Infrared SmallTarget Detection Based on BackgroundSuppression Proximal Gradient and GPU Acceleration
Abstract
:1. Introduction
 A novel continuation strategy based on the Proximal Gradient (PG) algorithm is introduced to suppress strong edges. This continuation strategy preserves heterogeneous backgrounds as lowrank components, hence reducing false alarms.
 The APSVD is proposed for solving the LRSD problem, which is more efficient than the original SVD. Subsequently, parallel strategies are presented to accelerate the construction and reconstruction of patch images. These designs can reduce the computation time at the algorithmic and hardware levels, facilitating rapid and accurate solution.
 Implementation of the proposed method on GPU is executed and experimentally validate its effectiveness with respect to the detection accuracy and computation time. The obtained results demonstrate that the proposed method outperforms nine stateoftheart methods.
2. Related Work
2.1. HVSBased Methods
2.2. Deep LearningBased Methods
2.3. PatchBased Methods
2.4. Acceleration Strategies for PatchBased Methods
3. Method
3.1. BSPG Model
Algorithm 1: BSPG solution via APSVD 
3.2. APSVD
3.3. GPU Parallel Implementation
3.3.1. Construction
3.3.2. Reconstruction
Algorithm 2: The mapping of patch image and prefilter image 
Input: Patch image D, original image size w and h, patch size $dw$ and $dh$, step s, patch number of per row ${p}_{r}$ Output: prefilter image F

3.3.3. APSVD Using CUDA
4. Experiments and Analysis
4.1. Experimental Setup
4.2. Visual Comparison with Baselines
4.3. Quantitative Evaluation and Analysis
4.4. Ablation Study
5. Discussion
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Data  Image Size  Target Size  SCR  Background Type  Target Type  Detection Challenges  

Strong Edge  Low Contrast  Heavy Noise  Cloud Clutter  
SIR_1  256 × 172  11  6.52  cloud + sky  Irregular shape  ✓  
SIR_2  256 × 239  3  8.63  building + sky  Weak  ✓  ✓  ✓  
SIR_3  300 × 209  12  1.04  sea + sky  Low intensity  ✓  ✓  
SIR_4  280 × 228  2  3.09  cloud + sky  Weak, hidden  ✓  ✓  
SIR_5  320 × 240  7  11.11  cloud + sky  Hidden  ✓  
SIR_6  359 × 249  6  6.14  building + sky  Irregular shape  ✓  
SIR_7  640 × 512  4  10.52  cloud + sky  Weak, hidden  ✓  ✓  
SIR_8  320 × 256  5  5.36  sea + sky  Weak  ✓  
SIR_9  283 × 182  8  1.59  cloud + sea  Hidden  ✓  ✓  
SIR_10  379 × 246  3  10.57  building + sky  Low intensity  ✓  ✓  
SIR_11  315 × 206  5  9.61  cloud + sky  Low intensity  ✓  ✓  
SIR_12  305 × 214  17  8.43  tree + sky  Irregular shape  ✓  
SIR_13  320 × 255  4  4.12  cloud + sky  Low intensity  ✓  ✓  ✓  
SIR_14  377 × 261  6  2.38  cloud + sky  Low intensity  ✓  ✓ 
Method  Patch Size  Step  Parameter 

IPI [17]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min(m,n)},\epsilon ={10}^{7}$ 
RIPT [36]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min({n}_{1},{n}_{2},{n}_{3})},\epsilon ={10}^{7}$ 
NIPPS [20]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min(m,n)},\epsilon ={10}^{7}$ 
NRAM [22]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min(m,n)},\epsilon ={10}^{7}$ 
NOLC [23]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min\left(size\right(D\left)\right)},p=0.5,\epsilon ={10}^{7}$ 
PSTNN [38]  $40\times 40$  40  $L=0.7,\lambda =L/\sqrt{min({n}_{1},{n}_{2})\ast {n}_{3}},\epsilon ={10}^{7}$ 
SRWS [34]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{min(m,n)},\gamma =0.09/\sqrt{min(m,n)},\epsilon ={10}^{7}$ 
PFA [37]  $25\times 25$  25  $\kappa =30,{\tau}_{0}=1e+5,\epsilon ={10}^{5}$ 
LogTFNN [39]  $40\times 40$  40  $L=1,\lambda =L/\sqrt{min({n}_{1},{n}_{2})\times {n}_{3}}$, $\beta =0.01$, $\mu =200$ 
HLV [26]  $50\times 50$  10  $L=1,\lambda =L/\sqrt{max(m,n)},\alpha =1.3,\beta =2.5,C=8$ 
ANLPT [42]  $50\times 50$  10  $\lambda =sigmoid(E/{n}_{3})/\sqrt{min({n}_{1},{n}_{2})\times {n}_{3}}$, $E=entropy\left(T\right)$ 
Ours  $50\times 50$  10  $L=1,\lambda =L/\sqrt{max(m,n)},\epsilon ={10}^{7}$ 
Methods  IPI [17]  RIPT [17]  NIPPS [20]  NRAM [22]  NOLC [23]  PSTNN [38]  SRWS [34]  PFA [37]  LogTFNN [39]  HLV [26]  ANLPT [42]  Ours  

