Infrared small target detection based on non‐convex triple tensor factorisation

Correspondence Sur Singh Rawat, Department of computer science and engineering, JSS Academy of Technical Education Noida, C-20/1, sec-62 Noida, U.P. 201301, affiliated to AKTU University, Lucknow, India. Email: sur.rawat@jssaten.ac.in Abstract In the present infrared target detection system, simultaneously achieving both the target detection performance, as well as, computing efficiency is considered as a big task. To, address the above said issue, a non-convex triple tensor factorisation is incorporated into the existing infrared patch tensor model in the proposed work. In the proposed model (triple tensor factorisation-infrared patch tensor), local prior information using linear structure tensor and corner strength is incorporated so that the strong clutters in the background can be easily suppressed and the target can be detected correctly. Finally, the method proposed, was solved by alternating direction method of the multiplier. Large number of experiments were conducted and the results presented in the experiments suggest that the method proposed has shown good performance for background suppression, as well as, for the target detection in the clutter environment, when compared with the other baseline methods.


INTRODUCTION
Infrared small target detection system has been a part of many keys areas such as early warning, military services, military surveillance and tracking system etc. Due to the less quantity of pixels of target in an image, most of the time the small target are left in the complex background and due to the detection task becomes very hard [1]. In the past, researchers have contributed greatly in terms of proposing some well-known approaches for infrared small target detection. There are two categories of methods for small target detection, namely: Sequential detection methods, as well as, the single-frame detection methods [2]. The sequential detection method, dynamic programming [3] adopt spatial, as well as, the temporal features for detecting the targets. The single frame detection methods on the other hand are more robust, efficient and fast. Some of the well-known single-frame detection methods are, two dimensional least mean square [4], max-mean and max-median filter [5]. Human visual system [6] was recently seen in small target detection system and this approach assumes that the target is the most salient information in an image as in local contrast measure [7]. Methods based on binary classification like principal component analysis PCA [8], where dictionary samples were created for target detection. Wang et al. [9] utilised a con-stant weighting parameter in the detection process, but all of these patch based methods required a large number of dictionary samples and this takes longer time to process these samples In our knowledge, Gao et al. firstly tried the patch-image based method to detection problem and proposed a method, infrared patch image-model (IPI) [1]. This method has exploited, nonlocal self-correlation features of background patch image and it believe that the background patches normally are from a single or the mixture of low-rank subspace clusters. To, recover the multi-subspace structure and to preserve, local features, a method, robust subspace discovery by block-diagonal adaptive locality-constrained representation was introduced by Zhao zhang et al. [10]. The IPI model has the l 1 -norm sparsity problem as well as the constant weighting parameter issue which predict the background inaccurately and this has miss classified target object. Dai et al. [11] proposed an approach which was based on structural properties of the background image. This method although has shown good result over the other methods but put an extra burden on column weights calculation. Dai et al. [12] proposed a non-negative IPI method based on partial sum of minimisation of singular values(NIPPS) so as to approximate the background and preserves the singular values. NIPPS has a problem of choosing a proper energy constraint ratio as well as the rank of the matrix. Gao et al. [13], reweighted IPI (ReWIPI) model was based on work discussed in [14] to constrain the background patch image, retains the background edge information. Problem with this approach was the improper tuning of weighting parameter which could affect the computation of singular value decomposition (SVD) of matrix. To, further improve the existing IPI based methods, non-convex rank approximation minimisation (NRAM) [15] was proposed. Rawat et al. [16] proposed a ReWIPI model via lp-norm minimisation along with the TV regularisation to improve further the existing IPI model, reweighted infrared patch-tensor model utilising both non-local and local priors for target detection (RIPT) [17] was recently proposed. Recently, based on Non-convex weighted nuclear norm, reweighted infrared patch tensor (IPT) based on weighted tensor nuclear norm [18] was proposed. Infrared small target detection by non-convex low rank constraint via partial sum of tensor nuclear norm (PSTN) [19] was proposed to suppress the complex background while preserving the target. Non-convex tensor rank surrogate joint local contrast energy was proposed in [20] where the local contrast energy feature was added as a weight to the target patch tensor of IPT model to preserve the target and supress the complex background.

