We will first introduce basic ideas of Compressive Sensing (CS), which
is an emerging
(some would say revolutionary) methodology in signal, image and data
processing.
The theory for CS has so far been built largely on a notion called
Restricted Isometry
Property or RIP. We will point out drawbacks of RIP-based analyses and
introduce
results from a non-RIP analysis including some new extensions. We will
also discuss
some related optimization algorithms.