esa-sceva/satcom-chunk-collection huggingface dataset:
# Cyclic Consistent Image Style Transformation: From Model to System
## 5 Experiment  
In this section, we utilized the Cityscapes dataset, a high-quality and widely used dataset in the field of computer vision, primarily for tasks such as semantic segmentation, object detection, and image synthesis. The dataset contains urban street scene images from 50 cities, with fine pixel-level semantic annotations, making it particularly suitable for visual tasks in urban environments. The dataset comprises a total of 5000 finely annotated images, which we split into a training set and a test set in an 8:2 ratio. Specifically, 4000 images were used for model training, while the remaining 1000 images were reserved for testing, ensuring the model's generalization ability across diverse scenes.  
The experiments were conducted on a Windows 11 operating system, using Python 3.8 and PyTorch 1.9.0 as the deep learning framework. To accelerate computation, CUDA 11.1 was employed, and the training was performed on an NVIDIA RTX 3090 GPU, paired with an Intel i7 13700k CPU and 32 GB of 3200 MHz memory.  
The models were trained with a batch size of 16, which provided a balance between memory usage and training stability. The Adam optimizer was utilized with default parameters (\(\beta_{1}=0.9\) and \(\beta_{2}=0.999\)) and a learning rate of 0.0002, which is commonly used in GAN training for effective convergence. The training process spanned 100 epochs, allowing ample time for the models to learn from the high-resolution dataset. Additionally, the weights of the networks were initialized using the Xavier initialization method to ensure stable training. This comprehensive setup ensured the efficiency and stability of both model training and evaluation.
## 2 Materials and Methods
### LOINC and the Property Axis  
LOINC is a clinical terminology developed by the Regenstrief Institute. It is used, among other applications, to identify laboratory observations and test results. LOINC's adoption into relevant communication standards such as HL7v2 with its OBX (observation) segment played a significant role in overcoming the heterogeneity introduced by countless local identifiers used across different institutions. An important aspect that helped facilitate the acceptance of LOINC was the freely available tool RELMA, which aids users in mapping their locally used, proprietary identifiers to standardized LOINC codes [13; 14].  
Each LOINC code corresponds to a combination of five to six axis elements, as shown in Figure 1. In this project, two of the axes play a major role: Firstly, the _Scale_ type differentiates between, for example, qualitative, quantitative or nominal observations. Secondly, the type of _Property_ differentiates between the kinds of quantities relating to the same substance. These _Properties_ include concepts such as \"Substance (Molar) Concentration\", \"Mass per Area\", \"Number per Volume\" and many more. Quantitative entries make up 44,299 out of 98,268 total LOINC codes (roughly 45%) in the current LOINC version 2.72.
## 3 Methodology
### Optimization
By applying the shrinkage operator to the singular values of \(S-\frac{M_{3}}{u}\) element-wisely, the optimal updation of \(H\) is given by  
\[H=U_{1}S_{\frac{\varepsilon}{\varepsilon}}[S_{1}]V_{1}^{T} \tag{35}\]  
in which \(U_{1}\), \(S_{1}\) and \(V_{1}\) are the SVD factorization  
\[\left[U_{1},\ S_{1},\ V_{1}^{T}\right]=\text{SVD}\bigg{(}S-\frac{M_{3}}{u} \bigg{)} \tag{36}\]  
(7) Update \(\tau\): By fixing the other variables, the optimization formula for \(\tau\) becomes  
