CN112737595A - Reversible projection compression sensing method based on FPGA - Google Patents
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Abstract
The invention discloses a reversible projection compression sensing method based on an FPGA (field programmable gate array). an approximate reversible projection matrix U is trained by an upper computer by utilizing a task-driven dictionary learning algorithm; the upper computer transmits the projection matrix U to the lower computer FPGA and stores the projection matrix U in the RAM; a signal conditioning circuit is adopted to condition the projection matrix U by the FPGA; mixing the conditioned U matrix and a tested signal sampling multiply-add device to obtain a mixing sampling digital signal Y; the ADC is used for carrying out digital sampling on the low-dimensional signal Y, and the FPGA sends the sampled low-dimensional signal Y to an upper computer; and the upper computer reconstructs the signal X after receiving the sampling signal Y. The algorithm provided by the invention has low complexity and good real-time performance, and is far superior to the traditional compressed sensing algorithm; and the parallel processing capability of the FPGA is utilized to realize the high data throughput of the compression algorithm.
Description
Technical Field
The invention belongs to the field of compressed sensing, and particularly relates to a reversible projection compressed sensing method based on an FPGA.
Background
The popularity of computers and the internet has brought great convenience to human production and life since the 70 s of the 20 th century. At the same time, the rapid increase in the amount of stored data and the increasing transmission rates have led to the widespread interest and use of data compression techniques. For example, the sampling rate of the LPD64 oscilloscope from Tektronix corporation is 25GS/s and 12bit resolution, and a single channel will produce 300Gb of data volume per second. In order to solve the problem of dimensionality disaster caused by massive data, researchers provide a compressed sensing system, compressibility, sparseness and non-coherence of signals are combined, an observation value containing all effective information of the signals is obtained after projection is measured in a compression and sampling combination mode, and therefore the sparse signals with limited dimensionality can be sampled through sampling frequency far less than the requirement of the Nyquist theorem, and sampling with the bandwidth lower than twice the original signal bandwidth is possible. However, the existing compression technology has the problems of limited reconstruction precision, high complexity of a reconstruction algorithm and the like, so that the application of the compressed sensing technology has a plurality of limitations.
Therefore, the invention provides a reversible projection compression sensing algorithm, which utilizes a driving dictionary to learn to obtain a reversible projection matrix and carries out dimension reduction on a sampling signal so as to improve the compression ratio of data and meet the speed requirements of data storage, transmission speed and instantaneity.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the existing problems, the reversible projection compression sensing method based on the FPGA is low in complexity, good in real-time performance and far superior to the traditional compression sensing method.
The technical scheme is as follows: the invention relates to a reversible projection compression sensing method based on an FPGA (field programmable gate array), which comprises the following steps of:
(1) training an approximate reversible projection matrix U by the upper computer by using a task-driven dictionary learning algorithm;
(2) the upper computer transmits the projection matrix U to the lower computer FPGA and stores the projection matrix U in the RAM;
(3) a signal conditioning circuit is adopted to condition a projection U matrix stored in the FPGA;
(4) mixing the conditioned U matrix and the X sampling multiply-add device of the measured signal to obtain a mixing digital signal;
(5) digitally sampling the mixing signal to obtain a digital signal Y;
(6) the FPGA sends the sampled low-dimensional signal Y to an upper computer;
(7) and the upper computer reconstructs the signal X after receiving the sampling signal Y.
Further, the step (1) includes the steps of:
(11) splitting a data set X into data columns Xi(n × 1), let X ═ X1,x2,…,xn](xi∈Rm) Dictionary D ═ D1,d2,...,dn](di∈Rm)diRepresenting dictionary atoms, and initializing the dictionary atoms into a DCT dictionary;
(12) and (3) decomposing singular values: d ═ M Λ VTWherein M represents a left singular matrix, Λ represents a singular value matrix, and V represents a right singular value matrix;
(13) calculating a low-dimensional dictionary: m is P ═ Mh TD, where h denotes the projection matrix dimension, Mh TRepresentation matrix MhTransposing;
(14) based on a low-dimensional dictionary P, carrying out sparse decomposition on a data set X by using an OMP algorithm to obtain a sparse coefficient A ═ a1,a2,…,an]；
(15) And (3) calculating an error:
and performing singular value decomposition with the error as 1: ej≈uλvTWherein u represents a left singular matrix array, λ represents a maximum singular value matrix, and v represents a right singular value matrix array;
(16) updating the dictionary: djAnd (e) updating a sparse coefficient: a isjλ v, where j denotes the dictionary D update index;
(17) j is j +1, judging whether j is larger than n, if so, executing (18), otherwise, repeating (15) to (17);
(18) determination of error
Whether convergence is achieved, if yes, executing the step (19), otherwise, repeating the steps (11) to (18);
(19) calculating projection matrix U-Mh T。
Further, the step (2) is realized by the following formula:
U'＝round(U*512)
where round (·) represents a rounding function, and U' represents a quantized projection matrix in the FPGA.
