comparison pyCSalgos/ABS/ABSexact.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 exact analysis recovery based on synthesis solvers (a.k.a. Analysis by Synthesis, ABS).
+Exact reconstruction.
+
+Author: Nicolae Cleju
+"""
+__author__ = "Nicolae Cleju"
+__license__ = "GPL"
+__email__ = "[e-mail]"
+
+
+import numpy
+
+# Import synthesis solvers from pyCSalgos package
+import pyCSalgos.BP.l1eq_pd
+import pyCSalgos.BP.cvxopt_lp
+import pyCSalgos.OMP.omp_QR
+import pyCSalgos.SL0.SL0
+import pyCSalgos.TST.RecommendedTST
+
+
+def bp(y,M,Omega,x0, pdtol=1e-3, pdmaxiter=50, cgtol=1e-8, cgmaxiter=200, verbose=False):
+  """
+  ABS-exact: Basis Pursuit (based on l1magic toolbox)
+  """
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+
+  return numpy.dot(D , pyCSalgos.BP.l1eq_pd.l1eq_pd(x0,Atilde,Atilde.T,ytilde, pdtol, pdmaxiter, cgtol, cgmaxiter, verbose))
+
+def bp_cvxopt(y,M,Omega):
+  """
+  ABS-exact: Basis Pursuit (based cvxopt)
+  """
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+
+  return numpy.dot(D , pyCSalgos.BP.cvxopt_lp.cvxopt_lp(ytilde, Atilde))
+
+
+def ompeps(y,M,Omega,epsilon):
+  """
+  ABS-exact: OMP with stopping criterion residual < epsilon 
+  """
+  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+  
+  opts = dict()
+  opts['stopCrit'] = 'mse'
+  opts['stopTol'] = epsilon
+  return numpy.dot(D , pyCSalgos.OMP.omp_QR.greed_omp_qr(ytilde,Atilde,Atilde.shape[1],opts)[0])
+
+def ompk(y,M,Omega,k):
+  """
+  ABS-exact: OMP with stopping criterion fixed number of atoms = k
+  """
+  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+  
+  opts = dict()
+  opts['stopTol'] = k
+  return numpy.dot(D , pyCSalgos.OMP.omp_QR.greed_omp_qr(ytilde,Atilde,Atilde.shape[1],opts)[0])
+
+def sl0(y,M,Omega, sigma_min, sigma_decrease_factor=0.5, mu_0=2, L=3, true_s=None):
+  """
+  ABS-exact: Smooth L0 (SL0)
+  """
+  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+  
+  return numpy.dot(D, pyCSalgos.SL0.SL0.SL0(Atilde,ytilde,sigma_min,sigma_decrease_factor,mu_0,L,true_s))
+
+def tst_recom(y,M,Omega, nsweep=300, tol=0.00001, xinitial=None, ro=None):
+  """
+  ABS-exact: Two Stage Thresholding (TST) with optimized parameters (see Maleki & Donoho)
+  """
+  
+  N,n = Omega.shape
+  D = numpy.linalg.pinv(Omega)
+  U,S,Vt = numpy.linalg.svd(D)
+  Aextra = Vt[-(N-n):,:]
+  
+  # Create aggregate problem
+  Atilde = numpy.vstack((numpy.dot(M,D), Aextra))
+  ytilde = numpy.concatenate((y,numpy.zeros(N-n)))
+  
+  return numpy.dot(D, pyCSalgos.TST.RecommendedTST.RecommendedTST(Atilde, ytilde, nsweep, tol, xinitial, ro))
+