high resolution isar imaging based on improved smoothed l0 norm recovery algorithm. - high resolution document camera

1.
Introduction to inverse synthetic aperture radar (ISAR)
Imaging technology has received a lot of attention in the past three decades. 1]-[3].
Inverse synthetic aperture radar imaging is widely used in military and civilian fields such as Target Recognition and aircraft traffic control.
In traditional ISARimaging, the observation interval must be long enough so that high cross-crossing can be performed
Distance resolution can be obtained by coherent integral.
In order to obtain high resolution, inverse synthetic aperture radar imaging always requires multiple measurements in the range of distance frequency and cross frequency
Time domain range.
Within a longer coherent processing interval, the target may move with maneuver.
If the rotation angle is too large, the radar cross section (RCS)
It may be time-varying, which increases the difficulty of consistency processing.
Therefore, it makes sense to achieve imaging in a short time.
In recent years, compressed sensing (CS)
It has become very popular in signal processing [4]-[9].
CS provides a new sampling paradigm that can accurately reconstruct sparse or compressed signals from limited measurements by solving optimization problems.
A technique is proposed to improve signal separation capability by using prior sparse characteristic information of signal.
Thinning can usually be understood [l. sub. p](0 [
Less than or equal to]p [
Less than or equal to]1)norm [10].
Sparse signal recognition is a key step in CS. Although [l. sub. 0]
Norm is better in describing the sparse nature of noise frequency, based on [sparse signal recovery algorithm]l. sub. 0]
Because they are sensitive to noise and need a combined search, the specification is difficult to solve.
Reconstruction algorithm based on [l. sub. 1]
Specification is the complexity of computing, which limits its practical application.
Simpler algorithms such as orthogonal matching tracing (OMP)[11][12]are proposed.
However, they are iterative greedy algorithms and do not give a good source estimate.
Mohimani et al. propose a smoothing function for approximation [l. sub. 0]
So the smallest problem [l. sub. 0]
Specification optimization can be transformed into an optimization problem for smooth functions.
A method called smoothing [l. sub. 0]norm (SL0)method[13].
The SL0 method is about two orders of magnitude faster [l. sub. 1]-
Magic method while providing better source estimation [l. sub. 1]-magicmethod.
For radar imaging, the target is usually considered to be composed of several strong scattering points, and the distribution of these strong scattering points is sparse in the imaging volume.
Sparse learning can improve the image quality of radar. 14]-[17]
Such as SAR/inverse synthetic aperture radar imaging [18][19]
MIMO radar imaging [20][21], and so on.
For inverse synthetic aperture radar imaging, this shows that combining inverse synthetic aperture radar and sparse learning can improve 2D image quality with limited measurement data [1 [22].
The combination of local sparse constraints and non-local full variation is discussed in [23].
This paper discusses the application of CS in inverse synthetic aperture radar imaging of sea clutter moving targets. 24]. A multi-
Applying the task Bayesian model [25].
Full polarization imaging based on CS in [discussion]26].
In order to improve the imaging quality of the inverse synthetic aperture radar, a new reconstruction algorithm based on onSL0 is proposed.
A new continuous sequence is proposed as a smoothing function to approximate [l. sub. 0]
A measure of spareness.
Then, a single loop step is used in the SL0 algorithm to replace the two loop layers, which increases the search density of the variable parameters.
The algorithm does not increase the amount of computation while ensuring the reconstruction accuracy.
Using the improved algorithm, the inverse synthetic aperture radar imaging is more intensive under the limited pulse volume.
The real data obtained using this method is competitive compared to several popular methods.
This article is organized as follows.
The necessary inverse synthetic aperture radar model and sparse learning imaging are introduced in section 2.
The third part introduces the reconstruction algorithm proposed in this paper in detail.
The fourth section introduces the inverse synthetic aperture radar imaging results of simulation and real data.
The fifth part is conclusion and discussion. 2.
In order to facilitate the analysis, the inverse synthetic aperture radar imaging model based on sparse learning can assume that the translation motion of the target has completely compensated the conventional method.
During the coherent processing interval (CPI)
The transmission of a linear FM modulation signal can be defined [
Mathematical expressions that cannot be reproduced in ASCII](i)where [? ? ]= t mod ([DELTA]t)
It's fast time, it's slow time ,[DELTA]
T is the pulse repeat duration ,[f. sub. c]
Is it carrier frequency ,[gamma]
Is the rate of chirp ,[T. sub. P]
Is the pulse width, CT (*)
Is a rectangular pulse function.