Motivation
Inspired by work done in IPT model [17] which utilised both local and non-local prior information simultaneously in the infrared small target detection problem. It is needless to say that, this model has performed exceptionally well as far as the existing state-of-the-art approaches are concerned. In this method, the low rank background patch tensor Β was constrained by the convex surrogate Tucker-rank denoted by the method CTrank(Β) which is defined as sum of nuclear norm (SNN) [21] of the mode-i unfolding which is defined as, CTrank(B) = ∑ i ‖B i )‖ * . Here, i = 1,2,3. The IPT model adopt SNN which gives suboptimal value because it is not the tight convex relaxation of low rankness of the background patch tensor [22]. So, this model found extremely difficult in approximating the background patch tensor. Also due to this, there is loss of inherent background patch structure. In addition to this, RIPT model [17] treats singular values equally, so, less weight should be allocated to the larger singular values. Also to lower down the burden of SVD computation, and to approximate the low rank background tensor patch properly, tensor nuclear norm (TNN) [23] has been applied recently in many infrared small target detection approaches [18,24,25,19,20]. Hence, our first motivation is to propose a method which could address the low-rank background tensor approximation, as well as, the SVD computational cost issue. Our second motivation is inspired from the work done in RIPT model [17], PSTN [19] where both local and non-local prior information were introduced to the IPT model. Although, all of these methods have done quite well, but still we can say that the structure descriptors as a local prior used by these method cannot completely eliminate the noise interference particularly, the stubborn edge interferences. Also, these approaches are computationally expensive. To address the above said challenges, and to improve the existing IPT model, a method for single frame infrared small target detection via (TTF-IPT) based on IPT model is proposed in this paper which is inspired by the work done in factorisation strategy for tensor robust PCA [26],which exploits the orthogonal invariance of TNN. And this motivates us to factorised the low-rank background tensor and propose a computationally efficient method.
Contributions of this paper are as follows: 1. IPT based infrared small target detection model on TTF-IPT is proposed here to reduce down the computational burden caused due to SVDs. Also, the TNN [27] is adopted to constrain the background image patch tensor 2. Secondly, in order to suppress the complex background and preserve the target component. The proposed work incorporates a local prior information using linear structure tensor (LST) and corner strength (CS) to preserve the target 3. The proposed method TTF-IPT model was solved by alternating direction method of the multiplier (ADMM) [28] 4. The experimental results shows that the proposed method has the better detection as well background suppresses ability Rest of the paper is organised as follows. In the Section 2 we have briefly introduced the notations and preliminaries. In Section 3, methodology of proposed method is described in detail. In Section 4, the experiment on infrared image sequences, images with Gaussian noise and the synthetic images are done. Experimental results are also compared with the base-line IPI and IPT models to validate the robustness of our approach, the discussion about the results obtained and the computational complexity was made. In the Section 5 conclusion is presented.

Notations and Preliminaries
In this section, some of the important preliminaries of tensor SVD, which are used in the paper are presented.

Definition 3. (T-SVD
where U ∈ R d 1 xd 1 xd 3 , V ∈ R d 2 xd 2 xd 3 are orthogonal tensor and ∈ R d 1 xd 2 xd 3 is a rectangular F-diagonal tensor. [27]) for  ∈ R d 1 xd 2 xd 3 , the tensor tubal rank, denoted as r t () is defined as the number of non-zero singular

Definition 4. (Tensor tubal rank
Definition 5. (Tensor nuclear norm [27]) let  = U × × V T be t-SVD of ∈ R d 1 xd 2 xd 3 , then the tensor nuclear norm is defined as: where r is the r t () and Δ(i, i, 1) is the entries on the diagonal of the first slice S. And the entries on the diagonal of̄(:,:,j) are the singular values of  (:,:,j). Definition 6. (Tubal nuclear norm ((TNN)), tensor spectral norm [27]) For any tensor ∈ R d 1 xd 2 xd 3 , represents the block diagonal matrix of the tensor, then the TNN ‖‖ * and the tensor spectral norm  of tensor  are respectively defined as the rescaled matrix nuclear norm and the non-scale matrix spectral norm of which means:

