def fista_l1(data, K, Kadj, Lambda, Lip=None, n_it=100, return_all=True):
'''
Beck-Teboulle's forward-backward algorithm to minimize the objective function
||K*x - d||_2^2 + Lambda*||x||_1
When K is a linear operators.
K : forward operator
Kadj : backward operator
Lambda : weight of the regularization (the higher Lambda, the more sparse is the solution in the H domain)
Lip : largest eigenvalue of Kadj*K
n_it : number of iterations
return_all: if True, an array containing the values of the objective function will be returned
'''
if Lip is None:
print("Warn: fista_l1(): Lipschitz constant not provided, computing it with 20 iterations")
Lip = power_method(K, Kadj, data, 20)**2 * 1.2
print("Lip = %e" % Lip)
if return_all: en = np.zeros(n_it)
x = np.zeros_like(Kadj(data))
y = np.zeros_like(x)
for k in range(0, n_it):
grad_y = Kadj(K(y) - data)
x_old = x
w = y - (1.0/Lip)*grad_y
w = _soft_thresh(w, Lambda/Lip)
x = w
y = x + ((k-1.0)/(k+10.1))*(x - x_old) # TODO : see what would be the best parameter "a"
# Calculate norms
if return_all:
fidelity = 0.5*norm2sq(K(x)-data)
l1 = norm1(w)
energy = fidelity + Lambda*l1
en[k] = energy
if (k%10 == 0): # TODO: more flexible
print("[%d] : energy %e \t fidelity %e \t L1 %e" % (k, energy, fidelity, l1))
#~ elif (k%10 == 0): print("Iteration %d" % k)
if return_all: return en, x
else: return x