SIR_1  SCRG  2.08  2.55  0.05  2.76  2.58  1.81  2.78  0.03  1.56  2.85  NaN  20.67 
BSF  1.51  2.26  3.45  2.82  1.98  1.31  5.54  4.50  1.14  2.14  Inf  32.40  
SIR_2  SCRG  3.29  2.38  1.17  2.89  NaN  3.13  5.20  0.91  1.82  4.24  3.40  23.50 
BSF  1.05  0.59  0.26  0.75  Inf  0.80  2.48  0.40  0.48  1.08  0.83  7.20  
SIR_3  SCRG  137.56  NaN  102.47  235.38  NaN  90.23  NaN  32.40  11.80  NaN  NaN  151.21 
BSF  11.39  Inf  5.99  17.02  Inf  18.42  Inf  12.10  1.28  Inf  Inf  19.48  
SIR_4  SCRG  16.36  15.36  9.46  Inf  39.94  Inf  60.86  NaN  NaN  16.74  NaN  Inf 
BSF  3.55  3.47  2.04  Inf  8.80  Inf  13.90  Inf  Inf  3.61  Inf  Inf  
SIR_5  SCRG  2.18  5.60  0.68  4.79  4.96  1.53  6.57  2.39  1.41  1.82  0.01  7.81 
BSF  0.77  2.07  0.16  1.63  1.72  0.49  2.49  0.80  0.71  0.61  0.68  3.59  
SIR_6  SCRG  28.99  17.08  7.77  Inf  26.84  NaN  Inf  NaN  NaN  2.56  NaN  Inf 
BSF  32.21  6.18  1.96  Inf  8.08  Inf  Inf  Inf  Inf  0.90  Inf  Inf  
SIR_7  SCRG  275.57  Inf  Inf  NaN  NaN  5.36  NaN  2.13  3.42  351.29  NaN  Inf 
BSF  169.41  Inf  Inf  Inf  Inf  3.30  Inf  1.69  2.47  215.97  Inf  Inf  
SIR_8  SCRG  7.53  32.22  7.89  17.04  41.07  6.16  NaN  2.40  3.48  8.75  4.76  90.97 
BSF  3.98  25.67  3.28  9.77  43.57  4.50  Inf  192.28  1.82  4.88  2.39  69.74  
SIR_9  SCRG  24.34  25.51  11.86  Inf  NaN  14.85  Inf  5.41  18.08  23.11  NaN  Inf 
BSF  12.92  24.33  9.04  Inf  Inf  7.95  Inf  10.00  9.44  12.42  Inf  Inf  
SIR_10  SCRG  1.94  Inf  0.38  Inf  3.37  Inf  4.31  NaN  NaN  2.39  2.02  Inf 
BSF  1.04  Inf  0.16  Inf  1.85  Inf  2.47  Inf  Inf  1.30  1.36  Inf  
SIR_11  SCRG  2.57  NaN  0.87  NaN  NaN  NaN  10.58  NaN  0.06  Inf  1.73  Inf 
BSF  0.28  Inf  0.07  Inf  Inf  Inf  1.46  Inf  0.05  Inf  0.18  Inf  
SIR_12  SCRG  1.47  Inf  1.42  Inf  NaN  1.91  1.11  Inf  0.52  1.75  1.14  Inf 
BSF  0.73  Inf  0.62  Inf  Inf  1.02  1.75  Inf  0.25  0.91  0.55  Inf  
SIR_13  SCRG  1.58  Inf  0.30  Inf  Inf  5.67  Inf  NaN  NaN  31.94  Inf  Inf 
BSF  0.53  Inf  0.08  Inf  Inf  3.40  Inf  Inf  Inf  6.23  Inf  Inf  
SIR_14  SCRG  4.28  7.69  1.87  8.26  Inf  3.25  Inf  1.58  0.52  7.25  5.73  Inf 
BSF  1.55  2.79  0.48  3.09  Inf  1.14  Inf  0.63  0.19  2.88  2.06  Inf 
Image id  SIR_1  SIR_2  SIR_3  SIR_4  SIR_5  SIR_6  SIR_7  SIR_8  SIR_9  SIR_10  SIR_11  SIR_12  SIR_13  SIR_14 

IPI [17]  3.28  5.23  7.63  6.45  12.52  12.93  12.67  11.28  4.12  15.32  7.88  7.29  14.87  18.72 
RIPT [36]  1.17  2.76  2.02  2.82  4.70  2.88  8.01  4.35  0.96  1.85  1.02  1.40  2.12  2.14 
NIPPS [20]  1.88  3.34  3.60  3.56  5.51  6.82  7.11  6.71  2.84  9.18  3.95  3.99  7.51  9.96 
NRAM [22]  2.17  2.14  1.55  2.61  2.99  3.88  2.38  4.79  1.44  4.20  2.09  2.27  3.94  4.20 
NOLC [23]  0.72  0.86  1.11  1.15  1.24  1.67  3.62  1.64  0.94  3.17  1.55  1.28  1.33  2.11 
SRWS [34]  2.01  2.01  1.10  3.12  2.12  2.60  3.65  1.63  0.78  1.57  1.01  1.29  1.46  1.77 
HLV [26]  1.13  1.76  2.32  1.55  2.86  4.51  4.26  3.54  1.44  4.47  2.30  2.27  4.01  6.09 
ANLPT [42]  1.53  1.79  1.91  1.73  2.05  2.18  8.07  2.57  1.53  2.29  1.99  2.15  2.52  2.80 
Ours (CPU)  0.49  0.76  0.94  0.93  1.55  1.94  2.10  1.29  0.53  1.77  0.86  0.87  1.64  1.89 
Ours (GPU)  0.34  0.42  0.54  0.52  0.87  0.98  0.54  0.90  0.36  0.84  0.47  0.42  0.82  0.85 
Method  SIR_1  SIR_2  SIR_3  

(Patch, Step)  (25,25)  (40,40)  (50,10)  (25,25)  (40,40)  (50,10)  (25,25)  (40,40)  (50,10) 
PFA [37]  9.96  0.33  1.39  12.68  0.26  1.69  0.33  0.26  2.19 
PSTNN [38]  0.04  0.05  1.15  0.06  0.07  3.90  0.16  0.06  1.44 
LogTFNN [39]  0.89  1.33  15.06  1.22  1.81  11.63  1.27  1.38  26.92 
Ours(CPU)  0.12  0.13  0.49  0.19  0.17  0.76  0.16  0.14  0.94 
Ours(GPU)  0.02  0.02  0.34  0.04  0.02  0.42  0.02  0.01  0.54 
Matrix Height  MATLAB  CUDA  

SVD  SVDS  Lanczos  RSVD  APSVD  SGESVD  SGESVDJ  APSVD  
1000  1.03  6.68  4.59  7.67  0.53  9.07  5.75  1.06 
10,000  6.27  19.93  22.08  10.05  1.83  16.71  7.36  1.24 
100,000  280.12  406.70  298.77  50.82  11.82  /  24.06  9.58 
Image Size  Base  +PASVD  +New Continuation  +GPU Parallelism 

$200\times 150$  1.42  0.86  0.29  0.09 
$280\times 228$  6.23  4.91  1.12  0.41 
$320\times 256$  12.77  9.24  1.99  0.74 
$640\times 512$  13.60  7.33  2.31  0.59 
$1020\times 750$  57.79  34.6  7.32  2.38 
$1260\times 1024$  207.13  116.58  22.20  3.65 
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Hao, X.; Liu, X.; Liu, Y.; Cui, Y.; Lei, T. Infrared SmallTarget Detection Based on BackgroundSuppression Proximal Gradient and GPU Acceleration. Remote Sens. 2023, 15, 5424. https://doi.org/10.3390/rs15225424
Hao X, Liu X, Liu Y, Cui Y, Lei T. Infrared SmallTarget Detection Based on BackgroundSuppression Proximal Gradient and GPU Acceleration. Remote Sensing. 2023; 15(22):5424. https://doi.org/10.3390/rs15225424
Chicago/Turabian StyleHao, Xuying, Xianyuan Liu, Yujia Liu, Yi Cui, and Tao Lei. 2023. "Infrared SmallTarget Detection Based on BackgroundSuppression Proximal Gradient and GPU Acceleration" Remote Sensing 15, no. 22: 5424. https://doi.org/10.3390/rs15225424