Infrared patch tensor model
In general, a single frame infrared image can be formulated as follows: where f D , f B , f T , f N , (x, y) are the original, the background, the target and the noise images, and x, y are the location of the pixel in the image respectively. Finally, like the IPI model [1], Equation (6) can be transferred to the tensor patch space model preserving the spatial structure as formulated below: where D, B, T , N ∈ R d 1 xd 2 xd 3 , are the original patch tensor, background patch tensor, target patch tensor and the noise patch tensor and d 1, d 3 are the patch height and the width and d 3 is the patch number. Background patch tensor: As illustrated in Figure 1(a), The background is normally considered to be slow and consistent so, there is always a high correlations among the local and the nonlocal patches. As analysed in [17] that the patch image is a mode-3 unfolding matrix of a patch tensor so, the patch model is a special case of a patch tensor model. So, it is important of take advantage of other two unfolding also. From Figure 1(b),(c),(d) it can be seen that the singular values of all the unfolding matrices are decreasing to zero so, it can be assumed that background patch tensor B can be treated as a low-rank as the unfolding matrices are of low-rank as defined below.
where r 1 , r 2 , r 3 all are constant which tells the complexity of the background. With the larger the value of r background also become complex. Target patch-tensor: It is assumed that, the size of the small target in infrared images keep changing and is always smaller as compared to the whole image. So, one can think that the target patch tensor as the sparse tensor. This means that where T 0 is the l 0 -norm which counts the number of non-zero entries, and k tells the number and the size of target.

Noise patch-tensor N:
Here it is assumed that the noise patch-tensor do follows the Gaussian noise distribution. So the noise patch can be described as below: Here, T F is Frobenius norm and noise N F ≤ assumed to be additive white Gaussian noise for noise level > 0.
Finally, the infrared small detection problem based on patch tensor model [17] was transformed in to a tensor robust principal component analysis [23] to recover the exactly the low rank and the sparse tensor as described below: min rank where rank(.) represents the "rank function" of a tensor, ‖.‖ 0 is l 0 -norm of a tensor and > 0 is the regularisation parameter. As the problem (13) is NP hard and intractable as both the rank function as well as the l 0 -norm are not convex. IPT model is reformulated as: where, is the controlling parameter which controls the lowrank background tensor and the sparse target tensor.

Proposed infrared patch tensor model
As SNN is not the tight convex envelope of ∑ i ‖B i )‖ * so, the problem [17] gives the suboptimal result. Hence it important to find a tractable solution for the above problem [17], inspired from [27,23] a new tensor nuclear norm from is adopted in the proposed method. But as the TNN as adopted in [27] requires a full matrix SVDs so it is computationally expensive and so this limits its capability for high dimension tensor data. So, to reduce the computational burden factorisation strategy for tensor robust (PCA) [26] is utilised in the proposed work. Secondly, as in problem (12) a global constant weighting was adopted. Also a large value of can over-shrink the small target and smaller value may invite the strong edges. So, this inspired us to adopt a proper weighting scheme and make use of both local as well as non-local prior as in [19] in our proposed method to improve the present IPT model.

Incorporating linear structure tensor as a local prior
Local prior information can play a pivotal role in identifying the local information like for the strong edges, as well as, for the corners in an image. LST [30] is a popular way to measure the local coherence of structure as well to identify the features like edges and corners. LST  (∇u ) for the structure descriptor ∇u within a matrix framework can be formulated as: Orientation information is averaged here by convolving  (∇u ) with the Gaussian kernel G which will make the structure more robust toward the edges, corners and the disturbing artifacts. Equation (15) can be rewritten as below to construct a structure tensor . (16) where  = ( ) is a positive semi definite symmetric matrix. The two eigenvalues of this structure tensors K 1 and K 2 are represented as: . .
K 1 , K 2 are the maximum and the minimum eigenvalues. The local structure with these descriptors in the flat region will have K 1 ≃ K 2 ≃ 0, at the edge K 1 ≫ K 2 ≃ 0 and at the corner K 1 ≫ K 2 > 0. Two important structure tensors one, W CS for CS and other W LS , local structure tensor for edge strength at (x, y) are used here. These structure tensors are formulated below: To, find the interest point, the edge strength information is utilised and the difference of two eigenvalues, K 1 − K 2 , that is, a large and the small eigenvalues is utilised. Applying Equations (16) and (17) on every pixel location (x, y), finally, a local structure tensor W LS constructed as: Here, h is the weight stretching parameter and d min , d max are the minimum and the maximum value of ( 1 −  2 ).
As W LS alone is not sufficient to the complete local prior information in an image. So we combine both the CS as well as the edge information as combined local prior weight patch tensor map W CLPM as below: Here w min , w max are the minimum and the maximum value of W CLPM . The patch tensor of local structure weight map W CLMP is constructed. Equation (14) can be re-formulated as follows:

