In the YALL1 package under ./Demos, you can find a set of demo files. They conclude

• demo_1d.m: recover 1d sparse real signals with L1
• demo_2d.m: recover 2d Shepp-Logan phantoms with L1
• demo_2dw.m: recover 2d Shepp-Logan phantoms with L1 of wavelets
• demo_complex.m: recover 1d sparse complex signals with L1
• demo_L1L2.m: solve the L1/L2 model; compare with the solver l1_ls
• demo_L1L2con.m: solve the L1/L2con model; compare with the solver SPGL1
• demo_nonneg.m: solve the L1/L2+ model (with constraints); compare with the solver l1_ls
• demo_rand.m: solve the BP, L1/L1, and L1/L2 models with explicit sensing matrices
• demo_weights.m: minimize the weighted L1 norm to recover a sparse signal

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