A discrete universal denoiser and its application to binary images

In a recent work, the authors introduced a discrete universal denoiser (DUDE) for recovering a signal with finite-valued components corrupted by finite-valued, uncorrelated noise. The DUDE is asymptotically optimal and universal, in the sense of asymptotically achieving, without access to any information on the statistics of the clean signal, the same performance as the best denoiser that does have access to such information. It is also practical, and can be implemented in low complexity. In this work, we extend the definition of the DUDE to two-dimensionally indexed data, and present results of an implementation of the scheme for binary images. Section 2 presents the problem setting, definitions, and notation used throughout the paper. Section 3 describes the DUDE for two-dimensional data (this description readily extends to higher dimensions). Section 4 presents theoretical performance guarantees establishing the DUDE's asymptotic optimality. The denoiser assumes a particularly simple form for binary alphabets, which is presented in Section 5. Practical considerations in the implementation of the binary scheme are presented in Section 6, while experimental results of its application to noisy binary images are presented in Section 7, In the examples considered we find that the DUDE outperforms current popular schemes for binary image denosing. Finally, in Section 8 we discuss conclusions and directions for ongoing and future research.