CN104598735A - Time-varying homotopy algorithm based on L1 homotopy recovery algorithm - Google Patents
Time-varying homotopy algorithm based on L1 homotopy recovery algorithm Download PDFInfo
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Abstract
The invention relates to a time-varying homotopy algorithm based on an L1 homotopy recovery algorithm. The current compression perception research mainly aims at a static bounded signal, a blocking processing mode is usually adopted when a time-varying current signal is processed, but the problems of low efficiency, blocking effect, high delay and the like can be easily caused by adopting the mode. Aiming at the problems, the invention provides the time-varying homotopy algorithm for dynamic compression sensing by aiming at the time-varying current signal, compression sampling is performed by constructing an overlapping flow time window convection signal, and then an original signal is reconstructed in real time by using the L1 homotopy recovery algorithm. Experiments shows that the compression sampling can be quickly performed in real time by using the algorithm, the time-varying signal can be accurately reconstructed, the relative error of the reconstructed signal is controlled to be within a 10 to 2 range, and dynamic tracking compression sampling can be effectively performed on the time-varying signal.
Description
Technical Field
The invention belongs to the field of signal processing, and particularly relates to a compressed sensing reconstruction algorithm for a dynamic flow signal, which can be used for reconstructing medical time-varying signals such as electrocardiosignals.
Background
Electrocardiosignals are one of the bioelectric signals which are researched by people at the earliest and applied to clinical medicine, and along with the development of an electrocardio remote monitoring (ECG Telemonitor) system, the data volume of the electrocardiosignals acquired by the system is very large, which brings huge pressure to data transmission bandwidth and data storage. Therefore, a completely new theoretical framework for data acquisition and reconstruction is needed to solve the above problems of the conventional method.
In the modern signal processing field, the bandwidth frequency of the signal is higher and higher, and the traditional shannon-nyquist sampling theorem requires the sampling rate of the signal to reach at least twice of the highest frequency, which means that the traditional sampling theorem can not meet the practical requirement. Compressed Sensing (CS) is a completely new theory proposed by cans, Tao, Donoho, etc. in the field of signal processing in 06 years, and it utilizes the sparsity or compressibility of signals to convert the traditional shannon-nyquist sampling into random measurement sampling, thereby breaking through the limit of the shannon-nyquist sampling theorem, and this new theory has a wide application prospect in the field of signal processing.
Until now, compressed sensing has mostly been applied to static systems, often to process signals of a limited determined dimension. One assumes that the unknown signal is of finite length and uses a specific set of linear measurements to accomplish the reconstruction of the signal by solving an L1 norm minimization problem. In real life, signals such as sound, images and radio signals which are frequently contacted by people are flow signals which change in real time, and the most remarkable characteristic is that the signal dimension is not fixed, and complete signals cannot be acquired at one time, so that the traditional compressed sensing signal processing model is obviously not suitable for a real-time system. In order to solve the problem, N.Vaswani et al, Kalman Filtered Compressed sensing, 15th IEEE International Conference on Image Processing, 2008 ICIP 2008 IEEE 2008, 2008: 893-. The main idea is as follows: a long stream signal is divided into a plurality of relatively independent finite-dimension signals, and each block is reconstructed by compressing and sampling independently by using a traditional finite-dimension signal processing method. However, the defects of this block processing mode are also obvious, for example, the blocking effect caused by ignoring the correlation between blocks is obvious, the problem of high input and output delay caused by obtaining a long-stream signal block in advance is also brought, and the method cannot be applied to a system with high real-time tracking requirements, which greatly restricts the development of compressed sensing in a dynamic system.
Disclosure of Invention
In order to solve the problems of obvious blocking effect, high input and output delay and the like in the conventional blocking processing mode, the invention provides a time-varying homotopy algorithm based on an L1 homotopy recovery algorithm.
The invention adopts the following technical scheme:
and firstly, selecting a proper time window length to sample the flow signal. Selecting a Bernoulli matrix as a measurement matrix to perform compression sampling on signals under the same time window, and performing real-time recovery by using the existing L1 homotopy algorithm;
and secondly, clipping the obtained estimated value, and taking only the previous N values as a final estimated value. But the unused values are shifted up by N units and filled in later with N0 s. Using the signal value as an initial value of the next time;
and thirdly, sliding N units of the time window, correspondingly modifying the measurement matrix, and repeating the process to realize real-time tracking and sampling of the convection signal.
Drawings
FIG. 1 is a flow chart of the time-varying homotopy algorithm based on the L1 homotopy recovery algorithm of the present invention
FIG. 2 is a diagram illustrating the reconstruction of a 16384-long time-varying cardiac signal according to the present invention
FIG. 3 is a graph of the absolute error of reconstruction of a time-varying electrocardiosignal according to the invention
FIG. 4 is a graph of the relative error of the reconstruction of time varying cardiac signals of the present invention.
Detailed Description
The invention will be further described with reference to the accompanying drawings.
