

Examples
The central idea in compressive sampling is that the number of samples As a concrete example, suppose that f is a discrete signal (of length
How many timedomain samples do we need Now suppose that we are given only 80 samples. Below is a plot
Of course, we will not be able to “fill




In general, if there are B sinusoids in the signal, we will be able to recover using L1 minimization from on the order of B log N samples (see the “Robust Uncertainty Principles…” paper for a full exposition).
The framework is easily extended to more general types of measurements Here is an example. The 1 megapixel image below has a perfectly
Instead of observing this image directly, say we took 100,000 “random
The lesson here is that the number of measurements needed to acquire this In the “real world”, signals and images are not perfectly sparse, and Another example in imaging is given below: we observe 25,000 random measurements 

65k pixel image

25k random measurements


quantized measurements

recovered image


The L1MAGIC package includes MATLAB code that solves these (and 