Add to ORKGThis paper describes the construction of second generation bandelet orthogonal bases. The decomposition on a ban-delet basis is computed using a wavelet filter bank followed by adaptive geometric orthogonal filters, that require O(N) operations. The resulting geometry is multiscale and calcu-lated with a fast procedure that minimizes a Lagrangian cost at each scale. Image compression with the resulting ban-delet transform code gives significantly better results than a wavelet transform code. 1