Intro to compressed sensing

September 14, 2021 1 min read

For almost a century the field of signal processing existed in the paradigm of Nyquist-Shannon theorem (also known as Kotelnikov theorem in Russian literature) that claimed that you cannot extract more than n Fourier harmonics from a signal, if you have n measurements. However, thanks to the results in functional analysis from 1980s, such as Lindenstrauss-Johnson lemma and Kashin-Garnaev-Gluskin inequality, it became evident, that you can do with as few as log(n)! After application of the L1-norm machinery developed in 1990s, such as LASSO and LARS, a new groundbreaking theory of compressed sensing emerged in mid-2000s to early 2010s. In this post I'll briefly cover some of its ideas and results.



Boris Burkov

Written by Boris Burkov who lives in Moscow, Russia and Cambridge, UK, loves to take part in development of cutting-edge technologies, reflects on how the world works and admires the giants of the past. You can follow me in Telegram