Radar mode recognition method based on clustering hypothesis and multivariate grey incidence model

Abstract

The application discloses a radar working mode recognition method based on clustering assumption and a multivariate grey correlation model, and comprises the following steps: S1, performing mean shift clustering on source domain and target domain data to obtain clustering centers; S2, constructing a multivariate grey correlation model of the source domain and the target domain to evaluate a domain difference index MGRDD of the source domain and the target domain; S3, selecting a migration method of the source domain and the target domain based on the size of the multivariate grey correlation domain difference index MGRDD; when MGRDD >= alpha, using a radar working mode migration recognition algorithm based on clustering assumption and the multivariate grey correlation model to recognize the radar working mode of the target domain; and when MGRDD < alpha, using a radar working mode adaptive multi-domain migration recognition algorithm based on clustering assumption and the multivariate grey correlation model to recognize the radar working mode of the target domain.

Description

Technical Field

[0001] This invention relates to the field of radar technology, and specifically to a radar operating mode recognition method based on clustering assumptions and multivariate grey relational models. Background Technology

[0002] With the application and development of science and technology in the military, and facing increasingly complex battlefield environments, radar jamming countermeasures have gradually become the core of modern military warfare, and radar operating mode identification is of paramount importance. Radar operating mode identification, namely passive detection systems such as RWR (Radar Warning Receiver), ELINTR (Electronic Intelligence Receiver), and ESM (Electronic Support Measurement), identifies the current operating mode of enemy radar by intercepting and analyzing enemy radar signals.

[0003] In recent years, radar operating mode recognition technology has developed rapidly, with increasingly better recognition effects and higher recognition accuracy. However, progress in radar operating mode recognition based on limited prior knowledge has been slow. The difficulties in radar operating mode recognition based on limited prior knowledge are mainly reflected in two aspects: (1) large amount of information, especially in many radar signal sequences, it is necessary to accurately distinguish the current radar operating mode. There can be multiple radar operating modes at the same time; (2) limited prior knowledge of the domain. If the domain to be identified has a small number of tags on its signals, it is difficult to use existing knowledge to transfer it. Summary of the Invention

[0004] The problem to be solved by this invention is to provide a radar operating mode recognition method based on clustering hypothesis and multivariate grey relational model. For radar operating mode recognition in the source domain and target domain with low grey relational degree and large distance, a source domain-target domain stepwise transfer network is built by using multiple source domains to transfer transferable knowledge from multiple source domains to the target domain step by step, avoiding the negative transfer problem caused by direct transfer.

[0005] The technical solution provided by this invention to solve the above problems is: a radar operating mode recognition method based on clustering assumptions and a multivariate grey relational model, the method comprising the following steps:

[0006] S1. Perform mean-shift clustering on the source and target domain data to obtain cluster centers;

[0007] S2. Construct a multivariate grey relational model of the source domain and the target domain to evaluate the domain difference index MGRDD between the source domain and the target domain;

[0008] S3. Select the migration method for the source and target domains based on the size of the multivariate grey relational domain difference index MGRDD;

[0009] When MGRDD≥α, a radar working mode migration identification algorithm based on clustering assumptions and multivariate grey relational model is used.

[0010] When MGRDD < α, the radar working mode adaptive multi-domain migration recognition algorithm based on clustering assumptions and multivariate grey relational model is used.

[0011] Where α is the set critical value.

[0012] Preferably, in S1, mean-shift clustering is a sliding window-based algorithm that divides the radar signal sequence into n units and uses the sliding window method to find dense regions of data points; let S be the source domain cluster center obtained by mean-shift clustering. i i = 1, 2, ..., M, and the target domain cluster center is T. j j = 1, 2, ..., N; the source domain cluster center matrix S is represented by the following equation (1):

[0013]

[0014] The cluster center matrix T of the target domain is expressed as shown in equation (2):

[0015]

[0016] Preferably, the domain difference measurement method of the multivariate grey relational model in S2 is MGRDD. The MGRDD method is a method for measuring the degree of correlation between the source domain and the target domain, and its formula is shown in the following formula (3):

[0017]

