CN117111000A - SAR comb spectrum interference suppression method based on dual-channel attention residual network - Google Patents

SAR comb spectrum interference suppression method based on dual-channel attention residual network Download PDF

Info

Publication number
CN117111000A
CN117111000A CN202310298046.5A CN202310298046A CN117111000A CN 117111000 A CN117111000 A CN 117111000A CN 202310298046 A CN202310298046 A CN 202310298046A CN 117111000 A CN117111000 A CN 117111000A
Authority
CN
China
Prior art keywords
signal
interference
network
output
channel attention
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.)
Pending
Application number
CN202310298046.5A
Other languages
Chinese (zh)
Inventor
周峰
樊伟伟
汪思瑶
田甜
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.)
Xidian University
Original Assignee
Xidian 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 Xidian University filed Critical Xidian University
Priority to CN202310298046.5A priority Critical patent/CN117111000A/en
Publication of CN117111000A publication Critical patent/CN117111000A/en
Pending legal-status Critical Current

Links

Classifications

    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S7/00Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
    • G01S7/02Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
    • G01S7/36Means for anti-jamming, e.g. ECCM, i.e. electronic counter-counter measures

Landscapes

  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Noise Elimination (AREA)

Abstract

The invention discloses an SAR comb spectrum interference suppression method based on a dual-channel attention residual network, which comprises the following steps: acquiring a time domain echo signal with comb spectrum interference; transforming the time domain echo signals to a frequency domain to obtain frequency domain echo signals with interference; extracting real parts and imaginary parts of the echo signals with the interference frequency domains to obtain real part signals with the interference and imaginary part signals with the interference; inputting the signal with the interference real part and the signal with the interference imaginary part into a pre-trained dual-channel attention residual error network, performing comb spectrum interference suppression, and outputting a frequency domain echo signal; the pre-trained two-channel attention residual network comprises two suppression networks with the same structure, and each suppression network comprises: a channel attention residual block and a global attention block; one of the suppression networks is used for reconstructing a real part signal according to an input real part signal with interference, and the other suppression network is used for reconstructing an imaginary part signal according to the input imaginary part signal with interference.

