CN112187283B - Orthogonal matching pursuit reconstruction method and system based on approximate calculation - Google Patents

Orthogonal matching pursuit reconstruction method and system based on approximate calculation Download PDF

Info

Publication number
CN112187283B
CN112187283B CN202011112261.4A CN202011112261A CN112187283B CN 112187283 B CN112187283 B CN 112187283B CN 202011112261 A CN202011112261 A CN 202011112261A CN 112187283 B CN112187283 B CN 112187283B
Authority
CN
China
Prior art keywords
matrix
calculation
signal
column
module
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011112261.4A
Other languages
Chinese (zh)
Other versions
CN112187283A (en
Inventor
钱慧
张金鹏
王仁平
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Fuzhou University
Original Assignee
Fuzhou University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Fuzhou University filed Critical Fuzhou University
Priority to CN202011112261.4A priority Critical patent/CN112187283B/en
Publication of CN112187283A publication Critical patent/CN112187283A/en
Application granted granted Critical
Publication of CN112187283B publication Critical patent/CN112187283B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Classifications

    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/60—General implementation details not specific to a particular type of compression
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M7/00—Conversion of a code where information is represented by a given sequence or number of digits to a code where the same, similar or subset of information is represented by a different sequence or number of digits
    • H03M7/30—Compression; Expansion; Suppression of unnecessary data, e.g. redundancy reduction
    • H03M7/55—Compression Theory, e.g. compression of random number, repeated compression

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Data Mining & Analysis (AREA)
  • Computational Mathematics (AREA)
  • Mathematical Analysis (AREA)
  • Mathematical Optimization (AREA)
  • Pure & Applied Mathematics (AREA)
  • Databases & Information Systems (AREA)
  • Algebra (AREA)
  • Software Systems (AREA)
  • General Engineering & Computer Science (AREA)
  • Computing Systems (AREA)
  • Complex Calculations (AREA)

Abstract

The invention relates to an orthogonal matching pursuit reconstruction method based on approximate calculation, which comprises the following steps: step S1: collecting an original signal and preprocessing the original signal; step S2, mapping the preprocessed input signal into a low-dimensional measurement signal based on a compressed sensing theory; and S3, reconstructing the measurement signal by adopting an orthogonal matching pursuit reconstruction algorithm based on approximate calculation, and further obtaining a reconstructed signal. The method can reduce the number of matrix inversion by reducing the number of least square operations, effectively reduce the calculation complexity of the algorithm and improve the signal reconstruction efficiency.

