My research project
I am a 3rd year PhD student at the Centre for Vision, Speech and Signal Processing (CVSSP), under the supervision of Wenwu Wang and Mark Plumbley.
My research interests include sparse decomposition and dictionary learning for various inverse problems in signal processing, such as denoising, inpainting or declipping. More generally, I am interested in matrix factorization, sparse/low-rank decomposition, statistical learning and optimization, with application to signal processing.
You can find more details on my personal webpage: http://www.cvssp.org/Personal/LucasRencker/
consecutive sparse signals, such as audio time frames or image
patches. A typical approach is to process each signal sequentially
and independently, with an arbitrary sparsity level fixed for each
signal. Here, we propose to process several frames simultaneously,
allowing for more flexible sparsity patterns to be considered. We
propose a multivariate sparse coding approach, where sparsity
is enforced on average across several frames. We propose a
Multivariate Iterative Hard Thresholding to solve this problem.
The usefulness of the proposed approach is demonstrated on
audio coding and denoising tasks. Experiments show that the
proposed approach leads to better results when the signal
contains both transients and tonal components.
Covariance-Assisted Matching Pursuit,IEEE Signal Processing Letters 25 (6) pp. 828-832 IEEE
(CAMP) method has recently been proposed. Given a priorknowledge
of the covariance and mean of the sparse coefficients,
CAMP balances the least squares estimator and the priorknowledge
by leveraging the Gauss-Markov theorem. In this
letter, we study the performance of CAMP in the framework
of restricted isometry property (RIP). It is shown that under
some conditions on RIP and the minimum magnitude of the
nonzero elements of the sparse signal, CAMP with sparse level
K can recover the exact support of the sparse signal from
noisy measurements. l2 bounded noise and Gaussian noise are
considered in our analysis.We also discuss the extreme conditions
of noise (e.g. the noise power is infinite) to simply show the
stability of CAMP.
declipping,Latent Variable Analysis and Signal Separation. LVA/ICA 2018. Lecture Notes in Computer Science 10891 pp. 446-455 Springer Verlag
signal processing. Recently, declipping techniques have been proposed
based on sparse decomposition of the clipped signals on a fixed dictionary,
with additional constraints on the amplitude of the clipped samples.
Here we propose a dictionary learning approach, where the dictionary
is directly learned from the clipped measurements. We propose a soft-consistency
metric that minimizes the distance to a convex feasibility
set, and takes into account our knowledge about the clipping process.
We then propose a gradient descent-based dictionary learning algorithm
that minimizes the proposed metric, and is thus consistent with the clipping
measurement. Experiments show that the proposed algorithm outperforms
other dictionary learning algorithms applied to clipped signals.
We also show that learning the dictionary directly from the clipped signals
outperforms consistent sparse coding with a fixed dictionary.
tool for audio analysis. However, it is not well suited
for learning on weakly labeled data, i.e. data where the exact
timestamp of the sound of interest is not known. In this paper
we propose a novel extension to NMF, that allows it to extract
meaningful representations from weakly labeled audio data.
Recently, a constraint on the activation matrix was proposed
to adapt for learning on weak labels. To further improve the
method we propose to add an orthogonality regularizer of the
dictionary in the cost function of NMF. In that way we obtain
appropriate dictionaries for the sounds of interest and background
sounds from weakly labeled data. We demonstrate
that the proposed Orthogonality-Regularized Masked NMF
(ORM-NMF) can be used for Audio Event Detection of rare
events and evaluate the method on the development data from
Task2 of DCASE2017 Challenge.
signal from clipped or quantized measurements. We show how
these two problems can be formulated as minimizing the distance
to a convex feasibility set, which provides a convex and
differentiable cost function. We then propose a fast iterative
shrinkage/thresholding algorithm that minimizes the proposed
cost, which provides a fast and efficient algorithm to recover
sparse signals from clipped and quantized measurements.