\[\underset{\tau_{q}^{i}}{\max}- \frac{1}{2}\sum_{p=1}^{l}\sum_{h,i=1}^{N}\beta_{p}^{h}\beta_{p}^{i }K(u_{i},u_{j})+\sum_{i=1}^{N}\sum_{p\in\Upsilon_{i}^{\tau}}\sum_{q\in \Upsilon_{i}^{\tau}}\tau_{pq}^{i}\] \[s.t.\ \ \tau_{jq}^{i}\in[0,C],\ \sum_{i=1}^{N}\sum_{j\in\Upsilon_{i}^{ \tau}}\sum_{q\in\Upsilon_{i}^{\tau}}c_{jq}^{i}\tau_{jq}^{i}=0,\text{for}\ p=1,\ldots,l \tag{37}\]  
Then, we can obtain the optimal solution of Equation (37) through the general Quadratic programming solution method or SMO algorithm. (8) Update \(u\), \(M_{1}\), \(M_{2}\) and \(M_{3}\): Finally, we need to update the ALM parameters  
\[M_{1}=\ M_{1}+u\Big{(}E-X+VUl^{T}\Big{)} \tag{38}\] \[S_{ij}-\left(N_{ij}-G_{ij}/2^{\tau}\right)-\eta-\zeta_{i}=0 \tag{31}\]0 (39) \[S_{ij}-\left(N_{ij}-G_{ij}/2^{\tau}\right)-\eta-\zeta_{i}=0 \tag{31}\]1\[S_{ij}-\left(N_{ij}-G_{ij}/2^{\tau}\right)-\eta-\zeta_{i}=0 \tag{31}\]2  
where the parameter \(\rho>1\) is the learning rate that controls the convergence speed. The flowchart of the proposed approach is presented in Algorithm 1. ```
1:Input: Training set \(\{X_{1},\ldots,X_{n}\}\in\mathbb{R}^{d\times n}\), parameter \(\alpha\), \(\gamma\), \(\theta\)
2:Initialize: \(M_{1}=M_{2}=M_{3}=0,U=0,V=0,E=0,Z=0,S=0,H=0\)
3:while not converged do
4: Fix others and update \(U\) by Equation (12)
5: Fix others and update \(V\) by Equation (16)
6: Fix others and update \(E\) by Equation (21)
7: Fix others and update \(Z\) by Equation (24)
8: Fix others and update \(S\) by Equation (32)
9: Fix others and update \(H\) by Equation (35)
10: Fix others and update \(\tau\) by solving Equation (37)
11:endwhile
12:Output: The correlation matrices \(U\), \(V\) and \(\tau\). ```  
**Algorithm 1** The proposed approach.
## 5 The Lattice Property
### Generalization of [PERSON]'s Theorem  
In this subsection, we show a lattice property of stable sets (rather than stable pairs).  
**Definition 14**.: Define a new partial order: for choice function \(F\), let \(S^{\prime}\leq_{F}S\) if \(F(S\cup S^{\prime})=S\).  
**Observation 1**.: _[_3_]_ _If \(F\) is substitutable and path independent, then \(\leq_{F}\) is indeed a partial order; in particular, \(A\leq_{F}B\leq_{F}C\) implies \(A\leq_{F}C\)._  
[PERSON] proved the lattice property of dominating stable sets assuming the path-independent property of the choice functions [3]. As we will see in Theorem 15, if \(F\) and \(G\) are both path independent, the dominating stability, three-stability and four-stability are equivalent, so [PERSON]'s theorem holds for each of these notions.  
**Theorem 10** ([PERSON]).: _[_3_]_ _If \(F,G:2^{E}\to 2^{E}\) are substitutable, path-independent choice functions, then the dominating stable sets form a lattice for partial order \(\leq_{F}\)._  
We generalize the above lattice property for four-stability, and there is a close connection between score-stability and four-stability. Now, we require path independency on only one side.  
**Theorem 11** (Generalization of [PERSON]'s theorem).: _If \(F\) and \(G\) are substitutable choice functions and \(F\) is path independent, then: The four-stable sets form a lattice for partial order \(\leq_{F}\); If \(S\) is a four-stable set, then, there is a unique four-stable pair \((A,B)\) that corresponds to \(S\); furthermore, \(S\leq_{F}S^{\prime}\) if and only if \((A,B)\leq(A^{\prime},B^{\prime})\)._  
If only one of \(F\) and \(G\) is path independent, dominating stable sets do not form a lattice. Moreover, dominating stable sets do not necessarily exist, as we have seen is Subsection 3.1.  
