Dictionary Learning with BLOTLESS Update

TY - JOUR

T1 - Dictionary Learning with BLOTLESS Update

AU - Yu, Qi

AU - Dai, Wei

AU - Cvetkovic, Zoran

AU - Zhu, Jubo

PY - 2020/2/6

Y1 - 2020/2/6

N2 - Algorithms for learning a dictionary to sparsely represent a given dataset typically alternate between sparse coding and dictionary update stages. Methods for dictionary update aim to minimise expansion error by updating dictionary vectors and expansion coefficients given patterns of non-zero coefficients obtained in the sparse coding stage. We propose a block total least squares (BLOTLESS) algorithm for dictionary update. BLOTLESS updates a block of dictionary elements and the corresponding sparse coefficients simultaneously. In the error free case, three necessary conditions for exact recovery are identified. Lower bounds on the number of training data are established so that the necessary conditions hold with high probability. Numerical simulations show that the bounds approximate well the number of training data needed for exact dictionary recovery. Numerical experiments further demonstrate several benefits of dictionary learning with BLOTLESS update compared with state-of-the-art algorithms especially when the amount of training data is small.

AB - Algorithms for learning a dictionary to sparsely represent a given dataset typically alternate between sparse coding and dictionary update stages. Methods for dictionary update aim to minimise expansion error by updating dictionary vectors and expansion coefficients given patterns of non-zero coefficients obtained in the sparse coding stage. We propose a block total least squares (BLOTLESS) algorithm for dictionary update. BLOTLESS updates a block of dictionary elements and the corresponding sparse coefficients simultaneously. In the error free case, three necessary conditions for exact recovery are identified. Lower bounds on the number of training data are established so that the necessary conditions hold with high probability. Numerical simulations show that the bounds approximate well the number of training data needed for exact dictionary recovery. Numerical experiments further demonstrate several benefits of dictionary learning with BLOTLESS update compared with state-of-the-art algorithms especially when the amount of training data is small.

KW - Dictionary learning

KW - Inverse problems

KW - Sparse representation

UR - http://www.scopus.com/inward/record.url?scp=85082399151&partnerID=8YFLogxK

U2 - 10.1109/TSP.2020.2971948

DO - 10.1109/TSP.2020.2971948

M3 - Article

SN - 1053-587X

VL - 68

SP - 1635

EP - 1645

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

M1 - 8985423

ER -