[0018] In equation (3), D S D T Let M and N represent the source domain and the target domain, respectively, where M represents the number of cluster centers in the source domain and N represents the number of cluster centers in the target domain. f(S) i ,T j ) represents the degree of grey correlation between the cluster centers of the source domain and the target domain, and its expression is shown in equation (4) below;

[0019]

[0020] In equation (4), n represents the number of radar sequence division units. The physical feature displacement difference representing the similarity between the source domain and the target domain is given by the following formula (5):

[0021]

[0022] In formula (4) The physical characteristic velocity difference (first-order slope difference) representing the similarity between the source domain and the target domain is given by the following formula (6):

[0023]

[0024] In formula (4) The physical characteristic acceleration difference (second-order slope difference) representing the similarity between the source domain and the target domain is given by the following formula (7):

[0025]

[0026] Preferably, the method for selecting the source and target domain migration based on the magnitude of the multivariate grey relational domain difference index MGRDD in S3 is as follows:

[0027] When the source domain and the target domain are highly correlated The value will be relatively small, f(S) i T j If the value is relatively large, then when MGRDD(D) S D T If α ≥ α, it is assumed that the source domain and the target domain are highly correlated. In this case, the radar operating mode classification knowledge of the source domain can be directly transferred to the target domain.

[0028] When the source domain and target domain are not closely related The value will be relatively large, f(S) i T j If the value is relatively small, then when MGRDD(D) S D T )<α assumes that the source domain and the target domain are not closely related, and therefore the radar operating mode classification knowledge of the source domain cannot be directly transferred to the target domain.

[0029] Preferably, MGRDD(D) S D T When α ≥ α, the transfer method of the source domain radar working mode classification knowledge is a radar working mode model transfer recognition algorithm based on clustering assumption and multivariate grey relational model. It directly transfers the model structure and some parameters of the already trained source domain radar working mode recognition model to the target domain radar working mode model, and then fine-tunes it with a small amount of training data from the target domain radar dataset. Specifically, the source domain output layer Softmax layer is replaced and a new Softmax layer with randomly initialized parameters is connected. Then, the model is trained on this new model with a relatively small dataset.

[0030] Preferably, MGRDD(D) S D TWhen α < α, the transfer method for the source domain radar operating mode classification knowledge is: an adaptive multi-domain transfer recognition algorithm for radar operating modes based on clustering assumptions and multivariate grey relational models. The features extracted by the neural network can be divided into general features and specific features. General features have little correlation with the task and can be directly used for other tasks; specific features have strong task correlation and are only applicable to specific tasks. In the network, the features in the front layer show stronger generality, while the features in the back layer have stronger specificity.

[0031] Preferably, to avoid the negative migration problem caused by directly transferring the target domain radar from the source domain radar operating mode recognition model, for the target domain T... D Select three (or more) source domains A, B, and C for radar operating mode identification, denoted as S. A S B and S C According to the relationship between their datasets and the target task dataset Arrange from largest to smallest. Using S... A Training data and constructing a recognition network N(S) A The network has a total of M layers. First, determine the layer by S. A Migrate to S B During the process N(S) A The general and specific characteristics of each layer. N(S) A The first l layers are fixed, the parameters of the (l+1)th to Mth layers are initialized, and task S is used. B The training data is used to update the parameters. If this new network is used in task S... B The pattern recognition rate on the test set is better than that of directly using task S. B Network N(S) constructed from training data B The recognition rate of S indicates that the recognition rate of S is high. A Migrate to S B During the process N(S) A If the l-th layer of a network is general, then it is considered general; otherwise, it is considered specific. By iteratively applying the above method, it is possible to determine which layers should be frozen and which layer parameters should be fine-tuned during the transition from one task to another, and the resulting network is denoted as N(S). A *S B These are passed and used sequentially to ultimately construct a system suitable for the target task T. D Network N(S) A *S B *S C *T D ).

