|dc.description.abstract||In the past decade, much progress has been made in image denoising due to the use
of low-rank representation and sparse coding, the performance of image denoising has
been boosted drastically by nonlocal algorithms and sparse coding techniques. In the
meanwhile, state-of-the-art algorithms also rely on an iteration step to boost the denoising
In this dissertation, first, we take a nonlocal approach to image denoising and formulate
the problem as one of collaborative least minimum mean square error (LMMSE) estimations
from grouped image patches. We show that our optimal LMMSE solution amounts
to shrinking the singular values of the matrix representation of the grouped image patches.
This interpretation of our solution allows us to relate our estimation-theoretic approach
to other nonlocal algorithms and sparse coding techniques in the literature. In addition,
we develop an iterative algorithm to find the best LMMSE estimate. Experimental results
show that our proposed denoising algorithm achieves better peak-signal-noise-ratio
(PSNR) and subjective performance than the state of the art.
Second, we advanced the boosting step from fixed or non-adaptive to adaptive, started
from the statistical analysis of boosting techniques, prove the advantage of adaptive boosting
approach, then performed rank-1 based fixed-point analysis, guided by our analysis,
we develop the first adaptive boosting (AB) algorithm, whose convergence is guaranteed.
Preliminary results on the same image dataset show that AB uniformly outperforms existing
denoising algorithms on every image and at each noise level, with more gains at higher