Seminario del 2026

Giugno
07
Domenica
Ivan Selesnick
Frequency-domain and sparsity in signal/image analysis
ore 08:00
presso Complesso Belmeloro
 https://site.unibo.it/mml-imaging26/en/teaching-units/teaching-unit-2
analisi numerica
The course sessions will introduce linear time-invariant (LTI) systems and the related concepts and techniques of convolution, the z-transform, transfer functions, pole-zero diagrams, difference equations, frequency responses, the discrete-time Fourier transform, and frequency spectra. The discrete Fourier transform and Fast Fourier transform will be described and utilized. We will discuss the design and use of digital filters including notch filters for the elimination of tonal noise from signals, with examples and exercises in Matlab. The short-time Fourier transform (STFT) will be introduced. To extend these methods (e.g., to signals with missing data or non-uniformly sampled data), we will explain the use of least-squares (in a deterministic setting) to a variety of signal processing problems through their formulation as inverse problems. Standard LTI filters will be viewed and implemented in matrix form, and matrix-free solvers will be noted. The optimization-based inverse problem formulation framework will be extended from least-squares to nonlinear filters based on sparse signal models. The concept of sparse signal models will be introduced, along with transform-domain sparsity. The STFT, discrete wavelet transform, and total variation will be introduced as examples of transform-domain sparsity. For solving the corresponding optimization problems, the majorization-minimization (MM) framework will be illustrated, leading to iterative reweighted least squares and iterative soft-thresholding algorithms.
organizzato da: Serena Morigi
nell'ambito del Progetto BIP_2024_MORIGI - BIP del prof. Serena Morigi

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