So the complex echo signal is [
Mathematical expressions that cannot be reproduced in ASCII](2)
Where is Guangyan c ,[T. sub. a]
It is CPI, A is the amplitude of the backward scattering, and it can be seen in the process that it is stationary.
After the distance is compressed, the received signal can be used [
Mathematical expressions that cannot be reproduced in ASCII](3)where [lambda]
Is the wavelength.
At different dwell times t, the received signal has different time delays in the fast time [? ? ].
By matching filtering and omitting the continuously introduced pulse compression, the received signal becomes [
Mathematical expressions that cannot be reproduced in ASCII](4)where f = 2x[omega]/ [lambda], [beta]= 2x[alpha]/ [lambda]
Doppler and Doppler frequency, respectively.
Assuming that the distance unit includes K scattering points, the signal in the distance unit corresponds [tau]= 2([R. sub. 0]+ y)
/C omitting the constant phase term can be written [
Mathematical expressions that cannot be reproduced in ASCII](5)where [A. sub. k]and [f. sub. k]
The reflection amplitude and Doppler frequency of the kth scattering center are respectively.
N is additive noise.
T = [in chronological order [[1: N]. sup. T]x [DELTA]t,[DELTA]t = 1/ [f. sub. r]
As a time interval ,[f. sub. k]
Is the frequency of petition. N = T / [DELTA]
T is the number of pulses. [DELTA][f. sub. d]
Is the resolution of the Doppler frequency, and the sparse Doppler sequence is [f. sub. d]= [1: Q]x [DELTA][f. sub. d], Q = [f. sub. r]/[DELTA][f. sub. d]
Q is the number of Doppler units corresponding [DELTA][f. sub. d].
Therefore, the base matrix can be constructed [PSI]={[[phi]. sub. 1], [[phi]. sub. 2], . . . , [[phi]. sub. q], . . . , [[phi]. sub. Q]},[[phi]. sub. q](t)= exp(-j2[phi][f. sub. d](q)t), 0 [
Less than or equal to]q [
Less than or equal to]Q.
Then rewrite the received discrete signal equation to s = [PSI][theta]+ n (6)
Non-zero component [theta]
In the sparse vector corresponding to the amplitude of the strong scattering point located in the grid.
For compressed sensing, the optimization algorithm has been applied to the real value. Equation (6)
Should be converted to realnumber case.
We divide the signal into real and imaginary parts,
Mathematical expressions that cannot be reproduced in ASCII](7)where R(*)and T(*)
Represent the real and imaginary parts of the complex vector, respectively.
So the equation (6)becomes y = A[eta]+ z (8)To solve [eta]
We can use the following sparse optimization strategy [? ? ]= arg mini [[parallel][eta][parallel]. sub. p]s x t[[parallel]y -A[eta][parallel]. sub. 2]< [epsilon], (9)where [epsilon]
Is a small positive number associated with z.
Pindicates [l. sub. p]norm.
In this paper, an improved SL0 algorithm is proposed and applied to inverse synthetic aperture radar imaging.
We describe the algorithm in 3 in detail.
Approximation of improved SL0 imaging algorithm [l. sub. 0]
Standard solution of [Smooth function]G. sub. [sigma]]([eta])= [[summation]. sub. i]exp(-[[eta]. sup. 2. sub. i]/2[[sigma]. sup. 2])
Used to replace [l. sub. 0]norm in [13].
When a parameter [sigma]
Function [close to zeroG. sub. [sigma]]([eta])approaches [l. sub. 0]norm. A two-
Aiming at the problem of sparse signal recovery, a layered method is proposed.
In order to improve the approximation performance of smoothing functions, we propose the following continuous sequences [f. sub. [sigma],[? ? ]]([eta])= e [Square root ()[[eta]. sup. 2]+[? ? ]/[sigma]])(10)where [sigma]
Is the variable parameter ,[? ? ]
It is a small positive element that guarantees the continuity of the function.
Obviously ,[
Mathematical expressions that cannot be reproduced in ASCII](11)Then denote [
Mathematical expressions that cannot be reproduced in ASCII](12)where [[parallel][eta][parallel]. sub. 0]
Number of non-zero elements representing vector [eta].
According to the definition [l. sub. 0]
Norm, we can get [
Mathematical expressions are not reproduced in ASCII].