Incorporating sparsity enhancement prior
Sparsity prior is needed in proposed model as the non-zero elements start reducing as the algorithm converges. Also, inspired by Candes [31] who proposed reweighted l1-norm minimisation for enhancing the sparsity scheme, sparsity enhancement weight map can be constructed as is defined as: where c is non-negative constant, > 0 is to use to avoid division by zero issue and t + 1 represents (t + 1) th iteration. Also along with the l1-norm of the target patch tensor, an adaptive weight W which includes both the local structure weight W CLPM as well as the sparsity enhancing weight W t SE was introduced to replace the global weighting parameter as defined below.
Finally the RIPT model [17] was formulated as below.

Proposed triple tensor factorisation-infrared patch tensor model
Based on the above information, we come up with IPT based (TTF-IPT) model which is inspired by the computationally efficient TriFac strategy based tensor robust PCA [26] model. Following are the lemma's utilised in the proposed model. [26]). Given a tensor, X ∈ R rxrxd 3 , let P ∈ R d 1 xrxd 3 , and Q ∈ R d 2 xrxd 3 be the two semiorthogonal tensors, means P T * P = I ∈ R rxrxd 3 , Q T * Q = I ∈ R rxrxd 3 and r < = min{d 1, d 2 } then, we have the following relationship.

Lemma 2 ([26]). Given any tensor
where U ∈ R d 1 xrxd 3 , V ∈ R rxrxd 3 ,then problem, has a close form solution as described below: Lemma 3 (Proximity operator of TNN [32]). For any 3-way tensor A ∈ R d 1 xd 2 xd 3 with reduced t-SVD, A T = U * * V T , where U ∈ R d 1 xrxd 3 , V ∈ R d 2 xrxd 3 are the orthogonal tensors and Δ ∈ R rxrxd 3 is the f-diagonal tensor of singular tubes, then the proximity operator (A) at A can be calculated as: Incorporating orthogonal invariant of TNN as described in Lemma 1 into IPT model, infrared small target detection method namely TTF-IPT model is proposed and can be formulated as follows: where I r ∈ R rxrxd 3 is an identity tensor.

The solution of triple tensor factorisation-infrared patch tensor model
To solve the proposed TTF-IPT model, ADMM [28] is utilised. In each of the iterations, we solve the above Equation (32) by minimising each of the variables P, C, Q and T at one time while keeping the other variables fixed.
The augmented Lagrangian function of Equation (32) can be formulated as: (34) where ⟨.⟩ represents the trace inner product for the tensor. Y 1 , Y 2 , Y 3 , Y 4 are the Lagrange multipliers tensors and > 0 is the penalty parameter. Finally, these Lagrange multipliers are updated as follows: P sub-problem can be formulated by updating P and fixing the other variables: where, and We solve Equation (36) by Lemma 2 [26] as described in the Equation (29). Q sub-problem can be formulated by updating Q and fixing the other variables: where and also (.) is defined in Lemma 2,so we can solve Equation (39) by Lemma 2 given in Equation (27). C sub-problem can be formulated by updating C and fixing the other variables: where (.) is the proximity operator of TNN [32], so Equation (42) can be solved using Lemma 3 (proximity operator of TNN [32]) T sub-problem can be formulated by updating T and fixing the other variables: (43) where ℑ (.) is the proximity operator of tensor l 1 -norm defined as follows:

Detection process of triple tensor factorisation-infrared patch tensor model
The whole target-background separation model is depicted Figure 2. The whole TTF-IPT model can describe as follows: 1. Local patch weight map construction: From the original image, cumulative local structure weight patch tensor W CLPM is computed using Equation (18) where f T , are the average and the standard deviation of the infrared target image f T and k and v min are the constants. If f T (x, y) > t up then its target, otherwise the pixels belongs to the background image.