[0032] Compared with existing technologies, the advantages of this invention are as follows: Compared with traditional radar operating mode recognition methods, this invention first calculates the multivariate gray correlation degree between the radar signal sequence that has been identified in the source domain and the radar signal sequence to be identified in the target domain, establishing the distance relationship between the source domain and the target domain; for radar operating mode recognition with large gray correlation degree and small distance between the source domain and the target domain, a transfer learning method is used with deep network fine-tuning to enable the transfer of radar operating mode recognition classification knowledge from the source domain to the target domain recognition work with fewer labels and less prior knowledge; for radar operating mode recognition with small gray correlation degree and large distance between the source domain and the target domain, a multi-source domain progressive transfer network is built to transfer transferable knowledge from multiple source domains to the target domain step by step, avoiding the negative transfer problem caused by direct transfer. Attached Figure Description

[0033] The accompanying drawings, which are provided to further illustrate the invention and constitute a part of this invention, are illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention.

[0034] Figure 1 This is a structural diagram of the radar operating mode recognition model based on the clustering hypothesis and multivariate grey relational model of this invention.

[0035] Figure 2 This is a schematic diagram of the mean-shift clustering method of the present invention;

[0036] Figure 3 This is a schematic diagram of the deep network fine-tuning model structure of the present invention;

[0037] Figure 4 This is a schematic diagram of the multi-domain migration recognition algorithm structure of the present invention. Detailed Implementation

[0038] The following will describe in detail the implementation of the present invention with reference to the accompanying drawings and embodiments, so that the process of how the present invention uses technical means to solve technical problems and achieve technical effects can be fully understood and implemented accordingly.

[0039] In the description of this invention, it should be noted that the directional terms such as "center", "lateral", "longitudinal", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", and "counterclockwise" indicate the orientation and positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. They should not be construed as limiting the specific protection scope of this invention.

[0040] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features. Thus, the use of "first" and "second" to define a feature may explicitly or implicitly include one or more of that feature, and in the description of this invention, "a number" means two or more, unless otherwise explicitly specified.

[0041] In this invention, unless otherwise explicitly specified and limited, the terms "assembly," "connection," and "joining" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can also refer to a mechanical connection; they can refer to a direct connection or a connection through an intermediate medium; or they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this invention according to the specific circumstances.

[0042] It should be understood that, when used in this specification and the appended claims, the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0043] It should also be understood that the terminology used in this specification of embodiments of the invention is for the purpose of describing particular embodiments only and is not intended to limit the embodiments of the invention. As used in this specification of embodiments of the invention and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0044] Reference Figures 1-4 A preferred embodiment of the present invention provides a method for identifying radar operating modes through transfer learning of clustering hypotheses and multivariate grey relational models, the method comprising the following steps:

[0045] S1. Perform mean-shift clustering on the source and target domain data to obtain cluster centers;

[0046] S2. Construct a multivariate grey relational model for the source and target domains to evaluate the domain difference index MGRDD (Domain Differences Based on Multivariate Grey Relational) between the source and target domains. T D S );

[0047] S3. Select the migration method for the source and target domains based on the size of the multivariate grey relational domain difference index MGRDD;

[0048] When MGRDD≥α, a radar working mode migration identification algorithm based on clustering assumptions and multivariate grey relational model is used.

[0049] When MGRDD < α, the radar operating mode adaptive multi-domain migration recognition algorithm based on clustering assumptions and multivariate grey relational model is used.

[0050] The specific transfer learning model used is a radar operating mode classification model combining BiGRU and an attention mechanism. Training is performed by incorporating grey relational analysis without altering the original recurrent convolutional network structure. The principle block diagram of the radar operating mode recognition algorithm based on the clustering hypothesis and the multivariate grey relational model is shown below. Figure 1 As shown.

