4 research outputs found
A Penalty Function Promoting Sparsity Within and Across Groups
We introduce a new weakly-convex penalty function for signals with a group
behavior. The penalty promotes signals with a few number of active groups,
where within each group, only a few high magnitude coefficients are active. We
derive the threshold function associated with the proposed penalty and study
its properties. We discuss how the proposed penalty/threshold function can be
useful for signals with isolated non-zeros, such as audio with isolated
harmonics along the frequency axis, or reflection functions in exploration
seismology where the non-zeros occur on the boundaries of subsoil layers. We
demonstrate the use of the proposed penalty/threshold functions in a convex
denoising and a non-convex deconvolution formulation. We provide convergent
algorithms for both formulations and compare the performance with
state-of-the-art methods
Sparsity Within and Across Overlapping Groups
Recently, penalties promoting signals that are sparse within and across
groups have been proposed. In this letter, we propose a generalization that
allows to encode more intricate dependencies within groups. However, this
complicates the realization of the threshold function associated with the
penalty, which hinders the use of the penalty in energy minimization. We
discuss how to sidestep this problem, and demonstrate the use of the modified
penalty in an energy minimization formulation for an inverse problem
SWAGGER: Sparsity Within and Across Groups for General Estimation and Recovery
Penalty functions or regularization terms that promote structured solutions
to optimization problems are of great interest in many fields. Proposed in this
work is a nonconvex structured sparsity penalty that promotes one-sparsity
within arbitrary overlapping groups in a vector. This allows one to enforce
mutual exclusivity between components within solutions to optimization
problems. We show multiple example use cases (including a total variation
variant), demonstrate synergy between it and other regularizers, and propose an
algorithm to efficiently solve problems regularized or constrained by the
proposed penalty.Comment: 7 pages, 5 figure
Determined BSS based on time-frequency masking and its application to harmonic vector analysis
This paper proposes harmonic vector analysis (HVA) based on a general
algorithmic framework of audio blind source separation (BSS) that is also
presented in this paper. BSS for a convolutive audio mixture is usually
performed by multichannel linear filtering when the numbers of microphones and
sources are equal (determined situation). This paper addresses such determined
BSS based on batch processing. To estimate the demixing filters, effective
modeling of the source signals is important. One successful example is
independent vector analysis (IVA) that models the signals via co-occurrence
among the frequency components in each source. To give more freedom to the
source modeling, a general framework of determined BSS is presented in this
paper. It is based on the plug-and-play scheme using a primal-dual splitting
algorithm and enables us to model the source signals implicitly through a
time-frequency mask. By using the proposed framework, determined BSS algorithms
can be developed by designing masks that enhance the source signals. As an
example of its application, we propose HVA by defining a time-frequency mask
that enhances the harmonic structure of audio signals via sparsity of cepstrum.
The experiments showed that HVA outperforms IVA and independent low-rank matrix
analysis (ILRMA) for both speech and music signals. A MATLAB code is provided
along with the paper for a reference