Further, the signal mixing projection process of step (5) is represented as:
Y＝U'X
wherein U' represents the quantized projection matrix in the FPGA.
Further, the formula for reconstructing the signal X in step (7) is as follows:
wherein, UTRepresenting the transpose of the projection matrix U.
Has the advantages that: compared with the prior art, the invention has the beneficial effects that: the method has the advantages that the algorithm complexity is low, the real-time performance is good, and the real-time performance is far superior to that of the traditional compressed sensing method; the invention provides the algorithm with low reconstruction complexity, which is beneficial to hardware realization; the parallel processing capability of the FPGA is utilized, so that the data throughput of the compression algorithm is high; the algorithm reconstruction precision of the invention is superior to the traditional compressed sensing algorithm.
Drawings
FIG. 1 is a schematic block diagram of a compressed sensing system;
FIG. 2 is a functional block diagram of dictionary learning;
FIG. 3 is a waveform diagram of modelsim simulated sampled signals;
FIG. 4 is a modelsim simulation reconstructed signal waveform diagram;
fig. 5 is a comparison graph of reconstruction results at different sampling rates.
Detailed Description
The invention will be further described with reference to the accompanying drawings in which:
the invention provides a reversible projection compression sensing method based on an FPGA (field programmable gate array). firstly, an approximately reversible projection matrix is trained by an upper computer by utilizing a driving dictionary learning algorithm. At the signal acquisition end, the FPGA projects the acquired signals through a projection matrix trained by an upper computer so as to realize the purpose of compressing mass data. As shown in fig. 1, the method specifically comprises the following steps:
As shown in fig. 2, the learning step of the driving dictionary learning is a learning step of offline on the MatLab simulation software of the upper computer, the training data is an AVIRIS hyperspectral data image IndianPine data set, the data set comprises 220 wave bands, each pixel is stored in a 16-bit integer, and the specific training steps are as follows:
(1) initialization: spreading each wave band of data set X by column, and dividing into data columns Xi(220 × 1), let X ═ X1,x2,…,xn](xi∈Rm) Dictionary D ═ D1,d2,...,dn](di∈Rm)diRepresenting dictionary atoms, initializing the dictionary atoms into a DCT dictionary, wherein n is 220, and m is 220;
(2) and (3) decomposing singular values: d ═ M Λ VTWherein M represents a left singular matrix, Λ represents a singular value matrix, and V represents a right singular value matrix;
(3) calculating a low-dimensional dictionary: m is P ═ Mh TD, where h represents the projection matrix dimension, and in the experiment, h is 11,22,44,66,88,110, corresponding to sampling rates of 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, M, respectivelyh TRepresentation matrix MhTransposing;
(4) based on a low-dimensional dictionary P, carrying out sparse decomposition on a data set X by using an OMP algorithm to obtain a sparse coefficient A ═ a1,a2,...,an]；
(5) And (3) calculating an error:
wherein j represents the dictionary D update index;
(6) singular value decomposition with rank 1 is performed on the error: ej≈uλvTWherein u represents a left singular matrix array, λ represents a maximum singular value matrix, and v represents a right singular value matrix array;
(7) updating the dictionary: djAnd (e) updating a sparse coefficient: a isj＝λv；
(8) j is j +1, whether j is larger than n is judged, if yes, 9 is executed, and if not, 5 to 8 are repeated;
(9) determination of error
Whether convergence is achieved, if yes, executing the step (19), otherwise, repeating the steps (1) to (9);
(10) calculating projection matrix U-Mh T。
Step 2: and the upper computer transmits the projection matrix U to the lower computer FPGA and stores the projection matrix U in the RAM.
The elements of the projection matrix are all in a decimal form, in order to save resources and clock overhead in the FPGA, the upper computer penetrates the projection matrix to the lower computer to be a quantized projection matrix, and the quantization formula is expressed as follows:
U'＝round(U*512)
where round (·) represents a rounding function, and U' represents a quantized projection matrix in the FPGA.
And step 3: and a signal conditioning circuit is adopted to condition the projection U matrix stored in the FPGA.
And 4, step 4: and mixing the conditioned U matrix and the X sample multiply-add device of the measured signal to obtain a mixing digital signal.