[0051] As a preferred embodiment of the present invention, it may also have the following additional technical features:

[0052] In this embodiment, the mean drift method in S1 is a sliding window algorithm that divides the radar signal sequence into n units and uses the sliding window method to find the dense region of data points. Let S be the source domain cluster center obtained by the mean drift method. i i = 1, 2, ..., M, and the target domain cluster center is T. j j = 1, 2, ..., N. The source domain cluster center matrix S is represented by the following equation (1):

[0053]

[0054] The cluster center matrix T of the target domain is expressed as shown in equation (2):

[0055]

[0056] In this embodiment, the domain difference measurement method of the multivariate grey relational model in S2 is MGRDD. The MGRDD method is a method for measuring the degree of correlation between the source domain and the target domain, and its formula is shown in the following formula (3):

[0057]

[0058] In equation (3), D S D T Let M and N represent the source domain and the target domain, respectively, where M represents the number of cluster centers in the source domain and N represents the number of cluster centers in the target domain. f(S) i T j ) represents the degree of grey correlation between the cluster centers of the source domain and the target domain, and its expression is shown in equation (4) below;

[0059]

[0060] In equation (4), n represents the number of radar sequence division units. The physical feature displacement difference representing the similarity between the source domain and the target domain is given by the following formula (5):

[0061]

[0062] In formula (4) The physical characteristic velocity difference (first-order slope difference) representing the similarity between the source domain and the target domain is given by the following formula (6):

[0063]

[0064] In formula (4) The physical characteristic acceleration difference (second-order slope difference) representing the similarity between the source domain and the target domain is given by the following formula (7):

[0065]

[0066] In this embodiment, the method for selecting the source and target domain migration based on the magnitude of the multivariate grey relational domain difference index MGRDD in step S3 is as follows:

[0067] When the source domain and the target domain are highly correlated The value will be relatively small, f(S) i ,T j If the value is relatively large, then when MGRDD(D) S D T If α ≥ α (α is a set critical value), it can be considered that the source domain and the target domain are highly correlated. At this time, the radar operating mode classification knowledge of the source domain can be directly transferred to the target domain.

[0068] When the source domain and target domain are not closely related The value will be relatively large, f(S) i ,T j If the value is relatively small, then when MGRDD(D) S D T If α < α, it can be considered that the source domain and the target domain are less correlated. In this case, the radar operating mode classification knowledge of the source domain cannot be directly transferred to the target domain.

[0069] In this embodiment, MGRDD(D S D TWhen α ≥ 0, the transfer method for the source domain radar operating mode classification knowledge is a radar operating mode model transfer recognition algorithm based on clustering assumptions and a multivariate grey relational model. This algorithm directly transfers the pre-trained source domain radar operating mode recognition model structure and some parameters to the target domain radar operating mode model, and then fine-tunes it using a small amount of training data from the target domain radar dataset. Specifically, it replaces the source domain output Softmax layer with a new Softmax layer whose parameters are randomly initialized, and then trains this new model using a relatively small dataset.

[0070] In this embodiment, MGRDD(D S D T When α < α, the transfer method for the source domain radar operating mode classification knowledge is: an adaptive multi-domain transfer recognition algorithm for radar operating modes based on clustering assumptions and multivariate grey relational models. The features extracted by the neural network can be divided into general features and specific features. General features have little correlation with the task and can be directly used for other tasks; specific features have strong task correlation and are only applicable to specific tasks. In the network, the features in the front layer show stronger generality, while the features in the back layer have stronger specificity.

[0071] To avoid the negative migration problem caused by directly transferring the target domain radar operating mode recognition model from the source domain radar, a solution is proposed for the target domain T. D Select three (or more) source domains A, B, and C for radar operating mode identification, denoted as S. A S B and S C According to the relationship between their datasets and the target task dataset Arrange from largest to smallest. Using S... A Training data and constructing a recognition network N(S) A The network has a total of M layers. First, determine the layers by S. A Migrate to S B During the process N(S) A The general and specific characteristics of each layer. N(S) A The first l layers are fixed, the parameters of the (l+1)th to Mth layers are initialized, and task S is used. B The training data is used to update the parameters. If this new network is used in task S... B The pattern recognition rate on the test set is better than that of directly using task S. B Network N(S) constructed from training data B The recognition rate of S indicates that the recognition rate of S is high. A Migrate to S B During the process N(S) AIf the l-th layer of a network is general, then it is considered general; otherwise, it is considered specific. By iteratively applying the above method, it is possible to determine which layers should be frozen and which layer parameters should be fine-tuned during the transition from one task to another, and the resulting network is denoted as N(S). A *S B These are passed and used sequentially to ultimately construct a system suitable for the target task T. D Network N(S) A *S B *S C *T D ).