**Example 8**.: _Given one college, \(C_{1}\), and two applicants, \(A_{1},A_{1}\), and two contracts, \(a=A_{1}C_{1}\) and \(b=A_{2}C_{1}\). The college has a quota of one, and both applicants want to go to \(C_{1}\); so, \(G=Q_{1},\)\(F=Q_{2}\). The dominating stable solutions are \(\{a\}\) and \(\{b\}\); however, \(a\) and \(b\) are uncomparable, since \(F(\{a,b\})=\{a,b\}\). Therefore, the dominating stable sets do not form a lattice._  
**Remark 4**.: _If \(F\) and \(G\) are substitutable choice functions, but none of them is path independent, then the lattice property does not always hold for four-stability. It is also false that for stable set \(S\) there is only one corresponding \((A,B)\) pair._  
**Example 9**.: _We have two contracts, \(a\) and \(b\). The choice function is \(Q_{1}\) for both sides. In this situation, we have four four-stable pairs:_  
\[A=\emptyset B=\{a,b\} S=\emptyset\] \[A=\{a\} B=\{a\} S=\{a\}\] \[A=\{b\} B=\{b\} S=\{b\}\] \[A=\{a,b\} B=\emptyset S=\emptyset\]  
_Now, \(\emptyset\leq_{F}\{a\}\) and \(\emptyset\leq_{F}\{b\}\), but \(\{a\}\) and \(\{b\}\) are uncomparable. Therefore, these two sets do not have a supremum._
# A Study of MANET Routing Protocols in Heterogeneous Networks: A Review and Performance Comparison
## 3 Simulation Environment and Settings
### Performance Metrics  
To study the performance of the four selected MANET routing protocols in heterogeneous networks, we considered the following three performance metrics, including the throughput, end-to-end delay, and packet delivery ratio, which were appropriate for our investigation. The simulation model we created can record several statistics, such as the number of packets being routed and delivered over a given period and the latencies in message forwarding. The throughput is measured in bits per second and is the total number of packets delivered to the receiver. The end-to-end delay (in sec) is the average time that a packet takes from a source node to the destination. The packet delivery ratio is a performance metric that measures the ratio of packets received to those generated by their sources.
## 3 Applications of the Tactile Internet
### Education  
The TI will empower enhanced learning dependent on the haptic overlay of the educator and learner. By consolidating TI with VR and AR, comprehension-based learning will boost the learner's interests and surpass traditional learning methods. Subsequently, the learner will pursue an opportunity to adapt generally through exploring and discovering the content available. A plus point will be that there will be less interference from the educator and no educator pressure on the learner to study. With the incorporation of VR-based study-related applications in the learner's curriculum, the learner would be fully immersed in tactile learning by touching virtual things provided with haptic feedback, as illustrated in Figure 7.
# SOUNET: Self-Organized Underwater Wireless Sensor Network
## 4 Construction and Operation of SOUNET
### Phase 2: Network Maintenance
#### 4.2.4 Temporary Closed Loop and Its Cure  
Since SOUNET relies on local information (neighbor table), which requires time to be updated, a temporal discrepancy between the neighbor tables occurs. Such a discrepancy may temporarily create a closed loop. However, it is easy to cure a _temporary closed loop_ through the neighbor table update. Figure 7 illustrates the formation and curing of a temporary closed loop.  
Assume that the node 3 accidently loses connection to the current parent node 1, which is alive. Then, not recognizing the existence of node 2, node 3 selects node 4 as the new parent (Figure 7a) and accordingly the \(LV\) of node 3 is changed from \(i+1\) to \(i+5\). Meanwhile, node 2 also accidently loses connection to node 1 before knowing the \(LV\) of node 3 is updated and selects node 3 as the parent based on the neighbor table which shows that the \(LV\) of node 3 is still \(i+1\). Consequently, a loop consisting of nodes from 2 to 6 is temporarily formed. However, the loop is easily eliminated if either node 2 or node 3 overhears a packet from node 1 anytime afterwards (Figure 7b).
## 3 Results and Discussion
### Investigation of Peptide Coupling Using UV-Visible Spectroscopy
#### 3.1.1 Evaluation of Ligand Coupling to Gold Nanoparticle Surfaces by FTIR  
FTIR spectroscopy was employed to detect changes to the characteristic bands of thiol after Au NP coupling, as free thiol is expected to bind to the Au NP surface via thiolate bonds. Generally, amino acids exist as zwitterions and display spectra featuring both primary amine and carboxylate functional groups. The bands for NH3\({}^{+}\) stretch (very broad), NH bend (asymmetric/symmetric), and COO\({}^{-}\) (carboxylate ion) stretch (asymmetric/symmetric) are typical for this type of compound [24]. In the case of the GPDCALNNC peptide composed of nine amino acids, the main focus was to look for changes in the thiol group in the cysteine. Figure 2 shows the FTIR spectra of the GPDCALNNC before and after coupling to Au NPs. The band in spectrum A at 1652 and 1385 cm\({}^{-1}\) corresponds to the asymmetric and symmetric stretching of COO\({}^{-}\). A band at 1522 cm\({}^{-1}\) corresponds to NH bend and the very broad band of NH3\({}^{+}\) stretch was observed in the 3000-3500 cm\({}^{-1}\) range. In addition, a weak band near 2550 cm\({}^{-1}\) confirms the presence of the SH group in the cysteine molecule. These values are in good agreement to those reported by [PERSON] et al. (2006) for cysteine-capped Au NPs [25].  
