Name: VINÍCIUS ÁVILA DA SILVA

Publication date: 24/08/2018
Advisor:

Name	Role
EVANDRO OTTONI TEATINI SALLES	Advisor *

Examining board:

Name	Role
EVANDRO OTTONI TEATINI SALLES	Advisor *

Summary: A denoising algorithm seeks to remove or reduce noise from signals, and it’s specially used
for white noise. For one-dimensional signals, the discrete wavelet transform (DWT) and
the short-time Fourier transform (STFT) are the main transformations used in denoising,
and both present several parameters that should be selected by the user. Due to the great
influence those parameters have on the algorithm’s performance, the proposal of this work
is to develop a variation of the DWT denoising (wavelet shrinkage) in which the basis and
scale parameters are adapted to maximize the sparsity of the signal’s representation in the
wavelet domain. Due to the orthogonality of the transformation, the l1 norm was used as
an objective sparsity measure. Two variations of the denoiser were presented, with respect
to the number of basis that make up the dictionary. Tests were performed on several
signals for a comparison with the time-frequency block denoising in terms of performance
and computational cost. The results showed that the proposed techniques presented, on
average, higher mean performance than the time-frequency block denoising. With the use
of the Wilcoxon non-parametric statistical test, it was concluded that the use of a reduced
dictionary does not significantly affect the performance, even with the reduction of the
processing time by four times, approximately.
Keywords: Denoising. Wavelet Shrinkage. Stein Unbiased Estimate of Risk. Sparsity.

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