Basis pursuit and its variations

Basis pursuit is a way of solving the sparse recovery problem via \(\ell_1\) minimization. We provide multiple implementations for different variations of the problem.

Note

These algorithms are dependent on the CVX toolbox. Please make sure to install them before using the algorithms.

Constructing the solver with dictionary and set of signals to be solved arranged in a signal matrix:

solver = spx.pursuit.single.BasisPursuit(Dict, Y)

Solving using LASSO method:

result = solver.solve_lasso(lambda)
result = solver.solve_lasso()

Solving using \(\ell_1\) minimization assuming that signals are exact sparse:

result = solver.solve_l1_exact()

Solving using \(\ell_1\) minimization assuming that signals are noisy:

result = solver.solve_l1_noise()