Toward properties of twice-universality in denoising

We propose a new sequence of universal denoisers motivated by the goal of extending the notion of twice-universality from universal data compression theory to the sliding window denoising setting. Given a sequence length n and a denoiser, we define the twice-universality penalty of the denoiser as the worst case excess expected denoising loss relative to sliding window denoisers with window length k above and beyond the worst case excess loss of DUDE with parameter k. Given a sequence of window parameters k_n, increasing in n sufficiently fast, we use loss estimators to construct a sequence of denoisers that achieves a much smaller twice-universality penalty for k <; k_n than the sequence of DUDEs with parameter k_n.