Advanced Hyperspectral Image Analysis: Superpixelwise Multiscale Adaptive T-HOSVD for 3D Feature Extraction

. 2024 Jun 22;24(13):4072. doi: 10.3390/s24134072

Algorithm 1: Superpixelwise Multiscale Adaptive T-HOSVD(SmaT-HOSVD)

Input:

Hyperspectral image X \in ℝ^{I_{1} \times I_{2} \times I_{3}}

, ground truth label L \in ℝ^{I_{1} \times I_{2}}

, number of superpixels S, reduction dimensionality n, threshold T¹ and T^2.

1:
The first principal component $X^{'}$ $is obtained by applying PCA to X$ is obtained by applying PCA to $X$ .
2:
Apply Equation (7) to get superpixels $I_{f}$
3:
$While X_{k}$ $in {I_{f}$ } do
4:
$Fill X_{k}$ $to get the standard tensor X_{k}^{'}$
5:
$Apply Equations (8) and (9) to compute the optimal rank of X_{k}^{'}$
6:
$Apply Equations (5) and (6) for X_{k}^{'}$ $to obtain the low - rank representations Y^{1} and Y^{2}$
7:
$Apply Equation (10) to get multiscale representation \tilde{Y} = [Y^{1}, Y^{2}]$
8:
Apply Equation (11) get results y
9:
$Update the superpixel X_{k}$ $with the result Y$ with the result $Y$
10:
k ← k+1
11:
End while
12:
$Updating X \in ℝ^{I_{1} \times I_{2} \times n}$ with superpixels $I_{f}$
13:
$Training and testing of X$ $and L$ using SVM

OUTPUT: Classification results