circuit. After the same operation as the positive number matrix MMVM circuit, the real number matrix MMVM result can be obtained at the grounded row line. By inputting the detection signal y at the input end, the sparse representation a can be obtained at the output end of the subtractor.

[0042] Figure 5 This is a typical application demonstration of the LCA circuit. The original image is sampled 50% using the observation matrix, and then the matrix cΨ is written into the variable resistor array as the device conductance value. The conductance value of the compensation resistor is adjusted, and the detection signal is converted into a voltage signal and input into the LCA circuit. The sparse representation of the signal in the transform domain A can be obtained, and then x=Aa can be used to restore the original image. Figure 5 In the coordinate diagram, the ordinate is the circuit measurement result and the abscissa is the ideal calculation result. It can be seen that the two are highly consistent, especially the semi-logarithmic coordinate diagram in the illustration shows that the elements with ideal output of 0 have very small circuit values, which proves that the circuit correctly solves the sparse representation of image restoration.

[0043] The embodiments described above are not intended to limit the present invention. Any person skilled in the art may make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention is defined by the scope of the claims.

Claims

1. A local competition algorithm LCA algorithm circuit for implementing a positive field matrix, characterized in that: The circuit includes m transimpedance amplifiers TIA, m subtractors, m voltage inverters and a positive matrix MMVM circuit. For an n×m matrix, the MMVM circuit is composed of a 2m×n variable resistor array and a 1×n compensation resistor. The matrix is ​​written into the upper and lower parts of the variable resistor array as analog conductance values. When the circuit is working, a voltage vector is input on the m row lines of the lower part, and an output current is obtained on the other m row lines connected to the ground, that is, the positive matrix MMVM operation result. The transimpedance amplifier TIA, the inverter, the subtractor and the positive matrix MMVM circuit in the LCA circuit form an analog circuit in a continuous time domain. The cΨ and the compensation resistor are mapped to the MMVM circuit in the LCA circuit. The input voltage λ at the reverse input end of the subtractor is used as the threshold of the soft threshold function STF. The output end of the transimpedance amplifier TIA is connected to the positive input end of the subtractor as μ. The detection signal y is input to the LCA circuit, and the sparse representation a of the signal in A is obtained at the output end of the subtractor, a=T λ (μ), where c is a constant, Ψ = ΦA is the perception matrix, A is the sparse transform domain, Φ is an n×m matrix, T λ () is a soft threshold function with a threshold of λ.

2. The local competition algorithm LCA algorithm circuit for implementing a positive field matrix as claimed in claim 1, characterized in that: The compensation resistor is composed of a column of variable resistor devices, one end of which is connected to the column line of the array and the other end is grounded. Its conductance value is determined by the sum of the conductance values ​​of other variable resistor devices on the column line of the variable resistor array to ensure that the sum of the conductance values ​​of all resistor devices on each column line is equal.

3. The local competition algorithm LCA algorithm circuit for implementing a positive field matrix as claimed in claim 1, characterized in that: The subtractor is composed of an operational amplifier OA powered by a single power supply and a fixed resistor. When the circuit is working, a threshold voltage is input to the negative input terminal of the OA, and a voltage signal is input to the positive input terminal as input, and a soft threshold function is implemented at the output terminal.

4. The local competition algorithm LCA algorithm circuit for implementing a positive field matrix as claimed in claim 1, characterized in that: The variable resistance device is a resistive memory, a phase change memory, a magnetic memory or a ferroelectric memory.

5. A local competition algorithm LCA algorithm circuit for implementing a real number field matrix, characterized in that: The circuit includes m transimpedance amplifiers TIA, m subtractors and real number matrix MMVM circuit. For an n×m matrix containing negative elements, the MMVM circuit is composed of two 2m×n variable resistor arrays, 1×n compensation resistors, m transimpedance amplifiers TIA with resistors connected in series at the output end and m inverters. The two variable resistor arrays share column lines, the m row lines in the lower half are connected through inverters, and the m row lines in the upper half are connected through the transimpedance amplifiers TIA with resistors connected in series at the output end. The original matrix is ​​converted into two non-negative matrices, which are then written into the array as analog conductance values ​​of the variable resistors. When the circuit is working, the m row lines in the lower half are input. Voltage vector, then the output current is obtained on the other m grounded row lines, that is, the real domain MMVM operation result. The transimpedance amplifier TIA, the subtractor and the real matrix MMVM circuit in the LCA circuit form an analog circuit in the continuous time domain. Decompose Ψ into two matrices Ψ=Ψ1-Ψ2 containing only non-negative elements, and map cΨ1, cΨ2 and the compensation resistor to the MMVM circuit in the LCA circuit. The input voltage λ at the reverse input of the subtractor is used as the threshold of the STF. The output of the transimpedance amplifier TIA is connected to the positive input of the subtractor as μ. The detection signal y is input to the LCA circuit, and the sparse representation a is obtained at the output of the subtractor, a=T λ (μ), where c is a constant, Ψ = ΦA is the perception matrix, A is the sparse transform domain, Φ is an n×m matrix, T λ () is a soft threshold function with a threshold of λ.

6. The LCA algorithm circuit for implementing a real-domain matrix according to claim 5, characterized in that: The compensation resistor is composed of a column of variable resistor devices, one end of which is connected to the column line of the array and the other end is grounded. Its conductance value is determined by the sum of the conductance values ​​of other variable resistor devices on the column line of the variable resistor array to ensure that the sum of the conductance values ​​of all resistor devices on each column line is equal.

7. The LCA algorithm circuit for implementing a real-domain matrix according to claim 5, characterized in that: The subtractor is composed of an operational amplifier OA powered by a single power supply and a fixed resistor. When the circuit is working, a threshold voltage is input to the negative input terminal of the OA, and a voltage signal is input to the positive input terminal as input, and a soft threshold function is implemented at the output terminal.

8. The LCA algorithm circuit for implementing a real-domain matrix according to claim 5, characterized in that: The variable resistance device is a resistive memory, a phase change memory, a magnetic memory or a ferroelectric memory.

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