Description

Orthogonal matching pursuit reconstruction method and system based on approximate calculation
Technical Field
The invention relates to the field of signal processing, in particular to an orthogonal matching pursuit reconstruction method and system based on approximate calculation.
Background
Compressed sensing (Compressed Sensing, CS) is one of the most well-known research developments in the field of signal processing over the last decade, consisting mainly of two steps, compressed sampling and reconstruction. The sampling process in compressed sensing is relatively simple, but the reconstruction is very complex, so the study of the reconstruction algorithm is a very important aspect in compressed sensing. Because the algorithm software has low realization speed and high power consumption, the effect of real-time reconstruction cannot be achieved, and partial researchers begin to accelerate the design of the algorithm by using the FPGA (Field Programmable GATE ARRAY) technology. The orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm is one of the very widely applied reconstruction algorithms and is relatively simple, facilitating hardware implementation. The OMP algorithm still involves a large number of inner product, comparison and matrix inversion operations. In particular, least Square (LS) computation involves a matrix inversion operation that is computationally complex and disadvantageous for hardware implementation.
Disclosure of Invention
In view of the above, the present invention aims to provide an orthogonal matching pursuit reconstruction method and system based on approximate calculation, which can reduce the number of least square operations, further reduce the number of matrix inversions, effectively reduce the calculation complexity of the algorithm, and improve the signal reconstruction efficiency.
In order to achieve the above purpose, the invention adopts the following technical scheme:
an orthogonal matching pursuit reconstruction method based on approximate calculation comprises the following steps:
Step S1: collecting an original signal and preprocessing the original signal;
step S2, mapping the preprocessed input signal into a low-dimensional measurement signal based on a compressed sensing theory;
and S3, reconstructing the measurement signal by adopting an orthogonal matching pursuit reconstruction algorithm based on approximate calculation, and further obtaining a reconstructed signal.
Further, the original signal is obtained by adding sine waves of two different frequencies.
Further, the step S2 specifically includes:
The method is provided with an original signal f epsilon R N and a measurement matrix phi epsilon R M×N, the original signal f is transformed into a K sparse signal x epsilon R N through a sparse basis psi epsilon R N×N, and the sampling process in compressed sensing is represented by the following formula:
y＝Φf＝ΦΨx＝Ax (1)
where a=Φψ is referred to as CS matrix, Φ is a random demodulation architecture matrix, and ψ is a fourier transform basis.
Further, the step S3 specifically includes:
Step S31: the residual r t-1 and the column vector phi j of the CS matrix A are subjected to inner product operation, the column index lambda t of the column with the largest inner product value is found, and the original subset is updated according to the maximum column index lambda t
Step S32, replacing least square calculation with approximate calculation method
Step S33 updating residual errorUpdating the iteration times t=t+1, judging that if the iteration times t is less than K, executing the step S31, otherwise executing the next step;
Step S34, outputting the final signal estimation value
Further, the step S32 specifically includes:
step (1): calculating the maximum value in the inner product of the residual r t-1 and the column vector phi j of the CS matrix A and recording the corresponding column index, namely Residual r t-1 is initialized to observation vector y;
step (2): updating the original subset according to the maximum column index lambda t A t is a new matrix that extracts the corresponding maximum column composition from CS matrix a according to the maximum column index lambda t for each iteration.
Further, the step S32 specifically includes:
for the least squares solution, the calculation is performed without extracting the maximum column:
substituting a=Φψ into formula (2) yields:
for ψ -1 in equation (3) to be replaced approximately with ψ T, (the result of ψ T)-1ΨT is that the identity matrix is directly reduced, and then equation (3) becomes the following equation:
Obtained by the formula (4) Is a 1024 x 1 dimensional column vector, and finds/>The value at the position corresponding to the maximum column sequence number is further simplified
The representation is composed of
A vector of values at the position corresponding to the maximum column sequence number; /(I)A matrix of columns representing the largest column number in ψ T;
By using To represent the approximate calculated least squares solution:
further, in the step S3, when the least square is solved in the last iteration, an improved Cholesky decomposition algorithm is adopted to perform matrix inversion operation:
Matrix is formed The following decomposition is carried out:
C＝LDLT (7)
wherein L is a lower triangular matrix with diagonal elements of 1, and D is a diagonal matrix, and the calculation is performed according to the following formulas:
c -1 is then calculated as follows:
C-1＝(L-1)TD-1L-1 (10)
Wherein matrix D -1 can be obtained by inverting the elements on the diagonal of matrix D, and matrix L -1 can be obtained by:
Solving with normal least squares step at the kth iteration:
An orthogonal matching pursuit reconstruction system based on approximate calculation comprises a calculation module, a storage module and a control module which are connected in sequence; the calculation module completes all operations in the algorithm iteration process; the storage module is used for storing the CS matrix, the sparse basis, the observation vector and all intermediate matrices, vectors and data; the control module controls the conversion of the various states of the algorithm, reads corresponding data from the memory module to the calculation module and writes the result back to the memory module.