Figure 1: UV-vis absorption spectrum of modified Au NPs. Inset: TEM images (scale bar 20 nm) (black: (**A**) GPDCALNNC-, blue: (**B**) GPG- EN-PEG4-LA-, and red: (**C**) C/G-capped Au NPs).  
These results are in good agreement with the IR spectra of peptides or amino acids, but the characteristic SH band around 2500-2600 cm\({}^{-1}\) seems to be very weak because of the low levels of sulphur in the peptide. However, small changes in the absorption spectra were detected in the case of GPDCALNN-capped Au NPs (spectra B). A shift in the position of COO\({}^{-}\) and NH\({}_{3}\)\({}^{+}\) stretching is likely due to a change in their dipole moment, when cysteine binds on a metal surface with high electron density. Although significant band changes due to SH were not observed in the spectra of the free and NP-coupled peptide, other bands of COO\({}^{-}\) and NH\({}_{3}\)\({}^{+}\) in spectrum B encountered a displacement that may indicate the peptide coupling to the Au NP surface.
# Energy-Aware System Design for Autonomous Wireless Sensor Nodes: A Comprehensive Review
## 3 Energy Supply for Wireless Sensor Nodes
### Overview of Energy Converters
\begin{table}
\begin{tabular}{c c c c c} \hline
**Sources** & **Harvesting Methods** & **Power Density** & **Characteristics** & **Availability** \\ \hline Solar [17] & Photovoltaic & 15 mW/cm\({}^{2}\) & Performance depending on the solar cell technology and & Outdoor \\  & & +10 \(\mu\)W/cm\({}^{2}\) & & on environmental conditions. & Indoor \\ \hline Wind [20] & Electromechanical conversion & 0.1-6 mW/m\({}^{3}\) & Impedance matching needed to achieve a good energy yield. & Outdoor \\ \hline Vibration [6; 14; 15; 18; 20; 21] & Piezoelectric/ & & & \\ electromagnetic/ & & & & \\ electromagnetic/ & & & & \\ magnetoelectric conversion/ & & & & \\ triboelectric vibration & & & & \\ \hline Thermal [19] & Thermoelectric conversion & 40 \(\mu\)W/cm\({}^{3}\) & Application needs to realize a sufficient temperature gradient. & Indoor/ \\  & & & & Impedance matching needed & Outdoor \\ \hline Ocean waves [34] & Piezoelectric conversion & 0.4-2 W/m\({}^{2}\) & & \\ Triboelectric conversion & 12 W/m\({}^{3}\) & & & \\ \hline Acoustic noise [35] & Piezoelectric conversion & & & \\ Triboelectric Conversion & & & \\ \hline RF [9] & Electromagnetic conversion & 0.1 \(\mu\)W/cm\({}^{2}\) (GSM 900 MHz) & & \\  & & 1 \(\mu\)W/cm\({}^{2}\) (WIF) & Impedance matching needed & \\ \hline \end{tabular}
\end{table} 
Table 1: Selection of energy sources for supplying wireless sensors.