Referring to fig. 1, the time-varying homotopy algorithm based on the L1 homotopy recovery algorithm of the present invention includes the following steps:
step one, initialization: initializing the external iteration number I = 0;
step two, before the time-varying signalFast wavelet transform is carried out on the signal value X and the signal value X is projected to a perception matrix to obtain a signal value XDimension measurement vector Y:
wherein X isA is oneThe Bernoulli perception matrix of, wherein<<；
Thirdly, reconstructing the original signal by utilizing an L1 homotopy recovery algorithm to obtain a reconstructed signalAnd taking the first N signal values to store as a final recovery estimation value;
step four, updating the perception matrix, namely after the perception matrix of the iterationAfter walkingWith columns as front of new sensing matrixBefore goingColumns, and the next diagonal regenerates a new setThe remaining elements are filled with 0. Where R is the down-sampling rate of the system, i.e.，；
Step five, updating the initial value of the L1 homotopy algorithm, namely reconstructing the iteration of this time to obtain a signalMove up N units and the next N values are filled with zeros;
step six, updating the iteration times: i = I + 1. And returning to the step two until the stream signal is finished.
Further, the reconstructing the original signal X by using the L1 homotopy algorithm described in step three includes the following steps:
(3-1) initialization: the number of iterations i =0 and,；
(3-2) calculating homotopy path direction:
whereinIs composed ofSupport set of
(3-3) finding the maximum length of the optimal solution move without changing the homotopy path direction (i.e. the support set does not change), i.e. the maximum length of the optimal solution moveIncreased lengthComprises the following steps:
wherein,
(3-4) judgmentIf the value is greater than 1, if the value is greater than or equal to 1, jumping out of the loop to obtain a result:
if less than 1, updatingAnd：
(3-5) judgmentWhether or not it is true, whenWhen, it means that x is inThe non-zero factor of (A) is set to 0, i.e. the support set of (X) is removed(ii) a When in useIt means that it needs to be added in the support concentration of xThe corresponding symbol vector is also changed;
(3-6) the number of iterations i = i +1, go to step (3-2).
The advantages of the present invention are further illustrated by the following simulation.
The experiment takes the measurement matrix window size asUpdating the signal value in one iterationAnd (4) respectively. The down-sampling rate of the system isI.e. on average, 128 hearts can be accurately reconstructed using 32 measurementsThe value of the electrical signal.
We set the starting values of the recovery algorithm as follows: when the ith iteration is finished, obtaining an estimated value of a section of signal, and setting the estimated value asAt i +1 iterations, the window of the signal is shifted down by R values and willAs the initial value of the homotopy algorithm of the next iteration L1 is very close to the final solution of the (i + 1) th iteration, the update of the optimal solution can be completed in a very short time.
All the recovered signal values are directly given in figure 2, and as can be seen from figure 4, the time-varying homotopy algorithm provided in the paper is utilized to compress and sample in real time and reconstruct a long section of electrocardiosignals, and the relative error of the recovered signals obtained by real-time tracking is always controlled at 10-2Within the range, the feasibility of the time-varying homotopy algorithm is proved from simulation experiments.
In conclusion, the time-varying electrocardiosignal compression sampling method can well compress, sample and reconstruct the time-varying electrocardiosignal.
Claims (4)
1. The time-varying homotopy algorithm based on the L1 homotopy recovery algorithm is characterized by comprising the following steps:
the method comprises the following steps: obtaining a reconstructed signal by using an L1 homotopy algorithmThen, only the first N signal values are taken and stored as the final signal recovery value;
step two: last timeIteratively reconstructed signalMoving up by N units, and filling the following N values with zeros as initial values of an L1 homotopy recovery algorithm used in the next iteration;
step three: considering signal correlation under a flow window of two iterations, the lower triangle content of a perception matrix in the last iteration is kept to be transferred to an upper triangle, and only one perception matrix is updatedThe submatrix of (a) is placed at the lower triangular position of the iteration sensing matrix.
2. With respect to the estimates of each final extraction in the flow overlap window as claimed in claim 1, we take the following:
assuming a signal under a flow window of a certain lengthUpdate per unit timeA signal value, a measured valueIs updated in a unit timeThe number of the measured values is,represents the down-sampling rate of the system; that we recover after each iterationFirst N out of the signal values ofThe value is used as the final recovery value, and the rest are not reserved and only used as the initial value of the recovery algorithm of the next iteration.
3. The determination of the initial value of the recovery algorithm when iterating down as claimed in claim 1, we take the following: when the ith iteration is finished, obtaining an estimated value of a section of signal, and setting the estimated value asAt i +1 iterations, the window of the signal is shifted down by R values and willThe zero padding is used as the initial value of the L1 homotopy algorithm of the next iteration, so that under the condition that a future signal value is unknown, no extra energy is added to the signal value as an estimation value, and the initial value is close to the final solution of the (i + 1) th iteration, so that the convergence speed of the recovery algorithm can be effectively improved.
4. The update problem of the perceptual matrix as claimed in claim 1, wherein we fully consider the correlation between two adjacent iterations, and apply the correlation to the perceptual matrix of the current iterationAfter walkingWith columns as front of new sensing matrixBefore goingColumns, and the next diagonal regenerates a new setThe remaining elements are filled with 0, where R is the down-sampling rate of the system, i.e.，。
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112534842A (en) * | 2018-08-07 | 2021-03-19 | 昕诺飞控股有限公司 | Compressive sensing system and method using edge nodes of a distributed computing network |
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| CN112534842A (en) * | 2018-08-07 | 2021-03-19 | 昕诺飞控股有限公司 | Compressive sensing system and method using edge nodes of a distributed computing network |
| CN112534842B (en) * | 2018-08-07 | 2024-05-28 | 昕诺飞控股有限公司 | Compressive sensing system and method using edge nodes of a distributed computing network |
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