Further, the calculation module comprises a matrix inner product unit, an approximation calculation unit, a residual calculation unit, a C matrix inversion unit and a least square calculation unit.
Further, the matrix inner product unit is composed of an adder tree composed of parallel multipliers composed of 256 complex multipliers and 255 complex adders and a comparator.
Compared with the prior art, the invention has the following beneficial effects:
The method can reduce the number of least square operations, further reduce the number of matrix inversion, effectively reduce the calculation complexity of the algorithm, improve the signal reconstruction efficiency, and is more suitable for hardware acceleration realization to achieve the effect of real-time reconstruction.
Drawings
FIG. 1 is a flow chart of a method for reconstructing a signal according to an embodiment of the present invention;
FIG. 2 is a diagram of an overall hardware architecture in one embodiment of the invention;
FIG. 3 is a block diagram of a matrix inner product unit hardware architecture in accordance with one embodiment of the present invention;
FIG. 4 is a diagram of a matrix factorization element calculation hardware architecture in an embodiment of the invention;
FIG. 5 is a diagram of a Newton-Lawson reciprocal hardware architecture in an embodiment of the invention
FIG. 6 is a diagram illustrating system state transitions according to an embodiment of the present invention;
FIG. 7 is a graph of reconstruction results in an embodiment of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings and examples.
Referring to fig. 1, the present invention provides an orthogonal matching pursuit reconstruction method based on approximate calculation, which includes the following steps:
Step S1: collecting an original signal and preprocessing the original signal;
step S2, mapping the preprocessed input signal into a low-dimensional measurement signal based on a compressed sensing theory;
The method is provided with an original signal f epsilon R N and a measurement matrix phi epsilon R M×N, the original signal f is transformed into a K sparse signal x epsilon R N through a sparse basis psi epsilon R N×N, and the sampling process in compressed sensing is represented by the following formula:
y＝Φf＝ΦΨx＝Ax (1)
where a=Φψ is referred to as CS matrix, Φ is a random demodulation architecture matrix, and ψ is a fourier transform basis.
And S3, reconstructing the measurement signal by adopting an orthogonal matching pursuit reconstruction algorithm based on approximate calculation, and further obtaining a reconstructed signal.
In this embodiment, the step S3 specifically includes:
Step S31: the residual r t-1 and the column vector phi j of the CS matrix A are subjected to inner product operation, the column index lambda t of the column with the largest inner product value is found, and the original subset is updated according to the maximum column index lambda t
Step (1): calculating the maximum value in the inner product of the residual r t-1 and the column vector phi j of the CS matrix A and recording the corresponding column index, namelyResidual r t-1 is initialized to observation vector y;
step (2): updating the original subset according to the maximum column index lambda t A t is a new matrix that extracts the corresponding maximum column composition from CS matrix a according to the maximum column index lambda t for each iteration.
Step S32, replacing least square calculation with approximate calculation method
For the least squares solution, the calculation is performed without extracting the maximum column:
substituting a=Φψ into formula (2) yields:
for ψ -1 in equation (3) to be replaced approximately with ψ T, (the result of ψ T)-1ΨT is that the identity matrix is directly reduced, and then equation (3) becomes the following equation:
Obtained by the formula (4) Is a 1024 x 1 dimensional column vector, and finds/>The value at the position corresponding to the maximum column sequence number is further simplified
Expressed by/>A vector of values at the position corresponding to the maximum column sequence number; /(I)A matrix of columns representing the largest column number in ψ T;
By using To represent the approximate calculated least squares solution:
Step S33 updating residual error Updating the iteration times t=t+1, judging that if the iteration times t is less than K, executing the step S31, otherwise executing the next step;
Step S34, outputting the final signal estimation value
Preferably, in this embodiment, in the step S3, when the least square is solved in the last iteration, the matrix inversion is performed by using a modified Cholesky decomposition algorithm:
Matrix is formed The following decomposition is carried out:
C＝LDLT (7)
wherein L is a lower triangular matrix with diagonal elements of 1, and D is a diagonal matrix, and the calculation is performed according to the following formulas:
c -1 is then calculated as follows:
C-1＝(L-1)TD-1L-1 (10)
Wherein matrix D -1 can be obtained by inverting the elements on the diagonal of matrix D, and matrix L -1 can be obtained by:
Solving with normal least squares step at the kth iteration:
In this embodiment, as shown in fig. 2, an orthogonal matching pursuit reconstruction system based on approximate calculation is provided, which includes a calculation module, a storage module and a control module connected in sequence; the calculation module completes all operations in the algorithm iteration process; the storage module is used for storing the CS matrix, the sparse basis, the observation vector and all intermediate matrices, vectors and data; the control module controls the conversion of the various states of the algorithm, reads corresponding data from the memory module to the calculation module and writes the result back to the memory module.
Preferably, in this embodiment, the calculation module includes a matrix inner product unit, an approximation calculation unit, a residual calculation unit, a C-matrix inversion unit, and a least square calculation unit.