And 5: the mixing signal is digitally sampled to obtain a digital signal Y.
And carrying out sampling projection on the signal X by using a projection matrix U to obtain a low-dimensional sampling signal Y.
The digital signal X low-dimensional samples are represented as:
Y＝U'X
wherein U' represents a quantized projection matrix in the FPGA, and Y ═ Y1,y2,…,yn](yi∈Rh). In order to further save FPGA resources, the matrix multiplication is set to:
where h is the dimension of the projection matrix, xj,iElements, y, representing a set X of original signalsiAnd representing a certain column of the original signal X after the dimension reduction of the projection matrix and the original signal Y, wherein each sigma represents a multiplication adder for the number of the multiplication adders in the FPGA program design.
As shown in fig. 3 and 4, the waveform diagram of the low-dimensional signal acquired by the lower-level computer FPGA shows that the original data dimension h is 220, and the data dimension h is 11 after the dimensionality reduction sampling.
Step 6: and the FPGA sends the sampled low-dimensional signal Y to an upper computer.
And 7: the upper computer reconstructs the signal X after receiving the sampling signal Y, as shown in fig. 5, the reconstructed data is a display image (180 th waveband) on the upper computer, and the original hyperspectral images are respectively hyperspectral reconstructed images at sampling rates of 0.05, 0.1, 0.2, 0.3 and 0.4 from left to right.
Because the projection matrix is quantized at the FPGA sampling end in order to save FPGA resources and clocks, the reconstruction signal is restored by the upper computer, and the digital signal X reconstruction expression formula is as follows:
wherein, UTRepresenting the transpose of the projection matrix U.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations made according to the technical spirit of the present invention are within the scope of the present invention as claimed.
Claims (5)
1. A reversible projection compression sensing method based on FPGA is characterized by comprising the following steps:
(1) training an approximate reversible projection matrix U by the upper computer by using a task-driven dictionary learning algorithm;
(2) the upper computer transmits the projection matrix U to the lower computer FPGA and stores the projection matrix U in the RAM;
(3) a signal conditioning circuit is adopted to condition a projection U matrix stored in the FPGA;
(4) mixing the conditioned U matrix and the X sampling multiply-add device of the measured signal to obtain a mixing digital signal;
(5) digitally sampling the mixing signal to obtain a digital signal Y;
(6) the FPGA sends the sampled low-dimensional signal Y to an upper computer;
(7) and the upper computer reconstructs the signal X after receiving the sampling signal Y.
2. The FPGA-based reversible projection compression sensing method according to claim 1, wherein the step (1) comprises the steps of:
(11) splitting a data set X into data columns Xi(n × 1), let X ═ X1,x2,…,xn](xi∈Rm) Dictionary D ═ D1,d2,…,dn](di∈Rm)diRepresenting dictionary atoms, and initializing the dictionary atoms into a DCT dictionary;
(12) and (3) decomposing singular values: d ═ M Λ VTWherein M represents a left singular matrix, Λ represents a singular value matrix, and V represents a right singular value matrix;
(13) calculating a low-dimensional dictionary: m is P ═ Mh TD, where h denotes the projection matrix dimension, Mh TRepresentation matrix MhTransposing;
(14) based on a low-dimensional dictionary P, carrying out sparse decomposition on a data set X by using an OMP algorithm to obtain a sparse coefficient A ═ a1,a2,...,an]；
(15) And (3) calculating an error:
and performing singular value decomposition with the error as 1: ej≈uλvTWherein u represents a left singular matrix array, λ represents a maximum singular value matrix, and v represents a right singular value matrix array;
(16) updating the dictionary: djAnd (e) updating a sparse coefficient: a isjλ v, where j denotes the dictionary D update index;
(17) j is j +1, judging whether j is larger than n, if so, executing (18), otherwise, repeating (15) to (17);
(18) determination of error
Whether convergence is achieved, if yes, executing the step (19), otherwise, repeating the steps (11) to (18);
(19) calculating projection matrix U-Mh T。
3. The FPGA-based reversible projection compression sensing method according to claim 1, wherein the step (2) is realized by the following formula:
U'＝round(U*512)
where round (·) represents a rounding function, and U' represents a quantized projection matrix in the FPGA.
4. The FPGA-based reversible projection compression sensing method according to claim 1, wherein the signal mixing projection process of step (5) is expressed as:
Y＝U'X
wherein U' represents the quantized projection matrix in the FPGA.
5. The FPGA-based reversible projection compression sensing method according to claim 1, wherein the reconstruction formula for the signal X in the step (7) is as follows:
wherein, UTRepresenting the transpose of the projection matrix U.
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