Low-pass filtering in CSD space and sparsity based denoising

Near-infrared spectroscopy (NIRS) is an optical imaging technique, in which light rays in near infra-red region are used to measure variations in hemoglobin concentrations, with response to variations in neuronal activity. The resulting time series obtained in NIRS technique is usually in the form of sparse signal with instrumental noise in the low-frequency background. Conventional de-noising and filtering techniques do not work well for these kinds of signals. In this paper the biomedical signals are recovered with an optimization approach which combines the low-pass filtering and sparsity based de-noising with LPF/TVD algorithm. The algorithm is formulated with majorization-minimization (MM) principle. Discrete-time non causal recursive filter of zero-phase type is used and formulated in the form of banded matrices. A dc-notch filter is proposed to eliminate the baseline drift in the signals. In order to reduce the computational complexity it is also proposed to represent the banded matrices in canonical signed digit (CSD) space. The technique is illustrated with a test signal and NIRS data.