[0072] It should be noted that, Figure 1 The diagram shows a radar operating mode recognition method based on clustering assumptions and a multivariate grey relational model. The mean shift method is used to obtain the cluster centers of each radar data sequence in the source and target domains. The multivariate grey relational model is used to calculate the grey relational degree between each sequence in the source and target domains based on the cluster centers. After obtaining the grey relational degree, the migration method from the source domain to the target domain is selected based on its magnitude.

[0073] More specifically, Figure 2 This illustrates the mean-shift clustering algorithm. When clustering input data, the algorithm selects an initial point as the starting point for mean-shift clustering. Using the starting point as the center and R (the sliding window setting) as the radius, it calculates the centroid of all data points within the circle and uses this centroid as the next cluster center. This process continues until the cluster center no longer changes position, thus obtaining the cluster center of this group of data points, which is the densest region of this set of data points.

[0074] in, Figure 3 The diagram shown is a block diagram of the radar operating mode model transfer recognition algorithm based on clustering assumptions and multivariate grey relational model:

[0075] Specifically, the working mode labels of each data in the A radar dataset are identified by the A radar working mode recognition network. Given that the correlation between A radar and B radar is known to be high, the A radar working mode recognition network that identifies the A radar dataset is directly applied to the working mode recognition of B radar. Its deep network weights are fixed, and the output layer is fine-tuned on a small amount of labeled data from B radar. Finally, it is transferred to the working mode recognition of the B radar dataset.

[0076] in, Figure 4 The diagram shown is a block diagram of the radar operating mode adaptive multi-domain migration recognition algorithm based on clustering assumptions and multivariate grey relational models:

[0077] This means that when the grey relational degree between the source domain A and the target domain D is confirmed to be small, in order to avoid negative transfer, the radar operating mode recognition network of the source domain A cannot be directly used. In this case, several similar operating mode recognition networks of radar B and radar C are found, and their datasets are compared with the target task dataset using MGRDD(D). T D S Arranged from largest to smallest, by identifying the general and specific characteristics of the preceding and following network layers, the number of preceding network layers that need to be frozen and the number of network layers related to the D radar's operating mode that need to be fine-tuned are determined. This process is then gradually transferred to the D radar's operating mode recognition, forming the D radar's operating mode recognition network N(S). A *S B *S C *T D ).

[0078] Compared to traditional radar operating mode recognition methods, this invention first calculates the multivariate gray correlation degree between the radar signal sequence already identified in the source domain and the radar signal sequence to be identified in the target domain, establishing the distance relationship between the source and target domains. For radar operating mode recognition methods with high gray correlation degree and low distance between the source and target domains, a transfer learning method is used with deep network fine-tuning to transfer the radar operating mode recognition classification knowledge from the source domain to the target domain recognition work with fewer labels and less prior knowledge. For radar operating mode recognition methods with low gray correlation degree and high distance between the source and target domains, a multi-source domain progressive transfer network is built to transfer transferable knowledge from multiple source domains to the target domain step by step, avoiding the negative transfer problem caused by direct transfer.

[0079] The above description only illustrates the preferred embodiments of the present invention and should not be construed as limiting the scope of the claims. The present invention is not limited to the above embodiments, and variations in its specific structure are permitted. All modifications made within the scope of the independent claims of this invention are also within the scope of protection of this invention.