Description

SAR comb spectrum interference suppression method based on dual-channel attention residual network
Technical Field
The invention belongs to the technical field of interference elimination, and particularly relates to an SAR comb spectrum interference suppression method based on a dual-channel attention residual network.
Background
The synthetic aperture radar (Synthetic Aperture Radar, SAR) has the advantages of all-day, all-weather, long-range and high-resolution imaging, and plays an important role in the civil and military fields such as ground detection, resource exploration, battlefield reconnaissance and the like. However, the existence of the interference can reduce the signal-to-interference-and-noise ratio of the SAR echo, and influence the subsequent imaging quality and SAR image interpretation accuracy. The SAR interference suppression problem under the complex electromagnetic environment is researched, and the SAR interference suppression method has important research significance for improving the anti-interference capability and the information acquisition capability of an SAR system.
Conventional SAR interference suppression methods can be divided into parametric estimation and non-parametric estimation interference suppression methods. The parameter estimation method needs to accurately model and estimate the parameters of the interference, and then reconstruct the interference according to the interference parameter estimation result, so that the interference is accurately inhibited, and although the method can theoretically obtain better interference inhibition performance, the requirement on interference modeling accuracy leads to lower efficiency and poorer universality of the method. The non-parameter estimation method generally converts SAR echo signals into a frequency domain, a time-frequency domain or a wavelet domain and other characterization domains, and suppresses interference by analyzing characteristic differences of target echo signals and interference and utilizing notch, adaptive filtering and subspace decomposition, and the method is simple and efficient, but is easy to cause target echo signal loss in the face of complex interference, reduces SAR imaging quality and is only suitable for interference with sparse characteristics. For example, when the number of interference points of comb spectrum interference is large, sparsity is not provided, and a non-parameterized method is utilized to easily cause loss of a target echo signal, so that SAR images are defocused. The conventional SAR interference suppression methods are used for performing interference suppression before imaging processing, and a learner can realize interference suppression in an image domain, so that sparse interference can be effectively suppressed, but the methods still can cause loss of target image information for complicated comb spectrum interference. Meanwhile, the image domain anti-interference method has the precondition that motion compensation is not needed in the imaging process, otherwise, the imaging parameter estimation precision can be seriously influenced under the condition that interference exists, and the imaging result is seriously defocused.
With the development of deep learning, the method is successfully applied to image defogging, voice noise reduction and the like, a plurality of students combine the deep learning with radar anti-interference, a time-frequency domain SAR intelligent interference suppression method based on the deep learning is provided, and the method can project interference and target echo to a high-dimensional abstract feature space through a deep nonlinear network to realize decoupling of the interference and the target echo. The method not only can effectively recover the amplitude of the target echo signal, but also can accurately reserve the phase information of the target echo, and ensure the reconstruction accuracy of the target echo. However, for comb spectrum interference which is densely distributed in a time-frequency domain and completely floods a target signal, coupling between interference and a target echo in a time-frequency spectrogram is serious, and accurate reconstruction of the target is difficult to realize.
That is, the prior art is only suitable for interference with sparse characteristics, and is difficult to realize accurate decoupling of interference and target echo in the face of comb spectrum interference with serious coupling with the target echo, which easily causes loss of target signals and reduces SAR imaging quality and interpretation accuracy.
Disclosure of Invention
In order to solve the problems in the related art, the invention provides a SAR comb spectrum interference suppression method based on a dual-channel attention residual network. The technical problems to be solved by the invention are realized by the following technical scheme:
The invention provides an SAR comb spectrum interference suppression method based on a dual-channel attention residual network, which comprises the following steps:
acquiring a time domain echo signal with comb spectrum interference;
transforming the time domain echo signals to a frequency domain to obtain frequency domain echo signals with interference;
extracting real parts and imaginary parts of the echo signals with the interference frequency domains to obtain real part signals with the interference and imaginary part signals with the interference;
inputting the real part signal with interference and the imaginary part signal with interference into a pre-trained dual-channel attention residual error network, performing comb spectrum interference suppression, and outputting a frequency domain echo signal; the pre-trained dual channel attention residual network comprises two suppression networks with identical structures, and each suppression network comprises: a channel attention residual block and a global attention block; wherein one suppression network is used for reconstructing a real signal from the input real signal with interference, and the other suppression network is used for reconstructing an imaginary signal from the input imaginary signal with interference.
The invention has the following beneficial technical effects:
the SAR comb spectrum interference suppression network based on the dual-channel attention residual network is utilized, so that the problem of serious target signal loss during comb spectrum interference suppression in the prior art is solved; in addition, the method and the system project the seriously coupled interference and target echo signals to the high-dimensional separable feature space through the network, and introduce channel attention and global attention to improve feature extraction and characterization precision, so that intelligent decoupling of the interference and the target echo is realized, loss of the target echo signals is greatly reduced, and SAR imaging quality and interpretation precision are improved.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 (a) is a schematic diagram illustrating a comparison of exemplary interference-free and interference-free signals in the time domain according to an embodiment of the present invention;
fig. 1 (b) is a schematic diagram illustrating comparison of exemplary non-interfering and interfering signals in the time-frequency domain according to an embodiment of the present invention;
FIG. 1 (c) is a schematic diagram illustrating a comparison of exemplary non-interfering and interfering signals in the frequency domain according to an embodiment of the present invention;
fig. 2 is a flowchart of a method for suppressing SAR comb spectrum interference based on a dual-channel attention residual network according to an embodiment of the present invention;
FIG. 3 is a schematic block diagram of an exemplary attention per channel residual block provided by an embodiment of the present invention;
FIG. 4 is a schematic diagram of an exemplary per-channel attention block provided by an embodiment of the present invention;
fig. 5 is a schematic structural diagram of an exemplary intra-frequency self-attention network according to an embodiment of the present invention;
FIG. 6 is a schematic diagram of a feature processing of an exemplary in-frequency self-attention network provided by an embodiment of the present invention;
FIG. 7 is a schematic diagram of processing an input signal by an exemplary dual channel attention residual network provided by an embodiment of the present invention;
FIG. 8 (a) is an exemplary simulated data imaging without interference suppression provided by an embodiment of the present invention;
FIG. 8 (b) is a diagram illustrating simulated data imaging results using a frequency domain notch method according to an embodiment of the present invention;
FIG. 8 (c) is an exemplary simulation data imaging result using a U-Net method provided by an embodiment of the present invention;
fig. 8 (d) is an exemplary simulation data imaging result obtained by using the dparet method according to the embodiment of the present invention;
FIG. 9 (a) is an exemplary raw recorded data provided by an embodiment of the present invention;
FIG. 9 (b) is an imaging result obtained by frequency domain notching of exemplary raw data provided by an embodiment of the present invention;
