def obfn_dfd(self):
r"""Compute data fidelity term :math:`(1/2) \| \sum_m
\mathbf{d}_m * \mathbf{x}_m - \mathbf{s} \|_2^2`.
"""
Ef = self.eval_Rf(self.Xf)
return sl.rfl2norm2(Ef, self.S.shape, axis=self.cri.axisN) / 2.0
def obfn_dfd(self):
r"""Compute data fidelity term :math:`(1/2) \| \sum_m
\mathbf{d}_m * \mathbf{x}_m - \mathbf{s} \|_2^2`.
"""
Ef = sl.inner(self.Zf, self.obfn_fvarf(), axis=self.cri.axisM) \
- self.Sf
return sl.rfl2norm2(Ef, self.S.shape, axis=self.cri.axisN) / 2.0
def obfn_dfd(self):
r"""Compute data fidelity term :math:`(1/2) \| \sum_m
\mathbf{d}_m * \mathbf{x}_m - \mathbf{s} \|_2^2`.
This function takes into account the unnormalised DFT scaling,
i.e. given that the variables are the DFT of multi-dimensional
arrays computed via :func:`rfftn`, this returns the data fidelity
term in the original (spatial) domain.
"""
Ef = self.eval_Rf(self.Xf)
return sl.rfl2norm2(Ef, self.S.shape, axis=self.cri.axisN) / 2.0
def evaluate(self):
"""Evaluate functional value of previous iteration."""
X = mp_Z_Y
Xf = mp_Zf
Df = mp_Df
Sf = mp_Sf
Ef = spl.inner(Df[np.newaxis, ...], Xf,
axis=self.xstep.cri.axisM + 1) - Sf
Ef = np.swapaxes(Ef, 0, self.xstep.cri.axisK + 1)[0]
dfd = spl.rfl2norm2(Ef, self.xstep.S.shape,
axis=self.xstep.cri.axisN) / 2.0
rl1 = np.sum(np.abs(X))
obj = dfd + self.xstep.lmbda * rl1
return (obj, dfd, rl1)
def evaluate(self):
"""Evaluate functional value of previous iteration."""
if self.opt['AccurateDFid']:
if self.dmethod == 'fista':
D = self.dstep.getdict(crop=False)
else:
D = self.dstep.var_y()
if self.xmethod == 'fista':
X = self.xstep.getcoef()
else:
X = self.xstep.var_y()
Df = sl.rfftn(D, self.xstep.cri.Nv, self.xstep.cri.axisN)
Xf = sl.rfftn(X, self.xstep.cri.Nv, self.xstep.cri.axisN)
Sf = self.xstep.Sf
Ef = sl.inner(Df, Xf, axis=self.xstep.cri.axisM) - Sf
dfd = sl.rfl2norm2(
Ef, self.xstep.S.shape, axis=self.xstep.cri.axisN) / 2.0
rl1 = np.sum(np.abs(X))
return dict(DFid=dfd,
RegL1=rl1,
ObjFun=dfd + self.xstep.lmbda * rl1)
else:
return None
def rsdl(self):
"""Compute fixed point residual in Fourier domain."""
diff = self.Xf - self.Yfprv
return sl.rfl2norm2(diff, self.X.shape, axis=self.cri.axisN)