This course aims to introduce regularization methods for high-dimensional signal processing. The background of modern signal processing is discussed with example applications in science and engineering. Techniques exploiting sparsity, low-rankness, and other norm constraints for solving inverse problems will be introduced, along with algorithms for compressive sensing, matrix completion, etc. The course will involve the review of the recent literature on regularization techniques and high-dimensional signal processing, the solution of typical regularization problems and the simulation study of the relevant techniques in signal and data processing examples. Through this course, the learner will develop an overview of regularized signal processing. The course will be concluded with the completion of mini projects on selected topics. Recommended readings: M.J. Wainwright. High-dimensional statistics: a non-asymptotic viewpoint. Cambridge series on statistical and probabilistic mathematics 48. Cambridge University Press, 2019H. W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, vol. 375. Berlin, Germany: SSBM, 1996. A. Lucas, M. Iliadis, R. Molina and A. K. Katsaggelos, "Using Deep Neural Networks for Inverse Problems in Imaging: Beyond Analytical Methods," in IEEE Signal Processing Magazine, vol. 35, no. 1, pp. 20-36, Jan. 2018, doi: 10.1109/MSP.2017.2760358.S. M. Kay, Fundamentals of statistical signal processing: estimation theory. Englewood Cliffs, NJ: Prentice-Hall, 1993.