Referring to fig. 3, in the present embodiment, the matrix inner product unit is composed of an adder tree composed of 256 complex multipliers and 255 complex adders and one comparator. One complex multiplier is implemented by invoking 4 DSP resources. The adder is implemented by invoking Slices resources. And reading one row of A and y or (r) from the memory module for each period to perform inner product operation, and sending the result into a comparator for comparison and recording the row serial number of a larger row. Finally, after the inner products of all the rows are compared, the row serial number of the row with the largest inner product value is output. Most of the operations of the approximation calculation unit, the residual calculation unit and the least squares calculation unit can be implemented by multiplexing the parallel multiplier and adder tree structures herein.
In this embodiment, a specific hardware implementation architecture of the C-matrix inversion unit is shown in fig. 4; since matrix C is a positive definite symmetric matrix, C -1 is also a symmetric matrix, so that only the elements on the diagonal of C -1 and the elements of the lower triangle are required. First, the elements of the L matrix and the D matrix need to be found from the C matrix using formulas (8) and (9). From formulas (8) and (9), it is known that the elements of the L matrix and the D matrix have correlation, so that the calculation can be performed only in a certain order. Division is then involved in solving for the elements of matrix D -1, which is chosen by the more classical newton-lavson method to solve for the inverse. This method finds a function f (X) with a solution x=1/M at zero, which is generally the following:
f(X)＝1/X-M (13)
the solution of this function at zero is the inverse of M. The newton-lavhson method gives an iterative formula:
In this embodiment, the initial value X 0 =3-2M is used, and then the iterative calculation is performed by using the formula (14), so that the value of X i converges to the inverse of M. In this way division operations are converted into multiplication and subtraction operations. A specific hardware implementation architecture is shown in fig. 5.
The elements of the L -1 matrix are then found using equation (11), which can also be implemented using the architecture of FIG. 5. Finally, matrix C -1 can be calculated according to equation (10).
In this embodiment, the storage module is mainly used to store data required for algorithm calculation, including CS matrix, observation vector, sparse basis, residual error, and the like, and various data written back from the calculation module. The storage details of the respective data are shown in table 1. In order to read out the data of one column of the matrix in one period and send the data into the parallel multiplier in parallel, the invention stores the data of one column of the matrix in the same address of BRAM. Wherein the CS matrix A is stored by a single block BRAM, the addresses are 0 to 1023, the Fourier transform basis ψ is stored by a single block BRAM, the addresses are 0 to 1023, the observation vector y and the residual error r are stored in the same block BRAM, the observation vector is stored to the 0 address, and the residual error r is stored behind the y vector in the iterative sequence.
TABLE 1 memory resource usage
In this embodiment, the control module mainly completes the control of the working conditions of each operation submodule through a state machine. The state transition diagram of the state machine is shown in fig. 6, and the state descriptions are shown in table 2. Each sub-module is provided with a control signal, when the sub-module needs to work, the state machine sets the control signal of the sub-module to be 1, when the task is completed, the sub-module feeds back a signal to the control module, and then the state machine sets the control signal of the sub-module to be 0, and the next state is entered. When the iteration times t is less than K, the State machine loops between State0 and State4, when t=K, the State machine jumps from State4 to State5 and then passes through State6, state7 and State8 end the loop, and the system resets to State0.
Table 2 state descriptions of the state machine
Example 1:
In the embodiment, the input original signal f is obtained by adding four sine waves with frequencies of 50Hz,70Hz,90Hz and 110Hz and amplitudes of 0.3,0.4,0.5,0.6, and the sampling sequence is 1:1024, and the sampling frequency is 1024; 2) An ACOMP program is operated in MALTAB to obtain the original data of a CS matrix A, a Fourier transform basis ψ and an observation vector y, and fixed-point quantization processing is carried out on the data; 3) Importing the obtained data into coe files, and performing simulation test in a development tool Vivado 2016.2 of the Xilinx company; 4) And importing a result obtained by simulation in the FPGA into MATLAB, performing inverse Fourier transform in the MATLAB to obtain a reconstructed signal, comparing the reconstructed signal with the original signal, and verifying whether the reconstruction is successful.
The ACOMP algorithm outputs the values of the original signals in the frequency domain in the FPGA, which are fixed-point data amplified by 2^9 times, and the data simulated in MATLAB corresponding to 169-140i,167+139i,148-105i,150+103i,62-138i,59+140i,35+103i,36-102i are 176-140i,181+139i,163-111i,158+111i,67-135i,63+136i,34+107i,35-111i respectively. Fig. 7 shows simulation results at k=8, which are the original signal and the signal reconstructed from the output result of the ACOMP algorithm in the FPGA, respectively, and the reconstructed signal-to-noise ratio is 22.8537dB. In contrast to the speed of reconstruction in the prior art, the reconstruction time of the present invention was 66.904us when k=8, 68.55us when k=36, 296.14us when k=36, 327us at the same 133.33MHz frequency. The invention effectively improves the accelerating effect, and the accelerating effect is more obvious when the sparsity is higher.
The foregoing description is only of the preferred embodiments of the invention, and all changes and modifications that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.