## 4 Using the Compact Topological Maps to Localize the Robot
### Distance Measures between Descriptors  
In order to know how similar two panoramic images are through their global appearance descriptors, some distance measurements have been used. This way, a comparison can be carried out by calculating the distance between the descriptors of two images captured from different positions of the environment. The lower the distance between those images is, the more similar they are. This kind of distance is used in the localization step. We consider two descriptors \(\overrightarrow{a}\in\mathbb{R}^{l\times 1}\) and \(\overrightarrow{b}\in\mathbb{R}^{l\times 1}\), where \(a_{i}\) and \(b_{i}\) are the \(i^{\text{th}}\) components of \(\overrightarrow{a}\) and \(\overrightarrow{b}\) with \(i=1,...,l\). The distances used in this work are:  
* Euclidean distance: This a particular case of the the weighted metric distance and is defined as: \[dist_{\text{euclidean}}(\overrightarrow{a},\overrightarrow{b})= \sqrt{\sum_{i=1}^{l}(a_{i}-b_{i})^{2}}\] (3)
* Cosine distance: Departing from a similitude metric, which is defined as the scalar product between two vectors, the distance is defined as: \[dist_{\text{cosine}}(\overrightarrow{a},\overrightarrow{b})=1- sim_{\text{cosine}}(\overrightarrow{a},\overrightarrow{b})\] (4) \[sim_{\text{cosine}}(\overrightarrow{a},\overrightarrow{b})= \frac{\overrightarrow{a}^{T}\cdot\overrightarrow{b}}{|\overrightarrow{a}|| \overrightarrow{b}|}\]
* Correlation distance: Again, departing from a similitude metric, which is defined as a normalized version of the scalar product between two vectors, the distance is defined as: \[dist_{\text{correlation}}(\overrightarrow{a},\overrightarrow{b})=1- sim_{\text{correlation}}(\overrightarrow{a},\overrightarrow{b})\] (5) \[sim_{\text{correlation}}(\overrightarrow{a},\overrightarrow{b})= \frac{(\overrightarrow{a}-\overrightarrow{a})^{T}(\overrightarrow{b}- \overrightarrow{b})}{\sqrt{(\overrightarrow{a}-\overrightarrow{a})^{T}( \overrightarrow{a}-\overrightarrow{a})}\sqrt{(\overrightarrow{b}- \overrightarrow{b})^{T}(\overrightarrow{b}-\overrightarrow{b})}}\] where: \[\overrightarrow{a}=\frac{1}{l}\sum_{i=1}^{l}a_{i};\hskip 28.452756 pt \overline{b}=\frac{1}{l}\sum_{i=1}^{l}b_{i}\] (6)  
Previous research works [21; 36] have evaluated the relation between the distance between the global appearance descriptors and the geometrical distance between capture points. These works show that even if the robot moves a short distance, the descriptor changes. Therefore, global appearance descriptors can be used to detect even small movements.
# Measurement of Static Stiffness after Motion on a Three-Axis CNC Milling Table
## 3 Experimental Comparison of Static Stiffness Measurement Methods
### Second Experiment (Measurement)--Modified Static Stiffness Measurement across All Positions  
The duration of one cycle was approximately 5 min. Over that time, the individual parts of the kinematic chain were heated and caused a thermal expansion of the table. With acceptable accuracy, the increase in expansion over the measured period can be considered linear. For example, in Figure 9, it is visible that after 9 load-free cycles, the first position shifted by about 10 micrometers. An average shift from the direction of the position change can be calculated at each position. The calculation procedure involving the direction is important in order to eliminate deviations caused by other random effects as much as possible. For example, in Figure 9, it is visible that in position 1, the temperature slope is 1.1283. This value is given by the trend line equation obtained by the least squares method.  
By the same procedure, the maximum thermal deviations for the load cycles at each position were determined. The difference between the maximum load-free and load displacement value yields a real deformation by the maximum load force. In Table 1, the maximum load force was 173 N. From this, the stiffness was determined at each position in both directions of the table's assumption of that position.  
The greatest stiffness was demonstrated at position 8. This corresponds to the fact that there is a small distance between the bearing and the nut in this position. The sliding screw is least likely to cause stiffness deterioration at this position, as its active distance is shorter.  
Figure 8: Stiffness measurement at position 8 (second round of load application). Trend line slope defines stiffness (169 N/\(\upmu\)m).  
Figure 9: Gradual thermal shift of the first position during 9 load-free cycles. The trend line equation determines the direction.
