Sparsity-Assisted Signal Denoising and Pattern Recognition in Time-Series Data

We address the problem of signal denoising and pattern recognition in processing batch-mode time-series data by combining linear time-invariant filters, orthogonal multiresolution representations, sparsity-based methods. propose a novel approach to designing higher-order zero-phase low-pass, high-pass, band-pass infinite impulse response filters as matrices, using spectral transformation state-space representation digital filters. also proximal gradient-based technique factorize special class high-pass so that factorization product preserves property filter incorporates sparse-derivative component input model. To demonstrate applications our designs, we validate new models simultaneously denoise identify patterns interest. or detect interest signal, proposed combine (LTI) methods with such wavelets short-time Fourier transform. illustrate capabilities sleep-electroencephalography (EEG) K-complexes sleep spindles. Reproducible research is available at https://github.com/prateekgv/sasdpr .