comparison pyCSalgos/ABS/ABSmixed.py @ 67:a8d96e67717e

Added the Analysis-By-Synthesis algorithms used in the papers "Analysis-based sparse reconstruction with synthesis-based solvers", "Choosing Analysis or Synthesis Recovery for Sparse Reconstruction" and "A generalization of synthesis and analysis sparsity"

+# -*- coding: utf-8 -*-
+"""
+Algorithms for approximate analysis recovery based on synthesis solvers (a.k.a. Analysis by Synthesis, ABS).
+Approximate reconstruction, ABS-mixed.
+
+Author: Nicolae Cleju
+"""
+__author__ = "Nicolae Cleju"
+__license__ = "GPL"
+__email__ = "[e-mail]"
+
+
+import numpy
+
+# Import synthesis solvers from pyCSalgos package
+import pyCSalgos.BP.l1qec
+import pyCSalgos.SL0.SL0_approx
+
+def bp(y,M,Omega,epsilon, x0, lbtol=1e-3, mu=10, cgtol=1e-8, cgmaxiter=200, verbose=False):
+  """
+  ABS-mixed: Basis Pursuit (based on l1magic toolbox)
+  """  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aeps = numpy.dot(M,D)
+  Aexact = Vt[-(N-n):,:]
+  
+  return numpy.dot(D , pyCSalgos.BP.l1qec.l1qec_logbarrier(x0,Aeps,Aeps.T,y,epsilon,Aexact,Aexact.T,numpy.zeros(N-n), lbtol, mu, cgtol, cgmaxiter, verbose))
+
+def sl0(y,M,Omega,epsilon, sigma_min, sigma_decrease_factor=0.5, mu_0=2, L=3, Aeps_pinv=None, Aexact_pinv=None, true_s=None):
+  """
+  ABS-mixed: Smooth L0 (SL0)
+  """  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aeps = numpy.dot(M,D)
+  Aexact = Vt[-(N-n):,:]
+  
+  #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
+  #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_robust_analysis(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
+  #return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis_unconstrained(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
+  return numpy.dot(D, pyCSalgos.SL0.SL0_approx.SL0_approx_analysis_dai(Aeps,Aexact,y,epsilon,sigma_min,sigma_decrease_factor,mu_0,L,Aeps_pinv,Aexact_pinv,true_s))
+