FIG. 9 (c) is an image of exemplary raw data over a U-Net network provided by an embodiment of the present invention;
fig. 9 (d) shows imaging results of exemplary raw data provided by the embodiment of the present invention through dparet proposed by the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but embodiments of the present invention are not limited thereto.
In the description of the present invention, the terms "first," "second," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include one or more such feature. In the description of the present invention, the meaning of "a plurality" is two or more, unless explicitly defined otherwise.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Further, one skilled in the art can engage and combine the different embodiments or examples described in this specification.
Although the invention is described herein in connection with various embodiments, other variations to the disclosed embodiments can be understood and effected by those skilled in the art in practicing the claimed invention, from a study of the drawings, the disclosure, and the appended claims. In the claims, the word "comprising" does not exclude other elements or steps, and the "a" or "an" does not exclude a plurality. A single processor or other unit may fulfill the functions of several items recited in the claims. The mere fact that certain measures are recited in mutually different dependent claims does not indicate that a combination of these measures cannot be used to advantage.
Comb spectrum modulated interference (Comb Spectrum Modulation Jamming, CSMJ) is the superposition of a series of narrowband interfering signals within a particular bandwidth. The time domain expression of comb spectrum modulation interference is:wherein A is k (t),f k And->Representing the amplitude, carrier frequency and phase of the kth narrowband interfering signal, respectively.
Fig. 1 (a), 1 (b), and 1 (c) are results of comparing features of measured comb spectrum interference in time domain, time-frequency domain, and frequency domain, respectively. Fig. 1 (a) is a comparison of a non-interfering signal and an interfering signal in a time domain, fig. 1 (b) is a comparison of a non-interfering signal and an interfering signal in a time-frequency domain, and fig. 1 (c) is a comparison of a non-interfering signal and an interfering signal in a frequency domain. It can be seen that the interference and the target echo signals are seriously coupled in the time domain and the time-frequency domain, and it is difficult to separate the interference and the target echo signals by using a conventional method. The interference spectrum is distributed as equally spaced instantaneous peak pulses on the frequency domain, and the maximum amplitude is far higher than the target echo, so that the obvious difference between the interference and the target signal can enable the interference spectrum and the target signal to have separability, and a foundation can be provided for further interference suppression.
Fig. 2 is a flowchart of a SAR comb spectrum interference suppression method based on a dual-channel attention residual network according to an embodiment of the present invention, as shown in fig. 2, the method includes the following steps:
S101, acquiring a time domain echo signal with comb spectrum interference.
Here, the acquired time domain echo signal with comb spectrum interference may be one or more.
S102, converting the time domain echo signals into a frequency domain to obtain the frequency domain echo signals with interference.
Here, the fourier transform may be employed for the time domain to frequency domain transform.
S103, extracting real parts and imaginary parts of the echo signals with the interference frequency domain to obtain real parts signals with the interference and imaginary parts.
S104, inputting the signal with the interference real part and the signal with the interference imaginary part into a pre-trained double-channel attention residual error network, inhibiting comb spectrum interference, and outputting a frequency domain echo signal; the pre-trained two-channel attention residual network comprises two suppression networks with the same structure, and each suppression network comprises: a channel attention residual block and a global attention block; one of the suppression networks is used for reconstructing a real part signal according to an input real part signal with interference, and the other suppression network is used for reconstructing an imaginary part signal according to the input imaginary part signal with interference.
In some embodiments, each suppression network may include: five channel attention residual blocks and one global attention block with the same structure; the five channel attention residual blocks are sequentially connected in series, the number of channels of the first channel attention residual block is the same as that of the fifth channel attention residual block, the number of channels of the second channel attention residual block is the same as that of the fourth channel attention residual block, and the number of channels of the third channel attention residual block is the largest; the global attention block includes: two self-attention networks with the same structure are connected in series in sequence.
Specifically, the global attention block may include: a self-attention network within the frequency band and a self-attention network between the frequency bands; the self-focusing network in the frequency band and the self-focusing network between the frequency bands are connected in series in sequence and have the same structure.
Illustratively, the number of channels of the five channel attention residual blocks included in sequence by each suppression network is 32, 64, 128, 64, 32 in sequence; therefore, the thinning separation of the echo signal and the interference signal is facilitated by increasing and then reducing the number of channels.
In some embodiments, each channel attention residual block comprises in order: two first convolution blocks, a second convolution block, a channel attention block, a feature combination block.
Illustratively, FIG. 3 is a schematic structural diagram of an attention residual block of each channel, and as shown in FIG. 3, the first convolution block is a convolution block composed of a one-dimensional convolution layer, a batch normalization layer and a LeakyReLU activation function; the second convolution block is a convolution block composed of a one-dimensional convolution layer and a batch of normalized layers. The feature combining block is composed of an element-by-element addition operation layer and a ReLU activation function, and the input of the feature combining block is the output of the channel attention block and the input of the first convolution block. The number of convolution kernels of the convolution layers of the first convolution block and the second convolution block is consistent with the number of output channels of the channel attention residual block, the convolution kernels are 3, the step size is 1, and the filling is 1. Assume that the input of the channel attention residual block is F.epsilon.R B×C×L Then output is F 1 ∈R B×C×L Where B is the number of input features (i.e., the number of interfering real-part signals or interfering imaginary-part signals input to the dual-channel attention residual network), C and L represent the number and length of channels for each input feature (i.e., each sequence), respectively, then the channel attention residual block can be expressed as: f (F) 1 =CA(W c (F) +f); wherein W is c Representing the weights of the convolutions blocks and CA representing the weights of the channel attention blocks.
Illustratively, fig. 4 is a schematic structural diagram of a channel attention block, and as shown in fig. 4, the channel attention block includes an average pooling layer, a one-dimensional convolution layer, a Sigmoid activation function, and a dot multiplication operation layer; the input of the dot multiplication operation layer is the input of the feature and average pooling layer processed by the Sigmoid activation function. The channel attention block can adaptively generate high-resolution channel characteristics on the premise that the introduced additional learning parameters and the added calculation cost are almost negligible, so that the performance of the network is further improved. Specifically, the self-adaptive average pooling aggregation feature is firstly utilized, then the dependency relationship among k channels is extracted by utilizing a one-dimensional convolution layer with the convolution kernel size of k, and the effect of self-adaptively selecting important channel features is realized. Assume that the input channel attention block is characterized by F (in) ∈R B×C×L Output is F (out) ∈R B×C×L The output of the channel attention block is:wherein sigma (·) is a Sigmoid activation function, GAP (·) represents adaptive average pooling, W C ∈R C×k Is a one-dimensional convolution layer weight. k is an important parameter for adaptive adjustment and varies according to the number of channels C of the channel attention residual block, wherein a large size k value facilitates capturing long distance dependencies and a small size k value facilitates capturing short distance dependencies. The k value is regulated by the channel number C, and the calculation expression can be as follows: />C represents the number of channels, b and γ being preset values (e.g., b and γ values may be set to 1 and 2, respectively). The convolution of the convolution layers in the channel attention block may have a step size of 1 and the padding may be (k-1)/2 rounding.
