Phase Transitions in Signal Processing

This lecture explores the concept of phase transitions in signal processing, focusing on the random energy model and its implications. The instructor discusses the computation of energy, the significance of free energy change, and the impact of noise variance on signal reconstruction. The lecture delves into the transition from perfect to impossible signal reconstruction as noise levels increase, highlighting the critical role of phase transitions in large-scale scenarios. Additionally, the application of threshold algorithms in signal processing, particularly in image denoising, is demonstrated using the example of the Lena picture transformed through wavelet basis. The lecture concludes by emphasizing the practical relevance of these concepts in real-world applications.