L1 minimization using ADMM

[shailesh1729]

This work provides implementations of algorithms in the paper: ALTERNATING DIRECTION ALGORITHMS FOR ℓ1-PROBLEMS IN COMPRESSIVE SENSING by Junfeng Yang and Yin Zhang.

Algorithms:

• Solve basis pursuit (1.3)
• Solve basis pursuit with inequality constraints (1.4)
• Solve basis pursuit denoising (1.5)
• Solve l_1/l_1 problem (1.6)

We also need to implement corresponding non-negative counterparts.

Evaluation:

• Recovery results from data corrupted by impulsive noise only
• Recovery results from data corrupted by white noise only
• Recovery results from data corrupted by both white and impulsive noise
• Relative error vs optimality for noiseless and noisy data