using Images, FileIO, LinearAlgebra, Plots

# Specify the path to your local image file
img_path = "C:\\Users\\User\\Downloads\\SVD_PAPER\\cats_medium.jpg"
img = load(img_path)
img_gray = float.(Gray.(img))

function rank_approx(F::SVD, k)
    U, S, V = F
    # Ensure k does not exceed the dimensions
    k = min(k, size(U, 2), size(V, 2))
    # Approximation using the first k singular values
    M = U[:, 1:k] * Diagonal(S[1:k]) * V[:, 1:k]'
    clamp01!(M)
    return M
end

# Compute SVD of grayscale image
svdfactor = svd(img_gray)

# Create compressed images for k = 10, 50, 100
ks = [10, 50, 100]
imgs = map(ks) do k
    Gray.(rank_approx(svdfactor, k))
end

plot(mosaicview(img_gray, imgs...; nrow=1, npad=10))