Complex and Quaternionic Principal Component Pursuit and Its Application to Audio Separation

01/09/2018
by   Tak-Shing T. Chan, et al.
0

Recently, the principal component pursuit has received increasing attention in signal processing research ranging from source separation to video surveillance. So far, all existing formulations are real-valued and lack the concept of phase, which is inherent in inputs such as complex spectrograms or color images. Thus, in this letter, we extend principal component pursuit to the complex and quaternionic cases to account for the missing phase information. Specifically, we present both complex and quaternionic proximity operators for the ℓ_1- and trace-norm regularizers. These operators can be used in conjunction with proximal minimization methods such as the inexact augmented Lagrange multiplier algorithm. The new algorithms are then applied to the singing voice separation problem, which aims to separate the singing voice from the instrumental accompaniment. Results on the iKala and MSD100 datasets confirmed the usefulness of phase information in principal component pursuit.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/09/2018

Polar n-Complex and n-Bicomplex Singular Value Decomposition and Principal Component Pursuit

Informed by recent work on tensor singular value decomposition and circu...
research
10/06/2021

Boosting RANSAC via Dual Principal Component Pursuit

In this paper, we revisit the problem of local optimization in RANSAC. O...
research
05/25/2019

Best Pair Formulation & Accelerated Scheme for Non-convex Principal Component Pursuit

The best pair problem aims to find a pair of points that minimize the di...
research
11/03/2020

Complex ratio masking for singing voice separation

Music source separation is important for applications such as karaoke an...
research
03/31/2011

Auto-associative models, nonlinear Principal component analysis, manifolds and projection pursuit

In this paper, auto-associative models are proposed as candidates to the...
research
07/03/2013

Separation of cardiac and respiratory components from the electrical bio-impedance signal using PCA and fast ICA

This paper is an attempt to separate cardiac and respiratory signals fro...
research
06/06/2017

Hyperplane Clustering Via Dual Principal Component Pursuit

We extend the theoretical analysis of a recently proposed single subspac...

Please sign up or login with your details

Forgot password? Click here to reset