In some embodiments, each suppression network further includes a feature slice layer, and the feature slice layer is concatenated after the 5 channel attention residual block and concatenated before the global attention block. The feature slicing layer is used for splicing the sub-outputs obtained after segmentation to a first preset dimension after segmenting (slicing) the input along the length dimension L of the input to obtainUpdated inputs. Assume that the input is F.epsilon.R B×C×L Segmentation is carried out along the dimension L and then the segments are spliced to new dimensions N and P, namely the expression is: f epsilon R B×C×L →F′∈R B×C×P×N The method comprises the steps of carrying out a first treatment on the surface of the Wherein N is the number of frequency bands, and P is the length of the frequency bands. Here, considering that the subsequent self-attention computation complexity is proportional to the square of the calculated sequence length, N can be set approximately toIn this way, the computational complexity can be reduced from O (L 2 ) Reduce toThe cost of attention calculation is reduced to the greatest extent.
In some embodiments, each self-attention network (intra-frequency self-attention network or inter-frequency self-attention network) comprises in order: a dimension recombination layer, a position coding layer, a global attention layer and an addition operation layer.
Fig. 5 and 6 are schematic structural diagrams and schematic feature processing diagrams of an intra-frequency self-attention network, respectively, by way of example. As shown in fig. 5 and 6, when the input to the in-frequency self-attention network is F' e R B×C×P×N When in use, F' E R is first of all restored by dimension recombination layer B ×C×P×N Combining the first dimension B and the fourth dimension N to obtain a recombined input F'. Epsilon.R (B×N)×C×P . The reorganization input is B frequency band sequences (B is an integer greater than or equal to 1), and each frequency band sequence comprises a plurality of frequency points. And carrying out position coding on the position information of each frequency point in each frequency band sequence through a position coding layer to obtain a position coding vector of each frequency point. And injecting the position information of each frequency point in the frequency band sequence to each frequency point through position coding, so that the input of the attention model is enhanced. For a segment of a sequence of frequency bands of length P, its position-coding vector length is C. Let t denote the position of the bin in the sequence, The value of the coding vector at i representing the frequency point t, the coding rule is defined as follows: />Wherein->q is used to represent odd, even, i is 0,1,2. After the position coding vector of the recombined input is obtained, the addition operation layer performs addition operation on the position coding vector and the recombined input to obtain superposition characteristics so as to continue to perform subsequent self-attention calculation by adopting the global attention layer.
The global attention layer includes two layers of normalization, two random inactivation, self-attention calculation and feed forward network layers. Firstly, the superimposed features normalize the same batch of feature data through a first layer normalization layer to obtain normalized features, and then the normalized features are input into a self-attention calculation layer to calculate a plurality of independent attention masks (the number of attention heads can be 8). Specifically, the query vector, key vector, and value vector for each attention header are generated from the input linear map, and can be expressed as:wherein d is k The dimensions representing the query vector, key vector, and value vector, h is the number of attention headers, j=1, 2. Each attention head performs matrix multiplication operation on the query vector and the key vector to obtain an attention mask, and then performs dot multiplication on the attention mask and the value vector to obtain a characteristic output of mixed attention, wherein a calculation formula of the characteristic output can be expressed as follows: / >In this way, a multi-headed attention feature output is obtained. And then, inputting the multi-head attention characteristic output to a first random inactivation layer, carrying out addition operation on the output of the first random inactivation layer and the superposition characteristic, inputting the characteristic obtained by the addition operation to a second layer normalization layer, and inputting the output of the second layer normalization layer to a feedforward network layer. The structure of the feedforward network layer is as follows: a linear link layer, a ReLU activation layer, a random deactivation layer, and a linear link layer, wherein a first linear link layer is to input featuresThe second linear connection layer restores the dimension to the input dimension by a factor of 4. After the output of the feedforward network layer is obtained, the output of the feedforward network layer is input to a second random inactivation layer, the output of the second random inactivation layer and the input of the feedforward network layer are subjected to element-by-element addition operation, and the characteristics obtained by the element-by-element addition operation and the recombined input F'. Epsilon.R (B ×N)×C×P Performing addition operation to restore dimension into R B×C×P×N The final output result F' "of the self-attention network is obtained.
Here, unlike the intra-frequency self-attention network, the inter-frequency self-attention network performs dimension reorganization by combining the first dimension B and the third dimension P, e.g., obtaining the sequence input K e R of the calculated self-attention (B×P)×C×N The other processing principles are the same, namely, position information is added to the frequency band by using the position code e firstly, then the same batch of samples are normalized by using layer normalization, then the multi-head attention mask is calculated to multiply the input feature map to obtain attention output, and finally, the final output result is obtained by the output of the feedforward network layer and the input jump link before the position code. By way of example, both in-band self-attention and inter-band self-attention computation processes can be expressed as:
K'=K+e;
K”=MultiHeadAttention(LayerNorm(K'))+K';
K”'=FeedForward(LayerNorm(K”)+K”);
Y=K+K”';
where Y is the output of the self-attention network and e is the position code.
In some embodiments, the step S104 may be implemented by:
s1041, inputting the signal with the real part of interference into a first suppression network, and inputting the signal with the imaginary part of interference into a second suppression network.
S1042, each suppression network processes the input signals through five channel attention residual blocks which are connected in series in sequence and have the same structure, so as to obtain a first output.
Specifically, after an input signal enters a 1 st channel attention residual block, the input signal sequentially passes through convolution of two first convolution blocks, batch normalization and first activation processing, and then passes through convolution of a second convolution block and batch normalization processing to obtain output of the second convolution block; the output of the second convolution block is subjected to the average pooling, rolling and second activation treatment of the channel attention block to obtain an intermediate output, and the intermediate output and the output of the second convolution block are subjected to the dot multiplication operation of the channel attention block to obtain the output of the channel attention block; the input of the 1 st channel attention residual block and the output of the channel attention residual block are subjected to addition of the feature combination block and third activation processing to obtain the output of the 1 st channel attention residual block; after the output of the m-th channel attention residual block is processed by the m+1th channel attention residual block, obtaining the output of the m+1th channel attention residual block until obtaining the output of the 5 th channel attention residual block, and taking the output of the 5 th channel attention residual block as the first output; m is an integer from 1 to 4.
S1043, after the first output is segmented along the length dimension, splicing the sub-outputs obtained after segmentation to a first preset dimension to obtain an updated first output.