While not converged do:
3. Fix the other and update P t +1 using Equation (36) 4. Fix the other and update Q t +1 using Equation (39) 5. Fix the other and update C t +1 using Equation (42) 6. Fix the other and update T t +1 using Equation (43) 7. Update the following Lagrange multipliers using Equation (35) 8. Fix the other and update W t +1 , W t +1 SE as follows

9.
Update the penalty parameter:

EXPERIMENTS
In this section we have validated our proposed model by conducting extensive experiments on real and synthetic infrared image dataset. This section includes, dataset preparation, useful metrics indicators, parameter setting for baseline methods, result analysis, parameter analysis and the computational complexity of the proposed algorithm. The proposed model is validated in the terms of background suppression performance, detection performance and the computational expensiveness.
In terms of robustness of the proposed method we have considered real and synthetic single, multiple target images in the experiments under the complex background environment.  , lambdal L = 2, r = 10 −3 , tolerance error, = 10 −7 , = 1.5 No. 7Methods RIPT [17]Parameter values patch size is 50 × 50, sliding step is 10, =

Dataset preparation
Dataset of 1380 infrared images under different background such as sea, sky, cloud and the ground was done in this section. Also brief description of all of the representative images are shown in Table 1 below. We have conducted experiment on real infrared single images, noisy and the synthetic images to validate the suppression as well as detection ability of our proposed method.

Parameter setting of baseline methods
The proposed model is evaluated and its robustness is compared with the 9 baseline methods: Max-mean filter [5], maxmedian filter [5], top-hat filter [34], IPI [1], RPCA [9] and NIPPS [12],RIPT [17] and NRAM [15] and PSTN [19] on the six different real infrared image sequences. The parameter setting of all baseline methods are given in the Table 2 given below. The proposed model was solved using ADMM. All of these algorithms are implemented in MATLAB 2015a on PC of 2.2 GHz and 4 GB RAM.

Background suppression performance
To, validate the performance of our proposed method, we have experimented on real infrared image sequences, images incorporated with Gaussian noise, self-prepared synthetic images with embedded targets at random locations.

Background suppression result of image sequences
This sub-section presents the background suppression result of the proposed methods when experimented on six different image sequences under the complex background. Here, Figure 3(a) depicts the original images, F igure 3(b) shows the background suppression ability of our proposed method. And

Experimental result on a synthetic dataset
This section presents the evaluated performance of our method on the synthetic dataset of image sequences which are prepared from the real infrared background images under different background, with the varying sized targets which are embedded into the background at random location. Synthetic dataset preparation method was inspired by the method mentioned in [1]. In our prepared dataset we have considered image containing 1 and 2 targets as we can see in Figure 4(a) The background suppression ability of the proposed method on this synthetic data set is shown in the Figure 4(b) and we can see that our model can not only suppress the background but also able detect the target properly.

Evaluation indicators
Two well-known standard evaluation metrics, namely: Signal to clutter ratio gain (SCRG) and background suppression factor (BSF) are utilised here to validate the robustness of our proposed method. And these indicators can be expressed as follows: where, the amplitude of the signal and the clutter standard deviation are represented by S and C, in and out in the expression are the input image and the output target image. The second important indicator which is known as the receiver operation curve (ROC) is also utilised here in the proposed model. This curve shows the relationship between the probability of target detection P d and the false alarm rate P f and their relationship can as defined as follows:

Comparison with the baseline methods
The proposed method here in this section is compared with the nine (09) state-of-art methods to evaluate its robustness. The Figure 5(a) below depicts the original image sequences and the image in Figure 5(b) to Figure 5(d) represents the background suppression result of top-hat, max-mean and maxmedian methods. The background assumption based methods like top-hat, max-mean and max-median show good performance in the image sequences where the background is quite slow and smooth, but these methods does not do well in the presence of non-smooth background. Similarly, as we can see that suppression ability of all the methods based on patch image like IPI, RPCA, NIPPS in Figure 6(b) to Figure 6(d). We can clearly observe that patch based IPI method detect the target quite well in smooth background, but in the presence of strong clutter, we can see that it lacks its performance and the reason is certainly due to the over shrink of image using l1 norm sparsity which leads to the detection of non-target element in the target patch image. We can observe that the RPCA method as seen in the Figure 6(c) has shown good result, but due to fixed controlling parameter job of this method becomes difficult in predicting the background information. We can see in Figure 6(d) that NIPPS method has performed quite well and is able to suppress background well but, problem here is that it only minimise the noise variance and not the whole data matrix also the energy constraint ratio, that is, the rank of a matrix with needs to be known in prior. Figure 7(b) to Figure 7(e) shows the suppression and detection result of RIPT, NRAM and PSTN and our proposed method. Methods RIPT and NRAM both work well as they are patch-based methods but as like other above approaches, RIPT and NRAM does not do well in the presence of noise. PSTN has perform well as it has turned the parameters according to the outcome, like patch size is taken as 40 × 40 and the step size is taken as 40 along with lambdal L = 0.6 and = 1.05. The proposed model as we can see in the Figure 7(e) suggest that our method is more effective in the presence of non-smooth background and this is due to the reason that we have taken care of both background as well as the target priors. In addition to this, all the baseline methods taken here in this paper have not considered the computational complexity as an important parameter in their model. Keeping this in view our model has taken computational complexity as an important parameter. Table 3 above shows the average SCRG and the BSF values of all the methods including our method on all the six image sequences. The best values of the indicators in each column has been marked in bold and the second best values are marked in blue. Our method has got the highest SCRG for sequence 1, 3, 4 and 6 and the highest BSF value for the sequences 1, 3, 4, 5 and in addition to this our method has second highest SCRG value for sequence 2. As we have considered both the background as