A property of [G. sub. [sigma]]([eta])is that when [sigma][rightarrow][infinity], N -[G. sub. [sigma]]([eta])approaches [l. sub. 2]norm. However, for [F. sub. [sigma],[? ? ]]([eta]), when, [sigma][rightarrow][infinity], N -[F. sub. [sigma], [? ? ]]([eta])approaches[l. sub. 1]norm. When [sigma]
Close to zero, close [l. sub. 0]norm. For [l. sub. 1]
Norm can describe thinning, and we can search for analytic solutions with high probability at the beginning of the iteration.
Sparse signal recovery algorithm based on functionF. sub. [sigma],[? ? ]]([eta])
The minimum can be described [
Mathematical expressions that cannot be reproduced in ASCII](13)
In the proposed algorithm, we used a loop layer in the SL0 algorithm to replace the two loop layers. For smoothed [l. sub. 0]
Specification algorithm proposed in [13]
Using two layers of circulation to get a solution.
In general, if the number of internal iterations is large enough, the step size can be reduced.
In fact, there is no need to get a precise solution in an internal loop.
The purpose of the inner loop is to provide an initial value for the outer loop.
Since the double loop does not need to find the real point, we use a single layer instead of the double loop layer to increase the search density of the variable parameter. sigma]
In each iteration, the search for a point is close to the solution at the same time.
The proposed algorithm is called issl0.
We added a step to compare the old and new cost functions.
If the new function is greater than the old function, the loop stops, otherwise the next loop continues.
When parameter [sigma]
Close to zero ,[F. sub. [sigma]]approaches [l. sub. 0]norm.
If the new function is larger than the old one, then the solution at this time is the minimum value.
Then the loop stops, which saves the amount of computation.
Compared with the SL0 algorithm, the issl0 algorithm guarantees that the reconstruction accuracy and the calculation amount are not increased.
The gradient projection method is used to project the new iterative position to the feasible set.
The overall ISSL0 optimization algorithm proposed in this paper is summarized as follows: Initialization: In the above algorithm, some initial parameters need to be selected. [[? ? ]. sub. 0]= [A. sup. H][([AA. sup. H]). sup. -1]
Y is the lowest [l. sub. 2]norm solution. In [13], [[sigma]. sub. 1]is chosen as[[sigma]. sub. 1]> [4max. sub. t][
Absolute value][? ? ]. sub. 0](i)]. In this paper,[sigma]. sub. 1]
Should choose [[sigma]. sub. 1]>[16max. sub. i][
Absolute value][? ? ]. sub. 0](i)]. For [l. sub. 0]
Norm is not suitable for many small elements to represent the selection of vectors [[sigma]. sub. j]
It should not be too small. [[sigma]. sub. J]
It is possible to estimate by selecting several noise samples and selecting the maximum value [
Absolute value]A. sup. H][([AA. sup. H]). sup. -1]z]
Take the average. We choose [[sigma]. sub. J]as [[sigma]. sub. J]=E(max([[A. sup. H][([AA. sup. H]). sup. -1]z])).
Selection of step size factor [mu]
At the beginning of the search, we select a larger step, which decreases when the search point is close to the minimum.
So in our algorithm, we choose the step size [mu]=[beta]max[
Absolute value]eta]]
/10, follow j (loopnumber)
Adjustment coefficient 【beta]
Reduce, then adjust the step size. max[
Absolute value]eta]]
Term adjusts the step size according to the solution.
The size is M × N.
The computational load of the algorithm is calculated by steps (c)to (d)in step 2)
Each iteration. A [eta]
MN multiplication is required for each iteration.
Therefore, the computational complexity of this method is O (MN). 4.
Simulation results 1.
The signal model with noise is y = [eta]
Size of Z, (M xN)
Is 128x256, it is passed from (0,1). [eta]
Sparse signal with uniform non-zero coefficient [+ or -]
1 Random spike signal.
We consider the SNR = 15, 20, 25, 30 dB conditions. For [SL. sub. 0]
Methods, the number of outer and inner cycles is 20 and 10, respectively.
For the ISSL0 algorithm, the number of cycles is200. The parameter [? ? ]= 0. 01.
MSE is defined as 1/N [[parallel][eta]-[? ? ][parallel]. sup. 2], where [eta]
Is it true? ? ? ]
Is the estimated value.
100 experimental implementation (
The parameters are the same, but for different randomly generated source and coefficient matrices).
Calculate the mean of time, probability of refactoring, and MSE. Fig.
1 shows the average calculation time in the case of 15 dB signal-to-noise ratio.