# Secure Proxy Re-Encryption Protocol for FANETs Resistant to Chosen-Ciphertext Attacks
## 3 Preliminaries
### Security Building Blocks
Given a public key pk and a message_ \(m\) _in the message space, the encryption algorithm EnC produces a ciphertext_ \(C\)_._
* _DeC(sk, C)_ \(\rightarrow\)__m. With the input of a secret key sk and a ciphertext_ \(C\)_, the decryption algorithm DeC robustly generates a message_ \(m\) _within the message space or_ \(\bot\)__[17]_._  
_ElGamal: ElGamal cryptography provides security based on the difficult mathematical problem of finding the private key_ \(x\) _from the public key_ \(y\)_._  
* _Key generation:_
* _Select a mathematically secure large prime_ \(p\) _and a primitive root_ \(g\) _modulo_ \(p\)_._
* _Choose a random private key_ \(x\)_. Compute the public key_ \(y=g^{x}\mod p\)_._
* _Encryption:_
* _Choose a random_ \(k\) _such that_ \(0<r<p-1\)_._
* _Compute:_ \(C_{1}=g^{r}\) _mod_ \(p\) _and_ \(C_{2}=\left(y^{r}\cdot m\right)\mod p\) _to generate the ciphertext_ \(C=\left(C_{1},C_{2}\right)\)_._
* _Decryption:_
* _Compute:_ \(D=C_{2}\cdot C_{1}^{-x}=m\)__[19]._  
**Definition 7**. : _Unidirectional Proxy Re-Encryption. The UniPRE(unidirectional proxy re-encryption) scheme is comprised of a set of PPT algorithms (KGen, RKeyGen, EnC, PrxyRE, DeC):_  
* _KGen, EnC, DeC: Similar to those found in public key encryption._
* _RKeyGen(sk\({}_{i}\), pk\({}_{j}\)) \(\to rk_{i\to j}\). Given a secret key \(sk_{i}\), a public key \(pk_{j}\), the re-encryption key generation algorithm, RKeyGen, produces a unidirectional re-encryption key \(rk_{i\to j}\)._
* _PrxyRE (rk\({}_{i\to j}\), C\({}_{1}\)) \(\to C_{2}\). Given a re-encryption key \(rk_{i\to j}\)  and a ciphertext C\({}_{1}\), the re-encryption algorithm PrxyRE produces a re-encrypted ciphertext C\({}_{2}\) or \(\bot\)[17]._  
**Definition 8**. : _Uni-PRE-CCA game. This security game based on [17] is too long and will be explained later in the proof. So, here, we will omit it for now and refer to [17] for details._  
**Definition 9**. : _Uni-PRE-CR(collusion resistance) security. It is said that a UniPRE scheme is collusion-resistant if, for any polynomially bounded adversary \(\mathcal{A}\), the probability described below is negligible:_  
\[ \begin{array}{l}\Pr[(sk_{1},pk_{1})\leftarrow\mathrm{KGen}(1^{k}),\{(sk_{i},pk_{i})\leftarrow\mathrm{KGen}(1^{k})\},\\ \{rk_{i\to 1}\leftarrow\mathrm{ReKeyGen}(sk_{i},pk_{1})\},\\ \{rk_{1\to i}\leftarrow\mathrm{ReKeyGen}(sk_{1},pk_{i})\},\\ i=2,\cdots,\\ \alpha\leftarrow\mathrm{A}(pk_{1},\{pk_{i},sk_{i}\},\{rk_{1\to i}\},\{rk_{i\to 1}\}).\end{array} \]  
_\(\alpha=sk_{1}\)[17]._
# Infrared Dim and Small Target Detection Based on the Improved Tensor Nuclear Norm
## 5 Construction and Solution of the Infrared Dim and Small Target Detection Model  
### Construction of the Model  
A previous study [17] obtained good detection results using the _PSTNN_ to constrain the background part of the infrared image; the _PSTNN_ was calculated as follows:  
\[\left\|\mathcal{A}\right\|_{PSTNN}=\sum_{i=1}^{n_{3}}\left\|\overline{A}^{(i)}\right\| \tag{20}\]  
where \(\overline{A}^{(i)}\) denotes the frontal slice i of tensor \(\mathcal{A}\) after the Fourier transform. The infrared dim and small target detection model constructed was also used in this study, and the model is as follows [17]:  
\[\begin{array}{l}\underset{\mathcal{A},\mathcal{T}}{\text{min}}\left\| \mathcal{A}\right\|_{PSTNN}+\lambda\left\|\mathcal{T}\odot\mathcal{W}\right\| _{1}\\ s.t.\mathcal{D}=\mathcal{A}+\mathcal{T}\end{array} \tag{21}\]  
where \(\odot\) denotes the Hadamard product, and \(\mathcal{D},\mathcal{A},\mathcal{T}\) represents the original tensor block image, the background tensor block image, and the target tensor block image, respectively. The flow chart of the model is shown in Figure 5. During the operation of the algorithm, we learned that the number of sparse components in the target tensor block image does not change after several iterations, so two bases were used as the judgment conditions for stopping the iteration, representing a relative error of \(\left(\left\|\mathcal{A}+\mathcal{T}-\mathcal{D}\right\|_{F}^{2}\right/\left\| \mathcal{D}\right\|_{F}^{2}\leq\sigma\), where \(\sigma\) is a given threshold) and \(\left\|\mathcal{T}^{k+1}\right\|_{0}=\left\|\mathcal{T}^{k}\right\|_{0}\).