For example, when the first output is F.epsilon.R B×C×L When the updated first output is F' ∈R B×C×P×N Wherein the first output comprises B frequency band sequences, B being the number of interfering real part signals or interfering imaginary part signals with inputs to the pre-trained two-channel attention residual network; c is the number of channels of each frequency band sequence, L is the length dimension of each frequency band sequence, N is the number of frequency bands, and P is the frequency band length; n and P are the first predetermined dimensions. I.e. each sequence of frequency bands has three dimensions C, P, N.
S1044, inputting the updated first output into a global attention block to obtain a second output, and taking the second output as a signal for inhibiting network output; wherein the first suppression network outputs a real predicted signal and the second suppression network outputs an imaginary predicted signal.
Here, the global attention block includes: the self-attention network between the self-attention network and the frequency band with the same structure is obtained after the updated first output is input into the global attention block and the self-attention network in the frequency band is processed; and after the output of the self-attention network in the frequency band is processed by the self-attention network among the frequency bands, obtaining a second output.
Specifically, after the updated first output is input into the self-attention network in the frequency band, combining second preset dimensions (for example, a first dimension B and a fourth dimension N) of the updated first output through a dimension recombination layer to obtain recombination features; the recombination characteristic is a frequency band sequence comprising a plurality of frequency points; the position coding layer performs position coding on each frequency point according to the position information of each frequency point in the frequency band sequence to obtain coding characteristics; the addition operation layer performs addition operation on the recombination feature and the coding feature to obtain a superposition feature; the superimposed features are processed by the global attention layer to obtain linear output; and the addition operation layer adds the recombination characteristic and the linear output to obtain the output of the self-attention network in the frequency band. The inter-frequency self-attention network adopts the same processing principle, and after the output of the inter-frequency self-attention network is processed, the output of the inter-frequency self-attention network is obtained, namely the output of the suppression network is obtained, and when the inter-frequency self-attention network performs dimension recombination, the first dimension B and the third dimension P are combined, unlike the inter-frequency self-attention network.
S1045, performing feature fusion on the real part predicted signal and the imaginary part predicted signal to obtain a frequency domain echo signal.
Illustratively, fig. 7 is a schematic diagram of the processing of an input signal by a dual channel attention residual network. As shown in fig. 7, after taking the real part and the imaginary part of the echo signal with interference in the frequency domain, the real part signal with interference and the imaginary part signal with interference are respectively and simultaneously input into two channels (two suppression networks) of the network, for example, taking the real part signal with interference as an illustration, the real part signal with interference sequentially passes through the processing of the attention residual blocks of 5 channels, then passes through the processing of the characteristic slice layer, then enters into the self-attention network in the frequency band for processing, then, the output of the self-attention network in the frequency band enters into the self-attention network between the frequency bands for processing, and then, the predicted real part signal is output. Similarly, for another input channel with an interfering imaginary signal, a predicted imaginary signal is output. Finally, the predicted real part signal and the predicted imaginary part signal are subjected to feature fusion to obtain a predicted frequency domain echo signal, so that comb spectrum interference is eliminated.
In some embodiments, prior to S104, the method comprises:
s001, acquiring a plurality of training samples; each training sample is an echo sample signal with an interference frequency domain; the frequency domain echo sample signal with interference corresponds to a frequency domain echo sample signal without interference.
Specifically, comb spectrum interference time domain signals can be generated in a simulation mode, interference frequency spectrums are obtained through Fourier transformation after the comb spectrum interference time domain signals are overlapped with actual measurement target echo signals, and normalization processing is carried out, so that the comb spectrum interference time domain signals are used as a reference data set for interference suppression.
S002, selecting a plurality of training samples each time, and determining the imaginary part and the real part of each selected training sample to obtain the imaginary part sample signal and the real part sample signal of each training sample.
S003, inputting the imaginary part sample signal and the real part sample signal of each training sample selected at this time into a dual-channel attention residual error network of the last training to obtain a predicted real part signal and a predicted imaginary part signal corresponding to each training sample selected at this time.
S004, determining the loss value according to the predicted real part signal and the predicted imaginary part signal corresponding to each training sample selected at the time and the real part signal and the imaginary part signal of the frequency domain echo sample signal without interference corresponding to a plurality of training samples selected at the time.
Specifically, when B training samples are selected this time, for each training sample, calculating a first loss between a predicted real signal corresponding to the training sample and a real signal of a frequency domain echo sample signal without interference corresponding to the training sample, and calculating a second loss between a predicted imaginary signal corresponding to the training sample and an imaginary signal of a frequency domain echo sample signal without interference corresponding to the training sample; taking the sum of the first loss and the second loss as the loss corresponding to the training sample to obtain B losses corresponding to B training samples; the sum of the B losses is taken as the current loss value.
And S005, according to the loss value of the current time, adjusting network parameters of the dual-channel attention residual error network of the last training to obtain the dual-channel attention residual error network of the current training, and repeating the steps until reaching the preset condition, stopping training, and obtaining the pre-trained dual-channel attention residual error network.
The calculation formula of the loss corresponding to each training sample is as follows:
L z =(f(x z1 )-y z1 ) 2 +(f(x z2 )-y z2 ) 2
wherein z is 1,2, once again, B, f (x z1 ) For the predicted real part signal corresponding to the z-th training sample, y z1 For the real part signal of the frequency domain echo sample signal without interference corresponding to the z-th training sample, f (x z2 ) For the predicted imaginary signal corresponding to the z-th training sample, y z2 The imaginary signal of the frequency domain echo sample signal without interference corresponding to the z-th training sample.
The method and the device firstly carry out the extraction operation of the real part and the imaginary part on the one-dimensional frequency domain signal of the input network, and respectively recover the real part and the imaginary part by utilizing the two suppression networks with the identical structures, so that the characteristics of the target echo signal and the interference signal can be effectively separated, the suppression effect is achieved, and the phase information of the target echo can be kept without losing in the suppression process; the feature processing is carried out by adopting a channel attention residual block, so that semantic information can be enriched by utilizing information interaction among channels, and the feature extraction capability of the model is enhanced; and then, the global information can be further utilized to correct the input feature map by utilizing the continuous processing of the features of the global attention block, and the information lost in the previous stage is recovered, so that the characterization and learning capacity of the model are enhanced.
