In signal processing, data are often compressed immediately after sensing, trading off storage for some error. For instance, when we take a picture using a digital camera, the image is usually compressed to JPEG format (unless RAW format -when possible- is selected). In this process, 90% of data or even more are thrown away. So is it possible to sample only a few measurements and recover the original data? The recent theory of Compressive Sensing (CS) states that it is indeed possible to recover certain signals from measurements at very low sampling rate. Then the questions arise about what signals can be recovered. What mathematical tools are needed to reconstruct the signals? How to best solve those problems? In this talk, I will give a brief review of CS and propose some reweighted algorithms based on alternating direction method for the non-convex optimizations in CS.