An Efficient Method For Compressive Sensing

by Seung-Jean Kim, Kwangmoo Koh, Michael Lustig and Stephen Boyd

This paper talks about how the interior point method is applied in L1 regularized least squared problem. The dual serves as an estimation of the duality gap, which then becomes the convergence judgement. The log barrier method formulates the primal objective function, which is solved by Newton's method. The Newtons's method requires solving a linear system, which addressed by conjugate gradient. The accuracy of the solution can be adjusted as the search evolves.

On a single machine this method may deal with millions of variables, in compressive sensing problems.