Introduction to the mathematics of data analysis. Bayes estimation, linear regression and classification methods. The singular value decomposition and the pseudo-inverse. Statistical models for inference and prediction in finance, marketing, and engineering applications. Regularization methods and principles of sparsity priors are applied. Streaming solutions. High dimensional problems. Concepts reinforced in Matlab and R programming experiments.
Dr. Gonzalo Arce teaches the following courses at UD.
This course is an introduction to digital image and audio signal processing. Sensor devices capturing energy across the electromagnetic spectrum provide a rich gamut of images that can be processed digitally for a myriad of applications including medical, surveillance, remote sensing, and consumer electronics. This course provides the fundamentals mathematical tools for image analysis covering topics in sampling, perception, color, Fourier analysis and representation, unitary transforms, noise reduction and restoration, computer tomography, compression. The course also provides an introduction to the processing of audio signals and in particular, the analysis, and manipulation of musical signals. It uses data analysis and signal processing methods, and the understanding of acoustics and basic music theory, to succinctly represent and process musical signals.
A first-course on the theory and applications of statistical signal processing. Topic will benefit students interested in the design and analysis of signal processing systems, i.e., to extract information from noisy signals — radar engineer, sonar engineer, geophysicist, oceanographer, biomedical engineer, communications engineer, economist, statistician, physicist, etc. The course provides numerous examples, which illustrate both theory and applications for problems such as high-resolution spectral analysis, system identification, digital filter design, adaptive beamforming and noise cancellation, and tracking and localization. Prerequisite is a background in probability and random processes and linear and matrix algebra and exposure to basic signal processing.
Compressed Sensing encompasses exciting and surprising developments in signal processing resulting from sparse representations. It is about the interplay between sparsity and signal recovery. Roots trace back to: mathematics and harmonic analysis, physical sciences and geophysics, vision, and optimization and computational tools.
Nonlinear signal processing methods find numerous applications in such fields as imaging, teletraffic, communications, hydrology, geology, and economics—fields where nonlinear systems and non-Gaussian processes emerge. Within a broad class of nonlinear signal processing methods, this course provides a unified treatment of optimal and adaptive signal tools that mirror those of Wiener and Widrow, extensively presented in the linear filter theory literature. The methods detailed in this course can thus be tailored to effectively exploit nonGaussian signal statistics in a system or it’s inherent nonlinearities to overcome many of the limitations of the traditional practices used in signal processing.