Denoising and Completion of 3D Data via Multidimensional Dictionary Learning

12/31/2015
by   Zemin Zhang, et al.
0

In this paper a new dictionary learning algorithm for multidimensional data is proposed. Unlike most conventional dictionary learning methods which are derived for dealing with vectors or matrices, our algorithm, named KTSVD, learns a multidimensional dictionary directly via a novel algebraic approach for tensor factorization as proposed in [3, 12, 13]. Using this approach one can define a tensor-SVD and we propose to extend K-SVD algorithm used for 1-D data to a K-TSVD algorithm for handling 2-D and 3-D data. Our algorithm, based on the idea of sparse coding (using group-sparsity over multidimensional coefficient vectors), alternates between estimating a compact representation and dictionary learning. We analyze our KTSVD algorithm and demonstrate its result on video completion and multispectral image denoising.

READ FULL TEXT

page 6

page 7

page 8

11/05/2015

Computational Intractability of Dictionary Learning for Sparse Representation

In this paper we consider the dictionary learning problem for sparse rep...
12/16/2014

Efficient GPU Implementation for Single Block Orthogonal Dictionary Learning

Dictionary training for sparse representations involves dealing with lar...
08/26/2014

ℓ_1-K-SVD: A Robust Dictionary Learning Algorithm With Simultaneous Update

We develop a dictionary learning algorithm by minimizing the ℓ_1 distort...
01/26/2019

Distributed Convolutional Dictionary Learning (DiCoDiLe): Pattern Discovery in Large Images and Signals

Convolutional dictionary learning (CDL) estimates shift invariant basis ...
03/14/2021

Exact Sparse Orthogonal Dictionary Learning

Over the past decade, learning a dictionary from input images for sparse...
03/19/2014

A Split-and-Merge Dictionary Learning Algorithm for Sparse Representation

In big data image/video analytics, we encounter the problem of learning ...
12/19/2013

An Adaptive Dictionary Learning Approach for Modeling Dynamical Textures

Video representation is an important and challenging task in the compute...