The SAR comb spectrum interference suppression framework based on the dual-channel attention residual network is utilized, so that the problem of serious target signal loss during comb spectrum interference suppression in the prior art is solved; in addition, the method projects the seriously coupled interference and target echo signals to the high-dimensional separable feature space through the deep nonlinear network, and introduces channel attention and global attention to improve feature extraction and characterization precision, so that intelligent decoupling of the interference and target echo is realized, and the interference suppression effect is obviously better than that of the existing interference suppression method.
The effects achieved by the embodiments of the present invention are further described through experimental verification.
1. Data set
In order to evaluate the performance of the interference suppression method, firstly, a MATLAB software platform is utilized to simulate comb spectrum interference, the number of interference frequency points is set between 100 and 300, the comb spectrum interference with the number of echo points being 16384 is overlapped with an actually measured SAR echo signal to generate a simulated interference echo, and an interference spectrum is obtained through Fourier transformation to generate 10000 samples in total.
The simulation test set is superimposed with simulation comb spectrum interference by using a measured SAR echo signal different from the training set, and test set data is generated through Fourier transformation and normalization. The number of interference frequency points is set to be about 600, 1410 samples are generated, and each sample size is 1×16384. The measured test set is derived from the measured SAR interference data.
2. Implementation details
(1) Experimental conditions
The hardware platform of the simulation experiment of the invention is: the CPU is AMD Ryzen 9 5900HX Radeon Graphics, sixteen cores, the main frequency is 3.30GHz, and the memory size is 32GB; the video memory size is 16GB.
According to the simulation experiment training sample set and the test set, target echo signals of the test set sample set are derived from actually measured non-interference echo data in different scenes at different times under TopSAR mode recorded by a Sentinel-1 satellite; the actual measurement test sample set is actual measurement interference echo data in TopSAR mode recorded by a Sentinel-1 satellite.
(2) The invention is realized on Pytorch, 200 rounds of training are performed by using an AdamW optimizer and a StepLR learning rate update strategy, the learning rate is set to be 0.001, the update step length and the update rate are respectively 50 and 0.1, and the batch size is 8. And constructing the data into a training pair consisting of a target echo signal and an echo signal containing interference, monitoring and parameter tuning the training by using a verification set after each round of training is completed, storing an optimal model with minimum mean square loss on the verification set, and finally evaluating the interference suppression effect and the target echo reconstruction accuracy of the model by using SAR imaging quality on a test set.
(3) Evaluation index
In order to verify the effectiveness of the proposed methods, quantitative and qualitative analyses of the interference suppression effect of the different WBI suppression methods were performed. For qualitative assessment, we can visually compare the recovered target echo signal SAR imaging results. Furthermore, we quantitatively evaluate SAR imaging results using three image quality evaluation indices (Image Quality Assessment, IQA). Three IQA include multiplicative Noise Ratio (Multiplicative Noise Ratio, MNR), peak Signal-to-Noise Ratio (PSNR), and structural similarity (Structural Similarity, SSIM).
1) Multiplicative-to-noise ratio (Multiplicative Noise Ratio, MNR)
The multiplicative noise ratio is defined as the ratio of the average image intensity of the image's weakly scattering region, which refers to a region substantially free of echoes, e.g. a very smooth region such as a calm river, and strongly scattering region, e.g. a city. MNR expression is defined as:
wherein M and N respectively represent the pixel numbers of the weak scattering region and the strong scattering region, I n And I m Representing the pixel values of the weakly scattering region and the strongly scattering region, respectively. The smaller the MNR value, the better the contrast of the restored image.
2) Peak Signal-to-Noise Ratio (PSNR)
The peak signal-to-noise ratio is defined as the ratio of the square of the maximum gray value in the image and the mean square error between the recovered image and the real image. The larger the PSNR, the less distortion of the representative image, and the higher the restored image quality. Its expression is defined as:
3) Structural similarity (Structural Similarity, SSIM)
The structural similarity is an index for measuring the similarity of two images, and the structural information is detected whether to change or not to sense the approximate information of image distortion. Its expression is defined as:
wherein mu x 、μ y 、/>Sum sigma xy Representing the mean, variance and covariance of the restored image and the target image, respectively, c 1 And c 2 Is two very small constants, avoiding zero denominator. The larger the value of SSIM, the smaller the image distortion, and the more similar the two images.
3. Experimental results
In order to highlight the performance of the proposed method, the interference suppression effect of the proposed method (DPARNet) and the Frequency domain notch method (Frequency domain-notched filtering, FNatch) and the U-Net network are compared, and the evaluation is carried out from the two aspects of qualitative and quantitative. The comparison of the imaging results is shown in fig. 8 (a) to 8 (d), and the evaluation results of the interference suppression efficacy are shown in table 1.
TABLE 1
Fig. 8 (a) shows the results of simulated data imaging without interference suppression, with white shadows completely covering the scene information due to the effects of dense comb spectrum interference. Fig. 8 (b) shows the result obtained using the frequency domain notch method, and loss of signal causes serious degradation of image quality. Fig. 8 (c) and fig. 8 (d) are images obtained by using U-Net and the proposed dparet respectively, and the two methods have similar performances, and the obtained images are good in quality, for example, cities, rivers and farmlands can be effectively distinguished, but white artifact residues are also generated after the U-Net is restrained, and the contrast of a white rectangular frame can be used for seeing that the SAR imaging result obtained by the proposed dparet shows better contrast and clearer edges. Table 1 quantitatively shows the comparison results of the DPARNet and the traditional frequency domain notch and U-Net frequency domain anti-interference effects, and can show that the MNR, PSNR, SSIM index of the DPARNet is superior to the comparison algorithm, and compared with the traditional frequency domain notch method, the indexes are obviously improved, MNR is improved by 7.37dB, PSNR is improved by 18.41dB, and SSIM is improved by 0.52dB.
The migration of the DPARNet proposed by the invention is verified by using measured data from interference echo data of a Septinel-1 satellite in TopSAR mode recorded in some areas. Fig. 9 (a) shows the original recorded data, in which the scene is seen with little scene information and most of the area is covered by bright lines, resulting in the loss of a large amount of useful information. Fig. 9 (b) is an image obtained by frequency domain notch of the original data, and almost no information can be interpreted from the SAR image due to image defocus caused by serious signal distortion. Fig. 9 (c) shows the imaging result of the raw data through the U-Net network, wherein most of the interference is suppressed, but the artifacts caused by the obvious residual interference exist. Fig. 9 (d) shows the imaging result of the dparet proposed in the present invention, and compared with the results of other algorithms, the target echo signal is effectively recovered from the interference, and the generated SAR imaging result has higher signal-to-noise ratio and contrast. The results were further quantitatively analyzed and are shown in Table 2.
TABLE 2
As can be seen from Table 2, compared with other comparison algorithms, the MNR, PSNR, SSIM index of the DPARNet provided by the invention has the advantages that each index is improved remarkably, MNR is improved by 5.5dB and 4.14dB respectively compared with the frequency domain notch and the U-Net network, PSNR is improved by 4.02dB and 2.39dB respectively compared with the frequency domain notch and the U-Net network, and SSIM is improved by 0.05 and 0.07. The result shows that the method can be popularized to actually measured interference data, and has good interference suppression effect and migration performance.
The foregoing is a further detailed description of the invention in connection with the preferred embodiments, and it is not intended that the invention be limited to the specific embodiments described. It will be apparent to those skilled in the art that several simple deductions or substitutions may be made without departing from the spirit of the invention, and these should be considered to be within the scope of the invention.

