This course is about Biological Signal and System Modeling. Modeling is the main core of any signal and system processing and analysis. For example, an image can be seen as a matrix (mathematical/deterministic model) and in this base for a conventional processing such as denoising average operator is used. However as we know this operator doesn’t lead to an optimum result (the produced image is usually blurry). In another point of view, the image can be seen as a random field (statistical model), and so the denoising process is converted to an estimation problem and better denoising results is achieved. Similarly we can solve the denoising problem by modeling an image using PDE, geometric and graph-based methods, etc. These model can be also used in transform domain using atomic representations such as x-let transforms (data preparation). The resulted denoising process is completely depended on the proposed model for noise-free image. In this base we will introduce various methods for modeling of biologic data including mathematical/statistical models, energy-based models (variational and PDE), transform-based models, and geometric and graph-based models. After that we will focus on using these methods to model biomedical signals

This course is about Advanced Biomedical Signal Processing. In this course we discuss about higher-order spectral (HOS) analysis and sparse representation. Topics in higher-order spectral analysis will include: definition of moments/cumulants, power spectrum, HOS for both stochastic and deterministic signals, higher-order cepstera, non-parametric higher-order spectra estimation methods, and parametric methods based on AR, MA and ARMA models, signal recovery from higher-order spectra, applications of higher-order spectra for biomedical signal analysis. Topics in sparse representation will include: Modern Harmonic Analysis, Sparse Transforms, Oriented and Non-Oriented Multi-Scale Pyramids, Compressed Sensing, Dictionary Learning, Sparse Inverse Problems. In this section we have a short review on the main properties of sparse transforms including definitions, and (statistical) properties. We discuss about sparse time-frequency representations and introduce several sparse transforms such as Wigner-Ville, Choi-Williams, (redundant) wavelet transform, etc. In the next part we introduce some sparse transforms for m-D signals (and image processing). For this reason we have several discussions about m-D wavelet transform, m-D (dual-tree) complex wavelet transform, curvelet transform, contourlet transform, steerable pyramid, etc. We also discuss about atomic representation based on adaptive atoms and introduce dictionary learning. Finally, we discuss about applications of sparse representation for signal processing especially for inverse problems including noise removal, super-resolution, blind source separation, deblurring, inpainting, etc.