Randomized SVD Methods in Hyperspectral Imaging

Algorithm 2

The basic rSVD algorithm.

Input: An 𝑚×𝑛 matrix 𝐴 and rank 𝑘 with 𝑘≤𝑛≤𝑚.

Output: The rSVD of 𝐴: 𝑈,Σ,𝑉.

(1)  Generate a Gaussian random matrix Ω∈ℝ^𝑛×𝑘.

(2)  Form the projection of 𝐴: 𝑌=𝐴Ω.

(3)  Construct 𝑄∈ℝ^𝑚×𝑘 by Algorithm 1.

(4)  Set 𝐵=𝑄^𝑇𝐴∈ℝ^𝑘×𝑛.

(5)  Compute the SVD of 𝐵, 𝐵=𝑈Σ𝑉^𝑇.

(6)  𝑈=𝑄𝑈.