Denoising Using Low-Pass Filtering Combined With Total Variation Filtering

Generally LTI filters are appropriate to denoise a signal that have low-frequency band. On the other hand, total variation denoising is appropriate to filter a signal having sparse representation. Some signals cannot be classified as having specific frequency band, or having sparse representation, such as the signal comprised in biomedical applications (near infrared spectroscopic imaging and nano-particle biosensing). This thesis introduces a new approach for denoising signals based on low-pass filtering combined with total variation denoising, assuming that the noisy observation is near infrared spectroscopic time series measurement, which can be modelled as a sum of two components, one of them low frequency and the other sparse or sparse derivative. The problem is formulated in terms of an optimization problem, and the cost function of the optimization problem is convex. As a consequence, two iterative algorithms are presented; the first one is derived using the majorization-minimization technique, and models the signals as consisted of low frequency and sparse derivative components. On the other hand, the second algorithm is derived using alternative direction method of multipliers, and models the signals as consisted of low frequency, sparse and sparse derivative components. In view of the above, simulation algorithms based on existing noisy observations are developed for validation and verification of the proposed approach. The simulation results show that the proposed approach for denoising signals recovers the signals well. Furthermore, it was found that the proposed approach is better in terms of run time. Keywords: NIRS, low-pass filter, total variation denoising, sparse derivative.