Design of measurement matrix for compressive sensing framework and its application to image processing

Abstract

Advancements in information and communication technology have resulted in proliferation of multimedia data in various application fields. Data processing, storage and security in these fields have thus become an important concern. Compressive sensing (CS) paradigm is used for addressing these issues. Compressive sensing is a novel signal sampling technique that was introduced initially as an alternative to the traditional Nyquist sampling theory especially to reduce the sampling cost. In recent years, CS techniques have been widely used for the development of compression - encryption algorithms in a more promising way. Implementation of CS in these domains or in general involves utilizing properly designed measurement matrix using which the compressed samples/measurements are obtained. Construction of this matrix plays an important role in designing CS recovery algorithms and in the recovery of under sampled data as well. In spite of vast literature related to matrix designs and recovery algorithms, CS domain still faces many challenges in recovering the exact samples using their measurements. Design of measurement matrix owing to recovery of signals without much loss of information is presented. Design of hybrid measurement matrix using Low Density Parity Check (LDPC) matrix and Vandermonde matrix for Compressive sensing framework is proposed. A row tensor product of LDPC matrix and Vandermonde matrix is used as measurement matrix for compressing the signals. The sparser representation of the signals to be compressed is initially obtained using an empirical dictionary learnt from a set of natural images. The acquired sparser data are subjected to compression and measurements are obtained from them using the designed measurement matrix. An iterative recovery algorithm that is proficient in recovering the sparser representation of the compressed signals is also developed. newline