Claims (2)

1. The orthogonal matching pursuit reconstruction system based on approximate calculation is characterized by comprising a calculation module, a storage module and a control module which are connected in sequence; the calculation module completes all operations in the algorithm iteration process; the storage module is used for storing the CS matrix, the sparse basis, the observation vector and all intermediate matrices, vectors and data; the control module controls the conversion of each state of the algorithm, reads corresponding data from the storage module to the calculation module and writes the result back to the storage module; the computing module comprises a matrix inner product unit, an approximation computing unit, a residual computing unit, a C matrix inversion unit and a least square computing unit; the matrix inner product unit consists of an adder tree formed by parallel multipliers formed by 256 complex multipliers and 255 complex adders and a comparator; the orthogonal matching pursuit reconstruction system based on approximate calculation operates an orthogonal matching pursuit reconstruction method based on approximate calculation, and comprises the following steps:
Step S1: collecting an original signal and preprocessing the original signal;
step S2, mapping the preprocessed input signal into a low-dimensional measurement signal based on a compressed sensing theory;
S3, reconstructing the measurement signal by adopting an orthogonal matching pursuit reconstruction algorithm based on approximate calculation, and further obtaining a reconstructed signal;
the step S2 specifically comprises the following steps:
The method is provided with an original signal f epsilon R N and a measurement matrix phi epsilon R M×N, the original signal f is transformed into a K sparse signal x epsilon R N through a sparse basis psi epsilon R N×N, and the sampling process in compressed sensing is represented by the following formula:
y＝Φf＝ΦΨx＝Ax (1)
Where a=Φψ is referred to as CS matrix, Φ is a random demodulation architecture matrix, and ψ is a fourier transform basis;
The step S3 specifically comprises the following steps:
Step S31: the residual r t-1 and the column vector phi j of the CS matrix A are subjected to inner product operation, the column index lambda t of the column with the largest inner product value is found, and the original subset is updated according to the maximum column index lambda t
Step S32, replacing least square calculation with approximate calculation method
Step S33 updating residual errorUpdating the iteration times t=t+1, judging that if the iteration times t is less than K, executing the step S31, otherwise executing the next step;
Step S34, outputting the final signal estimation value The step S32 specifically includes:
step (1): calculating the maximum value in the inner product of the residual r t-1 and the column vector phi j of the CS matrix A and recording the corresponding column index, namely Residual r t-1 is initialized to observation vector y;
step (2): updating the original subset according to the maximum column index lambda t A t is a new matrix of corresponding maximum column composition extracted from CS matrix a according to the maximum column index λ t for each iteration; the step S32 specifically includes:
for the least squares solution, the calculation is performed without extracting the maximum column:
substituting a=Φψ into formula (2) yields:
for ψ -1 in equation (3) to be replaced approximately with ψ T, (the result of ψ T)-1ΨT is that the identity matrix is directly reduced, and then equation (3) becomes the following equation:
Obtained by the formula (4) Is a 1024 x 1 dimensional column vector, and finds/>The value at the position corresponding to the maximum column sequence number is further simplified
Expressed by/>A vector of values at the position corresponding to the maximum column sequence number; /(I)A matrix of columns representing the largest column number in ψ T;
By using To represent the approximate calculated least squares solution:
And step S3, when the least square is solved in the last iteration, performing matrix inversion operation by adopting an improved Cholesky decomposition algorithm:
Matrix is formed The following decomposition is carried out:
C＝LDLT (7)
wherein L is a lower triangular matrix with diagonal elements of 1, and D is a diagonal matrix, and the calculation is performed according to the following formulas:
c -1 is then calculated as follows:
C-1＝(L-1)TD-1L-1 (10)
Wherein matrix D -1 is obtained by inverting the elements on the diagonal of matrix D, and matrix L -1 is obtained by:
Solving with normal least squares step at the kth iteration:
2. the system of claim 1, wherein the original signal is obtained by summing sine waves of two different frequencies.
CN202011112261.4A 2020-10-16 2020-10-16 Orthogonal matching pursuit reconstruction method and system based on approximate calculation Active CN112187283B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011112261.4A CN112187283B (en) 2020-10-16 2020-10-16 Orthogonal matching pursuit reconstruction method and system based on approximate calculation

