6 research outputs found
Discrete Denoising with Shifts
We introduce S-DUDE, a new algorithm for denoising DMC-corrupted data. The
algorithm, which generalizes the recently introduced DUDE (Discrete Universal
DEnoiser) of Weissman et al., aims to compete with a genie that has access, in
addition to the noisy data, also to the underlying clean data, and can choose
to switch, up to times, between sliding window denoisers in a way that
minimizes the overall loss. When the underlying data form an individual
sequence, we show that the S-DUDE performs essentially as well as this genie,
provided that is sub-linear in the size of the data. When the clean data is
emitted by a piecewise stationary process, we show that the S-DUDE achieves the
optimum distribution-dependent performance, provided that the same
sub-linearity condition is imposed on the number of switches. To further
substantiate the universal optimality of the S-DUDE, we show that when the
number of switches is allowed to grow linearly with the size of the data,
\emph{any} (sequence of) scheme(s) fails to compete in the above senses. Using
dynamic programming, we derive an efficient implementation of the S-DUDE, which
has complexity (time and memory) growing only linearly with the data size and
the number of switches . Preliminary experimental results are presented,
suggesting that S-DUDE has the capacity to significantly improve on the
performance attained by the original DUDE in applications where the nature of
the data abruptly changes in time (or space), as is often the case in practice.Comment: 30 pages, 3 figures, submitted to IEEE Trans. Inform. Theor
Discrete denoising of heterogenous two-dimensional data
We consider discrete denoising of two-dimensional data with characteristics
that may be varying abruptly between regions.
Using a quadtree decomposition technique and space-filling curves, we extend
the recently developed S-DUDE (Shifting Discrete Universal DEnoiser), which was
tailored to one-dimensional data, to the two-dimensional case. Our scheme
competes with a genie that has access, in addition to the noisy data, also to
the underlying noiseless data, and can employ different two-dimensional
sliding window denoisers along distinct regions obtained by a quadtree
decomposition with leaves, in a way that minimizes the overall loss. We
show that, regardless of what the underlying noiseless data may be, the
two-dimensional S-DUDE performs essentially as well as this genie, provided
that the number of distinct regions satisfies , where is the total
size of the data. The resulting algorithm complexity is still linear in both
and , as in the one-dimensional case. Our experimental results show that
the two-dimensional S-DUDE can be effective when the characteristics of the
underlying clean image vary across different regions in the data.Comment: 16 pages, submitted to IEEE Transactions on Information Theor
A Universal Scheme for WynerâZiv Coding of Discrete Sources
We consider the WynerâZiv (WZ) problem of lossy compression where the decompressor observes a noisy version of the source, whose statistics are unknown. A new family of WZ coding algorithms is proposed and their universal optimality is proven. Compression consists of sliding-window processing followed by LempelâZiv (LZ) compression, while the decompressor is based on a modification of the discrete universal denoiser (DUDE) algorithm to take advantage of side information. The new algorithms not only universally attain the fundamental limits, but also suggest a paradigm for practical WZ coding. The effectiveness of our approach is illustrated with experiments on binary images, and English text using a low complexity algorithm motivated by our class of universally optimal WZ codes