Claims

1. A radar operating pattern recognition method based on clustering assumptions and a multivariate grey relational model, characterized in that: The method includes the following steps: S1. Perform mean-shift clustering on the source and target domain data to obtain cluster centers; S2. Construct a multivariate grey relational model for the source and target domains to evaluate the domain difference indicators between the source and target domains. ; S3, Based on the difference index of multiple grey relational domain The size of the target domain determines the choice of migration method for the source and target domains; when The radar operating mode migration identification algorithm based on clustering assumptions and multivariate grey relational models is used. when An adaptive multi-domain migration recognition algorithm for radar operating modes based on clustering assumptions and a multivariate grey relational model is used. in, The set critical value; The domain difference measurement method for the multivariate grey relational model in S2 is as follows: , The method is a way to measure the degree of correlation between the source domain and the target domain, and its formula is shown in equation (1) below: ； In formula (1) Let them represent the source domain and the target domain, respectively. Indicates the number of cluster centers in the source domain. Indicates the number of cluster centers in the target domain. The gray correlation degree between the cluster centers of the source domain and the target domain is expressed as shown in equation (2) below; ； In formula (2) Indicates the number of units in the radar sequence. The physical feature displacement difference representing the similarity between the source domain and the target domain is given by the following formula (3): ； In formula (2) The physical characteristic velocity difference representing the similarity between the source domain and the target domain is given by the following formula (4): ； In formula (2) The physical characteristic acceleration difference representing the similarity between the source domain and the target domain is given by the following formula (5): ； In this context, the knowledge transfer method for source domain radar operating mode classification is as follows: an adaptive multi-domain transfer recognition algorithm for radar operating modes based on clustering assumptions and multivariate grey relational models. The neural network extracts features that can be divided into general features and specific features. General features have little correlation with the task and can be directly used for other tasks. Specific features have strong task correlation and are only applicable to specific tasks. Features in the earlier layers of the network exhibit stronger generality, while features in the later layers exhibit stronger specificity. To avoid the negative migration problem caused by directly transferring the target domain radar operating mode recognition model from the source domain radar operating mode recognition model, a solution is proposed for the target domain radar. Select 3 or more source domains , and Radar operating mode recognition, respectively represented as , and According to the relationship between their datasets and the target task dataset Arrange from largest to smallest; utilize Training data and building a recognition network The network has a total of First, determine the layers. Migrate to During the process The general and specific characteristics of each layer; The former The first layer is fixed, for the second layer The layer parameters are initialized, and the task is used. The training data updates the parameters; if this new network is used in the task... The pattern recognition rate on the test set is better than that of directly utilizing the task. Network constructed from training data The recognition rate indicates that the recognition rate is high. Migrate to During the process The The layers must be general; otherwise, they must be specific. By iteratively applying the above methods, we can determine which layers should be frozen and which layer parameters should be fine-tuned during the migration from one task to another, and denote the migrated network as follows: ; passed and used sequentially, ultimately constructing a system suitable for the target task. network .

2. The radar operating mode recognition method based on clustering assumptions and a multivariate grey relational model according to claim 1, characterized in that: The mean-shift clustering in S1 is based on a sliding window algorithm that divides the radar signal sequence into... For each unit, the sliding window method is used to find the dense regions of data points; let the source domain cluster centers obtained by mean-shift clustering be . The target domain cluster center is Source domain cluster center matrix It is expressed as shown in the following formula (6): ； Target domain cluster center matrix It is expressed as shown in the following formula (7): 。 3. The radar operating mode recognition method based on clustering assumptions and a multivariate grey relational model according to claim 1, characterized in that: The S3 is based on the multivariate grey relational domain difference index The size of the target domain determines the selection of the migration method for the source and target domains, and the method is as follows: When the source domain and the target domain are highly correlated , , The value will be relatively small. The value is relatively large, so when It is believed that the source domain and the target domain are highly correlated, and in this case, the radar operating mode classification knowledge of the source domain can be directly transferred to the target domain; When the source domain and target domain are not closely related , , The value will be relatively large. The value is relatively small, so when It is assumed that the source domain and the target domain are not closely related, and therefore the radar operating mode classification knowledge of the source domain cannot be directly transferred to the target domain.

4. The radar operating mode recognition method based on clustering assumptions and multivariate grey relational models according to claim 3, characterized in that: In this case, the knowledge transfer method for source domain radar operating mode classification is a radar operating mode model transfer recognition algorithm based on clustering assumptions and multivariate grey relational models. It directly transfers the pre-trained source domain radar operating mode recognition model structure and some parameters to the target domain radar operating mode model, and then fine-tunes it using a small amount of training data from the target domain radar dataset. Specifically, it replaces the source domain output layer Softmax layer and connects a new Softmax layer with randomly initialized parameters. Then, it trains on this new model using a relatively small dataset.

Images