Compliant Ternary Matrices based on Restricted Isometry Property: Construction and Application to Image Retrieval

By : R. Ramu Naidu, M. Srinivas, C. S. Sastry

Page No: 285-298

Abstract: 
The class of matrices possessing compliance with the Restricted Isometry Property (RIP) provides data of certain types with sparse representation. The ternary matrices with 0, ±1 as their elements have the potential to result in fast algorithms. The existing ternary constructions combine binary and bipolar (Hadamard) matrices. In the present work, however, we construct deterministic and sparse ternary matrices from the known binary matrices. The resulting ternary matrices are shown to be better-behaved, in terms of their sparse recovery properties, than the input binary matrices. As our construction does not use bipolar matrices, it avoids the need for bipolar matrices. This saves memory space and computational cost when our method is implemented on computer. In addition, our matrices are very sparse compared to their generating binary matrices. We demonstrate that the ternary matrices constructed herein work well for dimensionality reduction in wavelet domain. In particular, through experimental work, we show that the wavelet weighted ternary matrices are capable of being used for applications like content based image retrieval.

Authors :
R. Ramu Naidu
Department of Mathematics, Indian Institute of Petroleum & Energy,Visakhapatnam-530003, India.

C. S. Sastry
Department of Mathematics, Indian Institute of Technology, Hyderabad, Medak, Telangana, 502205, India.

M. Srinivas
Department of Computer Science and Engineering, National Institute of Technology, Warangal, 506004, India.
 

DOI: https://doi.org/10.32381/JCISS.2019.44.1-4.15