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011112261.4A CN112187283B (en) 2020-10-16 2020-10-16 Orthogonal matching pursuit reconstruction method and system based on approximate calculation

Publications (2)

Publication Number Publication Date
CN112187283A CN112187283A (en) 2021-01-05
CN112187283B true CN112187283B (en) 2024-05-31

Family

ID=73950653

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011112261.4A Active CN112187283B (en) 2020-10-16 2020-10-16 Orthogonal matching pursuit reconstruction method and system based on approximate calculation

Country Status (1)

Country Link
CN (1) CN112187283B (en)

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103532567A (en) * 2013-11-01 2014-01-22 哈尔滨工业大学 Signal reconstruction method of OMP (orthogonal matching pursuit) based on rapid inner product calculation under distributed type CS (compressed sensing) framework
CN107561367A (en) * 2017-08-15 2018-01-09 北京航空航天大学 A kind of wide spectrum impedance measurement device and method based on compressive sensing theory
CN108322409A (en) * 2018-01-25 2018-07-24 杭州电子科技大学 Sparse OFDM channel estimation method based on generalized orthogonal matching pursuit algorithm

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN107919938B (en) * 2016-10-10 2021-08-10 广州滴普科技有限公司 Signal sampling recovery method and device suitable for OvXDM system and OvXDM system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103532567A (en) * 2013-11-01 2014-01-22 哈尔滨工业大学 Signal reconstruction method of OMP (orthogonal matching pursuit) based on rapid inner product calculation under distributed type CS (compressed sensing) framework
CN107561367A (en) * 2017-08-15 2018-01-09 北京航空航天大学 A kind of wide spectrum impedance measurement device and method based on compressive sensing theory
CN108322409A (en) * 2018-01-25 2018-07-24 杭州电子科技大学 Sparse OFDM channel estimation method based on generalized orthogonal matching pursuit algorithm

Also Published As

Publication number Publication date
CN112187283A (en) 2021-01-05

Similar Documents

Publication Publication Date Title
Bai et al. High-speed compressed sensing reconstruction on FPGA using OMP and AMP
Gao et al. Additive fast Fourier transforms over finite fields
CN106646595B (en) A kind of seismic data compression method that adaptive order based on tensor is blocked
CN109033030B (en) Tensor decomposition and reconstruction method based on GPU
CN110765709A (en) FPGA-based 2-2 fast Fourier transform hardware design method
WO2018027706A1 (en) Fft processor and algorithm
CN114297571A (en) Polynomial multiplication hardware implementation system suitable for lattice cipher algorithm
CN112231626A (en) FFT processor
Ju et al. Derivation and analysis of fast bilinear algorithms for convolution
CN112187283B (en) Orthogonal matching pursuit reconstruction method and system based on approximate calculation
CN116578819A (en) Sparse fraction Fourier transform FPGA implementation method and system
CN115511004A (en) Five-dimensional seismic data low-rank constraint reconstruction method, system, medium and equipment
Panda Performance Analysis and Design of a Discreet Cosine Transform processor Using CORDIC algorithm
Liu et al. Accelerated augmented Lagrangian method for total variation minimization
Yang et al. Recursive discrete cosine transforms with selectable fixed-coefficient filters
CN108983600B (en) Mixed domain compression sampling control system and control method thereof
Zhang et al. An FPGA implementation of orthogonal matching pursuit for random demodulation real-time reconstruction
Mozafari et al. Hartley stochastic computing for convolutional neural networks
CN104820581B (en) A kind of method for parallel processing of FFT and IFFT permutation numbers table
Ge et al. Efficient algorithm for 2-D arithmetic Fourier transform
Andersson FFT hardware architectures with reduced twiddle factor sets
CN108199714A (en) A kind of circuit system of improvement OMP algorithms restored applied to AIC architecture signals
Oh et al. A method for structured linear total least norm on blind deconvolution problem
Bricogne Fourier transforms in crystallography: theory, algorithms and applications
US9311274B2 (en) Approach for significant improvement of FFT performance in microcontrollers

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant