Flying Small Target Detection for Anti-UAV Based on a Gaussian Mixture Model in a Compressive Sensing Domain

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. 2019 May 10;19(9):2168. doi: 10.3390/s19092168

Algorithm 1 Approach to flying small target detection based on GMM_CS.

Input: Flying small target image sequence

Output: Detection results of each image in sequence

1:
Initialize $N_{t r a i n}$ , $N_{d e t e c t}$ , s, m, $ξ$ , $α$ , $β$ , R, K, $ϵ$
2:
for $i = 1 to N_{t r a i n}$ do
3:
Break image into patches by Equation (11) and compressive sensing by Equation (3)
4:
Make GMM_CS for each patch by Equations (7)–(10)
5:
end for
6:
for $i = 1 to N_{d e t e c t}$ do
7:
Break image into patches by Equation (11) and compressive sensing by Equation (3)
8:
Identify candidate patches by Equations (7), (12), (13)
9:
for $j = 1 to N_{p a t c h}$ do
10:
Designate successive patches and compose a data matrix G
11:
repeat
12:
Set $k = 0$ , ${\hat{L}}_{0} = 0$ , ${\hat{S}}_{0} = 0$ , ${\hat{Ω}}_{L} = {}$ , ${\hat{Ω}}_{S} = {}$ , $P_{0} = G$
13:
Update indicator $k = k + 1$
14:
Identify supports: $Ω_{L}^{'} = arg max_{Ω \subset O} {∥ F_{Ω} (P_{k - 1}) ∥_{F} : | Ω | \leq 2 R}$
15:
Merging: ${\tilde{Ω}}_{L} = {\hat{Ω}}_{L} \cup Ω_{L}^{'}$
16:
Estimating: ${\tilde{L}}_{k} = arg min_{L} {∥ G - L - {\hat{S}}_{k - 1} ∥_{F} : L \in span ({\tilde{Ω}}_{L})}$
17:
Pruning: ${\hat{Ω}}_{L} = arg max_{Ω \subset O} {∥ F_{Ω} ({\tilde{L}}_{k}) ∥_{F} : | Ω | \leq R}$ , ${\hat{L}}_{k} = F_{{\hat{Ω}}_{L}} ({\tilde{L}}_{k})$
18:
Update residue: ${\tilde{P}}_{k} = G - {\hat{L}}_{k} - {\hat{S}}_{k - 1}$
19:
Identify supports: $Ω_{S}^{'} = arg max_{Ω \subset Q} {∥ H_{Ω} \cdot {\tilde{P}}_{k} ∥_{F} : | Ω | \leq 2 K}$
20:
Merging: ${\tilde{Ω}}_{S} = {\hat{Ω}}_{S} \cup Ω_{S}^{'}$
21:
Estimating: ${\tilde{S}}_{k} = arg min_{S} {∥ G - {\hat{L}}_{k} - S ∥_{F} : S = H_{Ω} \cdot {\tilde{P}}_{k}, Ω \subset {\tilde{Ω}}_{S}}$
22:
Pruning: ${\hat{Ω}}_{S} = arg max_{Ω \subset Q} {∥ H_{Ω} \cdot {\tilde{S}}_{k} ∥_{F} : | Ω | \leq K}$ , ${\hat{S}}_{k} = H_{{\hat{Ω}}_{S}} \cdot {\tilde{S}}_{k}$
23:
Update residue: $P_{k} = G - {\hat{L}}_{k} - {\hat{S}}_{k}$
24:
until $∥ G - {\hat{L}}_{k} - {\hat{S}}_{k} ∥_{F} / {∥ G ∥}_{F} \leq ϵ$
25:
end for
26:
Detect target over reconstructed sparse images by threshold segmentation
27:
end for