Parameter analysis
In this section, we have utilised three important parameters which plays a pivotal role in the robustness of the proposed method under various background scenes. Patch size, step size and the controlling parameter are the important parameters. In order to attain better result we need to tune these parameters. We can observe here that the tuning parameter may not always give the global optimal solution. The performance of the proposed method using these parameters can be analysed from ROC curves drawn for the different image sequences as shown in the Figure 9 in the subsequent section.

Patch size
In the experiment we have incorporated variable patch sizes to observe the result of our approach and we can observe that by increasing the patch size, we can improve the sparsity the target, but by doing this will also increase the burden on computation cost. In the experiment, we have taken patch size of 20, 30, 40, 50 and 60 in the interval of 10 unit respectably and an appro-priate patch size is considered for better response of the proposed model. We have plotted the ROC curve for the two image sequences as we can see in the Figure 9(a). From the ROC curve, we can notice that the detection ability, as well as the computing complexity, can be very much affected by increasing the image patch size. The patch size 60 in the proposed method is showing the less detection performance, and this is due to the loss that the non-local self-similar patches and also this will certainly affect the target and background separation. We can observe that the patch size of 40 × 40 ideal for the better performance.

4.5.2
Step size Similar to patch size we need to tune properly the step size also. In the experiment, we have fixed the patch size 40 × 40 and then we have varied the step size in the interval of 2 unit and considered step sizes as 10, 12, 14, 16 and 18, respectively. From the ROC curve on step size for the two image sequences as shown in the Figure 9(b), we can say that by taking a small step the can be increase in the computation time and also can affect the detection performance of the proposed algorithm. Similarly, by increasing the step size may decrease the computation time.
From the observation we have concluded that the ideal step size can be taken as 12.

Controlling parameter
In the proposed .
(52)    Table 4 above, gives computational cost of running per image frame for the sequence no. 2 of Figure 3(a). The computational cost of top-hat method with structuring size of K 2, and the image size of M*N is computed as  (K 2 log K 2 MN), cost of max-mean and max-median methods is (M*N*K 2 ). In the IPI model based methods we can see that these methods takes large amount of time in SVD operations in the algorithm. So for the image patch size of m*n, the cost for the IPI, RPCA,   2 )). For our method one iteration cost of the algorithm after updating the sub-problem is given by d 3 (d 1 d 2 log(d 3 + r 2 (r + d 1 + d 2 + logd 3 ) + r(d 1 + d 2 ) logd 3 )). In order to approximate this the value of rank r = min{d 1, d 2 ) is taken as a small scale . So the cost of algorithm is (d 1 d 2 d 3 log(d 3 )) which much better than the other tensor based algorithms.

CONCLUSION
In order to further improve the existing IPI and IPT based model for small target detection. A method namely (TTF-IPT) is proposed in this paper which incorporated TTF into the existing IPT model which helps to reduce the computation burden of SVD operations. Moreover (LST) and the (CS) was incorporated as the local prior information so that the strong clutters in the background can be suppressed and the target can be detected correctly. Finally, the proposed method was solved by ADMM. The results presented in the experiments, depicts that the proposed method when compared with the other baseline methods shows better background suppression, as well as, target detection ability in the clutter environment. The proposed method like other IPT methods need to know the rank of a tensor in prior, which may not be feasible always. So, a better solution needs to be developed in future to resolve this issue.