Claims (10)

1. The SAR comb spectrum interference suppression method based on the dual-channel attention residual network is characterized by comprising the following steps of:
acquiring a time domain echo signal with comb spectrum interference;
transforming the time domain echo signals to a frequency domain to obtain frequency domain echo signals with interference;
extracting real parts and imaginary parts of the echo signals with the interference frequency domains to obtain real part signals with the interference and imaginary part signals with the interference;
inputting the real part signal with interference and the imaginary part signal with interference into a pre-trained dual-channel attention residual error network, performing comb spectrum interference suppression, and outputting a frequency domain echo signal; the pre-trained dual channel attention residual network comprises two suppression networks with identical structures, and each suppression network comprises: a channel attention residual block and a global attention block; wherein one suppression network is used for reconstructing a real signal from the input real signal with interference, and the other suppression network is used for reconstructing an imaginary signal from the input imaginary signal with interference.
2. The dual channel attention residual network based SAR comb spectrum interference suppression method of claim 1, wherein each suppression network comprises: five structurally identical channel attention residual blocks and one said global attention block; the five channel attention residual blocks are sequentially connected in series, the number of channels of the first channel attention residual block is the same as that of the fifth channel attention residual block, the number of channels of the second channel attention residual block is the same as that of the fourth channel attention residual block, and the number of channels of the third channel attention residual block is the largest; the global attention block includes: two self-attention networks with the same structure are connected in series in sequence.
3. The method for suppressing SAR comb spectrum interference based on a dual-channel attention residual network according to claim 1, wherein said inputting the real signal with interference and the imaginary signal with interference into a pre-trained dual-channel attention residual network performs comb spectrum interference suppression, and outputs a frequency domain echo signal, comprising:
inputting said real-part signal with interference into a first suppression network while inputting said imaginary-part signal with interference into a second suppression network;
Each suppression network processes the input signals through five channel attention residual blocks which are sequentially connected in series and have the same structure to obtain a first output;
after the first output is segmented along the length dimension, splicing the sub-outputs obtained after segmentation to a first preset dimension to obtain an updated first output;
inputting the updated first output into the global attention block to obtain a second output, and taking the second output as a signal output by the suppression network; wherein the first suppression network outputs a real prediction signal and the second suppression network outputs an imaginary prediction signal;
and performing feature fusion on the real part predicted signal and the imaginary part predicted signal to obtain the frequency domain echo signal.
4. A method of SAR comb spectrum interference suppression based on a dual channel attention residual network according to claim 3, wherein each attention residual block in turn comprises: two first convolution blocks, a second convolution block, a channel attention block and a feature combination block; each suppression network processes an input signal through five channel attention residual blocks which are sequentially connected in series and have the same structure to obtain a first output, and the method comprises the following steps:
After the input signal enters a 1 st channel attention residual block, the input signal sequentially passes through convolution of two first convolution blocks, batch normalization and first activation processing, and then passes through convolution of a second convolution block and batch normalization processing to obtain output of the second convolution block;
the output of the second convolution block is subjected to the average pooling, convolution and second activation processing of the channel attention block to obtain an intermediate output, and the intermediate output and the output of the second convolution block are subjected to the dot multiplication operation of the channel attention block to obtain the output of the channel attention block;
the input of the 1 st channel attention residual block and the output of the channel attention block are subjected to addition of a feature combination block and third activation processing to obtain the output of the 1 st channel attention residual block;
after the output of the m-th channel attention residual block is processed by the m+1th channel attention residual block, the output of the m+1th channel attention residual block is obtained until the output of the 5 th channel attention residual block is obtained, and the output of the 5 th channel attention residual block is used as the first output; m is an integer from 1 to 4.
5. A dual channel attention residual network based SAR comb spectrum interference suppression method according to claim 3, wherein said first output is F e R B×C×L The method comprises the steps of carrying out a first treatment on the surface of the The updated first output is F' ∈R B×C×P×N Wherein the first output comprises B frequency band sequences, B being the number of the interfered real part signals or the interfered imaginary part signals input to the pre-trained dual channel attention residual network; c is the number of channels of each frequency band sequence, L is the length dimension of each frequency band sequence, N is the number of frequency bands, and P is the frequency band length;n and P are the first preset dimensions.
6. A method of SAR comb spectrum interference suppression based on a dual channel attention residual network according to claim 3, wherein the global attention block comprises: a self-attention network within the frequency band and a self-attention network between the frequency bands; the self-attention network in the frequency band and the self-attention network between the frequency bands are connected in series in sequence and have the same structure; the step of inputting the updated first output into the global attention block to obtain a second output includes:
after the updated first output is input into the global attention block, the output of the self-attention network in the frequency band is obtained after the processing of the self-attention network in the frequency band;
and the output of the self-attention network in the frequency band is processed by the self-attention network between the frequency bands to obtain the second output.
7. The dual channel attention residual network based SAR comb spectrum interference suppression method of claim 6, wherein each self-attention network in turn comprises: the system comprises a dimension recombination layer, a position coding layer, a global attention layer and an addition operation layer; after the updated first output is input into the global attention block, the output of the self-attention network in the frequency band is obtained after the processing of the self-attention network in the frequency band, which comprises the following steps:
after the updated first output is input into the self-attention network in the frequency band, combining the second preset dimension of the updated first output through a dimension recombination layer to obtain recombination features; the recombination feature is a frequency band sequence comprising a plurality of frequency points;
the position coding layer performs position coding on each frequency point according to the position information of each frequency point in the frequency band sequence to obtain coding characteristics;
the addition operation layer performs addition operation on the recombination feature and the coding feature to obtain a superposition feature;
the superposition characteristics are processed by the global attention layer to obtain linear output;
and adding the recombination characteristic and the linear output by an adding operation layer to obtain the output of the self-attention network in the frequency band.
8. The method for suppressing SAR comb spectrum interference based on a dual channel attention residual network according to claim 1, wherein before said inputting said real part signal with interference and said imaginary part signal with interference into a pre-trained dual channel attention residual network for suppressing comb spectrum interference, outputting a frequency domain echo signal, said method comprises:
acquiring a plurality of training samples; each training sample is an echo sample signal with an interference frequency domain; the frequency domain echo sample signal with interference corresponds to a frequency domain echo sample signal without interference;
selecting a plurality of training samples each time, and determining the imaginary part and the real part of each selected training sample to obtain an imaginary part sample signal and a real part sample signal of each training sample;
inputting the imaginary part sample signal and the real part sample signal of each training sample selected at this time into a dual-channel attention residual error network of the last training to obtain a predicted real part signal and a predicted imaginary part signal corresponding to each training sample selected at this time;
determining a loss value according to the predicted real part signal and the predicted imaginary part signal corresponding to each training sample selected at the time and the real part signal and the imaginary part signal of the frequency domain echo sample signal without interference corresponding to a plurality of training samples selected at the time;
According to the loss value of the time, the network parameters of the dual-channel attention residual error network of the last training are adjusted to obtain the dual-channel attention residual error network of the time training, the iteration is circulated until the preset condition is reached, and the pre-training dual-channel attention residual error network is obtained.
9. The method for SAR comb spectrum interference suppression based on the dual-channel attention residual network according to claim 8, wherein determining the loss value according to the predicted real part signal and the predicted imaginary part signal corresponding to each training sample selected at the time and the real part signal and the imaginary part signal of the frequency domain echo sample signal without interference corresponding to the plurality of training samples selected at the time comprises:
when B training samples are selected at the time, for each training sample, calculating a first loss between a predicted real part signal corresponding to the training sample and a real part signal of a frequency domain echo sample signal without interference corresponding to the training sample, and calculating a second loss between a predicted imaginary part signal corresponding to the training sample and an imaginary part signal of the frequency domain echo sample signal without interference corresponding to the training sample; b is an integer greater than 1;
Taking the sum of the first loss and the second loss as the loss corresponding to the training sample to obtain B losses corresponding to B training samples;
and taking the sum of the B losses as a current loss value.
10. The dual-channel attention residual network-based SAR comb spectrum interference suppression method of claim 9, wherein the calculation formula of the corresponding loss of each training sample is as follows:
L z =(f(x z1 )-y z1 ) 2 +(f(x z2 )-y z2 ) 2
wherein z is 1,2, once again, B, f (x z1 ) For the predicted real part signal corresponding to the z-th training sample, y z1 For the real part signal of the frequency domain echo sample signal without interference corresponding to the z-th training sample, f (x z2 ) For the predicted imaginary signal corresponding to the z-th training sample, y z2 The imaginary signal of the frequency domain echo sample signal without interference corresponding to the z-th training sample.
CN202310298046.5A 2023-03-24 2023-03-24 SAR comb spectrum interference suppression method based on dual-channel attention residual network Pending CN117111000A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202310298046.5A CN117111000A (en) 2023-03-24 2023-03-24 SAR comb spectrum interference suppression method based on dual-channel attention residual network