For other Snr cases, the calculation time is similar to this case. From Fig.
1, we can see that the calculation cost of sl, SL0 and ISSL0 is less than that of Bayesian and 11-ls methods.
Figure 1 shows the reconstruction probability and MSE of different methods of different K. 2 and Fig. 3.
With the increase of k, the probability of reconstruction of different methods is gradually reduced.
With the increase of kincreases', the MSE of different methods gradually increases.
We can see that as the signal-to-noise ratio increases, 1-
The Ls and OMP ISSL0 methods improve the speed, SL0 and Bayesianmethods.
The performance of ISSL0 algorithm is very competitive compared with other algorithms, especially when the signal-to-noise ratio is high and the K is large. Simulation 2.
This section uses real data for inverse synthetic aperture radar imaging, which is real data for a group of yaks
The performance of the proposed inverse synthetic aperture radar imaging algorithm is verified by 42 planes.
The relevant parameters of the radar data are described as follows: the carrier frequency is 10 GHz, the signal bandwidth is 400 MHz, and the arange resolution is 0. 375 m.
The pulse repetition frequency is 50Hz. e.
, 256 pulses were used in this experiment.
Two different quantities of pulses (32-Snapshots and 64-snapshot)
Execution.
The inverse synthetic aperture radar image is reconstructed with 256 Doppler boxes (
This means that the size of the accounting standards expert group is 256 x)
As shown in the figure. 4 (a).
The experimental results were compared intuitively and quantitatively with images obtained by some sparse signal recovery methods (including OMP, Bayesian method and Laplaceprior and SL0 method. From Fig. 4 (b), (c), (d), (e),(f)and Fig. 5.
It is worth noting that an increase in the amount of pulses usually results in better image results.
In the case of 32 snapshots, there are a lot of messy points in the image using the OMP method.
Compared with the other four imaging methods, the proposed inverse synthetic aperture radar imaging framework has better visual quality and competitive power.
We can see that the ISSL0 method produces better visual quality, and the imaging of the inverse synthetic aperture radar is more intensive.
A significant advantage of the ISSL0 imaging method is that the strong scattering points of the target can be well extracted, while the false points are reduced.
The time for 32 snapshots is only 256 of the time taken by 1 snapshot out of the original 8.
Using the sparse signal recovery algorithm, the maneuvering target can be imaged in a short time. 5.
Conclusion This paper presents an improved sparse signal recovery algorithm based on SL0 algorithm, which is used to improve inverse synthetic aperture radar imaging with limited pulse number.
We propose a new continuous function to approximate as a sequence of smoothing functions [l. sub. 0]
In SL0 algorithm, the two loop layers are replaced by a single loop step, and the reconstruction accuracy is guaranteed without increasing the amount of calculation.
The simulation results show that the performance of the ISSL0 algorithm is better than that of the Bayesian method with a prior of LA, l1-
Ls and sl0 methods.
The experimental results show that the algorithm can improve the image quality effectively.
The work was supported by the National Natural Science Foundation of China.
61201367, 61271327 and 61471191, some of which are preferred by Jiangsu Higher education institutions (PADA).
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Feng Junjie received B. E. and M. S.
In 2006 and 2010, respectively, they received degrees from Baoji College of Arts and Sciences and Zhongyuan University of Technology.
He is currently working on a PhD. D.
Bachelor's degree from Nanjing University of Aeronautics and Astronautics, China.
His research interests include radar signal processing and wireless communication.
Zhang Gong took Ph. D.
Degree in electronic engineering, Nanjing University of Aeronautics and Astronautics (NUAA)
NANJING, China, 2002.
From 1990 to 1998, he was a technician at the no724 Research Institute of China Shipbuilding Corporation (CSIC), Nanjing.
He has been working at NUAA's Faculty of Electronics and Information Engineering since 1998 and is currently a professor at the faculty.
His research interests include radar signal processing and classification recognition. Dr.
Zhang is a member of the Electronic Information Committee of the China Aerospace Society (CEI-CSA)
Senior member of China Electronics Society (CIE). Junjie Feng (1,2)
And chapter (1,2)(1)
Key Laboratory of radar imaging and microwave photon, Ministry of Education, Nanjing, 210016, China [e-
Email: fzy028 @ 163com](2)
School of Electronic and Information Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016 [e-
Email: gong chapter _ nuaa @ 163com]
* Author of the newsletter: Feng Junjie received September 2, 2015;
Revised in October 21, 2015;
28. 2015;