International Journal of Advanced Robotic Systems
Analysis Sparse Representation Based on
Subset Pursuit and Weighted Split
Bregman Iteration Algorithm
Regular Paper
Ye Zhang
1
*, Tenglong Yu
1
and Wenquan Zhang
1
1 Department of Electronic Information Engineering, Nanchang University, Nanchnag, China
*Corresponding author(s) E-mail: zhangye@ncu.edu.cn
Received 23 January 2014; Accepted 09 September 2014
DOI: 10.5772/61543
© 2015 Author(s). Licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License
(http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the
original work is properly cited.
Abstract
Recently, a sparse representation model - called an analysis
sparse model - where the signal is multiplied by an analysis
dictionary and the outcome is assumed to be sparse, has
received increasing attention since it has potential and
extensive applications in the area of signal processing. The
performance of the analysis model significantly depends
on an appropriately chosen dictionary. Most existing
analysis dictionary learning algorithms are based on the
assumption that the original signals are known or can be
estimated from their noisy versions. Generally, however,
the original signals are unknown or need to be estimated
by using greedy-like algorithms with heavy computation.
To solve the problems, we introduce a subset pursuit
algorithm for analysis dictionary learning, where the
observed signals are directly employed to learn the analysis
dictionary. Next, a weighted split Bregman iteration
algorithm is proposed to estimate original signals by the
learned analysis dictionary. The experimental results
demonstrate the competitive performance of the proposed
algorithms compared with the state-of-art algorithms.
Keywords Sparse representation, synthesis model, analy‐
sis model, dictionary learning, image denoising
1. Introduction
Sparse representation has become a well-known topic in a
wide range of fields, such as image processing [1], com‐
pressed sensing [2], sensor networks [3], robotics [4, 5, 6, 7,
8], and more. A popular model for sparse representation is
the synthesis model. In this model, a signal
x∈ R
M
is
represented as
x= Da, where D ∈ R
M ×N
is a possibly over-
complete dictionary (
N ≥M
) and
a∈ R
N
is the coefficient
vector which is assumed to be sparse, i.e.,
∥a∥
0
= L ≪ N
,
where the
ℓ
0
quasi-norm ⋅
0
counts the number of non-
zero components in its argument. In the synthesis model,
the signal x
can be described as a linear combination of only
a few columns (i.e., atoms) of
D
. In the past decade, the
synthesis model has been extensively studied [1, 2, 3, 4, 5,
6, 7, 8, 9, 10, 11, 12]. In robotics, face recognition is used to
satisfy person identification tasks and sparse representa‐
tion-based classification can deal with facial recognition
very well. The basic idea is to combine the sub-dictionaries
which are learned from various classes’ images and then
represent the query image using a small number of atoms
indicating the class of the image [5]. Sparse representation-
based classification can also be applied to action recogni‐
tion for human-robot interaction [6, 7] and object
classification for robot perception [8].
1
Int J Adv Robot Syst, 2015, 12:149 | doi: 10.5772/61543