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202310298046.5A CN117111000A (en) 2023-03-24 2023-03-24 SAR comb spectrum interference suppression method based on dual-channel attention residual network

Publications (1)

Publication Number Publication Date
CN117111000A true CN117111000A (en) 2023-11-24

Family

ID=88804467

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202310298046.5A Pending CN117111000A (en) 2023-03-24 2023-03-24 SAR comb spectrum interference suppression method based on dual-channel attention residual network

Country Status (1)

Country Link
CN (1) CN117111000A (en)

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117708657A (en) * 2024-02-05 2024-03-15 华东交通大学 Echo signal resonance peak range detection optimization method and system
CN117853371A (en) * 2024-03-06 2024-04-09 华东交通大学 Multi-branch frequency domain enhanced real image defogging method, system and terminal
CN117853371B (en) * 2024-03-06 2024-05-31 华东交通大学 Multi-branch frequency domain enhanced real image defogging method, system and terminal

Cited By (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117708657A (en) * 2024-02-05 2024-03-15 华东交通大学 Echo signal resonance peak range detection optimization method and system
CN117853371A (en) * 2024-03-06 2024-04-09 华东交通大学 Multi-branch frequency domain enhanced real image defogging method, system and terminal
CN117853371B (en) * 2024-03-06 2024-05-31 华东交通大学 Multi-branch frequency domain enhanced real image defogging method, system and terminal

Similar Documents

Publication Publication Date Title
Bianco et al. Travel time tomography with adaptive dictionaries
US11880903B2 (en) Bayesian image denoising method based on distribution constraint of noisy images
CN105913393A (en) Self-adaptive wavelet threshold image de-noising algorithm and device
Deora et al. Structure preserving compressive sensing MRI reconstruction using generative adversarial networks
CN112269168A (en) SAR broadband interference suppression method based on Bayesian theory and low-rank decomposition
Thakur et al. Agsdnet: Attention and gradient-based sar denoising network
CN117111000A (en) SAR comb spectrum interference suppression method based on dual-channel attention residual network
Portilla et al. Image denoising via adjustment of wavelet coefficient magnitude correlation
CN112885368A (en) Multi-band spectral subtraction vibration signal denoising method based on improved capsule network
CN113204051B (en) Low-rank tensor seismic data denoising method based on variational modal decomposition
CN114418886B (en) Robust denoising method based on depth convolution self-encoder
CN116699526A (en) Vehicle millimeter wave radar interference suppression method based on sparse and low-rank model
Ashraf et al. Underwater ambient-noise removing GAN based on magnitude and phase spectra
Koh et al. Underwater signal denoising using deep learning approach
Perera et al. Sar despeckling using overcomplete convolutional networks
Yağan et al. A spectral graph wiener filter in graph fourier domain for improved image denoising
Genser et al. Spectral constrained frequency selective extrapolation for rapid image error concealment
Krishnan et al. A novel underwater image enhancement technique using ResNet
Satapathy et al. Bio-medical image denoising using wavelet transform
Cocianu et al. Neural architectures for correlated noise removal in image processing
CN115526792A (en) Point spread function prior-based coding imaging reconstruction method
Chirtu et al. Seismic Signal Denoising using U-Net in the Time-Frequency Domain
Oral et al. Plug-and-Play Reconstruction with 3D Deep Prior for Complex-Valued Near-Field MIMO Imaging
Leftwich Denoising and Deconvolving Sperm Whale Data in the Northern Gulf of Mexico using Fourier and Wavelet Techniques
Salekin et al. Image De-Noising Through Symmetric, Bell-Shaped, and Centered Weighted Median Filters Based Subband Decomposition

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