plt.title('Sparse Coefficient (' + dictype + ')')
plt.colorbar()
plt.subplot(224)
plt.imshow(Phi)
plt.title('Measurement matrix (' + mestype + ')')
plt.tight_layout()
plt.show()
# ===========way 1=================
Y = np.matmul(Phi, X)
X1 = pys.romp(Y,
Phi,
k=k1,
alpha=alpha,
normalize=True,
tol=1e-16,
verbose=True)
if dictype is not None:
X1 = np.matmul(D, X1)
X1 = pys.scale(X1, sto=[0, 255], sfrom=sfrom, istrunc=True)
X1 = X1.astype(X.dtype)
PSNR1, MSE1, Vpeak1, dtype = pys.psnr(X, X1, Vpeak=None, mode='rich')
print("---PSNR1, MSE1, Vpeak1, dtype: ", PSNR1, MSE1, Vpeak1, dtype)
# ===========way 2=================
Y = np.matmul(Phi, X)
k4 = 100
R = 4
alpha = 1e-6
M = np.size(y)
N = int(M * R)
ff = np.linspace(0, Fs, int(Ns * R))
A = pys.gaussian((M, N))
A = pys.odctdict((M, N), isnorm=True)
# A = pys.dctdict(N)
# A = pys.odctndict((M, N))
print(A.shape)
x1 = pys.romp(y, A, k=k1, alpha=alpha, verbose=False)
y1 = np.matmul(A, x1)
x2 = pys.romp(y, A, k=k2, alpha=alpha, verbose=False)
y2 = np.matmul(A, x2)
x3 = pys.romp(y, A, k=k3, alpha=alpha, verbose=False)
y3 = np.matmul(A, x3)
x4 = pys.romp(y, A, k=k4, alpha=alpha, verbose=False)
y4 = np.matmul(A, x4)
print("---MSE(y, y1) with k = " + str(k1) + ": ", pys.mse(y, y1))
print("---MSE(y, y2) with k = " + str(k2) + ": ", pys.mse(y, y2))
print("---MSE(y, y3) with k = " + str(k3) + ": ", pys.mse(y, y3))
print("---MSE(y, y4) with k = " + str(k4) + ": ", pys.mse(y, y4))
def cs1d(y,
Phi,
Psi=None,
optim='OMP',
k=1000,
tol=1e-8,
osshape=None,
verbose=True):
r"""Solves the 1-d Compressive Sensing problem
for sparse signal :math:`\bm x`
.. math::
{\bm y} = {\bm \Phi}{\bm x} + {\bf n},
for non-sparse signal :math:`{\bm x} = {\bm \Psi}{\bm z}`
.. math::
{\bm y} = {\bm \Phi \Psi}{\bm z} + {\bm n},
see https://iridescent.ink/aitrace/SignalProcessing/Sparse/LinearCompressiveSensing/index.html for details.
Arguments
----------------------
y : ndarray
the mesurements :math:`{\bm y}`, if ndarray, each colum is a mesurement
Phi : 2darray
the mesurement matrix :math:`{\bm \Phi}`
Keyword Arguments
----------------------
Psi : 2darray
the dictionary :math:`{\bm \Psi}` (default: {None})
optim : str
optimization method, OMP, LASSO (default: {'OMP'})
k : integer
sparse degree for OMP, max iter for LASSO (default: size of :math:`{\bm x}` )
tol : float
tolerance of error (LASSO) (default: {1e-8})
osshape : tuple
orignal signal shape, such as an H-W image (default: {None})
verbose : bool
show log info (default: {True})
Returns
----------------------
x : ndarray
reconstructed signal with sieof osshape
"""
print("================in cs1d================")
if y is None:
print("===No raw data!")
if verbose:
print("===Type of Phi, y: ", Phi.dtype, y.dtype)
cplxFlag = False
if Psi is not None:
# =================step1: Construct===========
if verbose:
print("===Construct sensing matrix: A = Phi*D...")
A = np.matmul(Phi, Psi)
Phi = None
if verbose:
print("===Done!...")
else:
A = Phi
Phi = None
if np.iscomplex(A).any() or np.iscomplex(y).any():
cplxFlag = True
if verbose:
print("===Convert complex to real...")
y = np.concatenate((np.real(y), np.imag(y)), axis=0)
ReA = np.real(A)
ImA = np.imag(A)
A1 = np.concatenate((ReA, -ImA), axis=1)
A2 = np.concatenate((ImA, ReA), axis=1)
A = np.concatenate((A1, A2), axis=0)
if verbose:
print("===Done!")
# if np.ndim(y) > 1:
# y = y.flatten()
if optim is 'OMP':
print(A.shape, y.shape)
z = pys.romp(y,
A,
k=k,
alpha=1e-6,
normalize=False,
tol=1e-16,
verbose=verbose)
if cplxFlag:
z = np.split(z, 2)
z = z[0] + 1j * z[1]
if verbose:
print("===size of z: ", z.shape)
if Psi is not None:
x = np.matmul(Psi, z)
else:
x = z
z = None
if osshape is not None:
x = np.reshape(x, osshape)
if verbose:
print("===shape of x: ", x.shape)
print("===Done!")
return x
plt.subplot(224)
plt.imshow(Phi)
plt.title('Measurement matrix (' + mestype + ')')
plt.tight_layout()
plt.show()
# ===========way 1=================
Y = np.matmul(Phi, X)
# XX = pys.omp0(
# Y, A, normalize=True, tol=1e-38, verbose=True)
# XX = pys.omp(
# Y, A, k=k, normalize=True, tol=1e-16, verbose=True)
X1 = pys.romp(Y, A, k=k1, alpha=alpha, normalize=True, tol=1e-16, verbose=True)
if dictype is not None:
X1 = np.matmul(D, X1)
X1 = pys.scale(X1, sto=[0, 255], sfrom=sfrom, istrunc=True)
X1 = X1.astype(X.dtype)
PSNR1, MSE1, Vpeak1, dtype = pys.psnr(X, X1, Vpeak=None, mode='rich')
X2 = pys.romp(Y, A, k=k2, alpha=alpha, normalize=True, tol=1e-16, verbose=True)
if dictype is not None:
X2 = np.matmul(D, X2)
X2 = pys.scale(X2, sto=[0, 255], sfrom=sfrom, istrunc=True)
X2 = X2.astype(X.dtype)
PSNR2, MSE2, Vpeak2, dtype = pys.psnr(X, X2, Vpeak=None, mode='rich')
X[:, n] = x
if vecflag:
X = np.reshape(X, N)
if verbose:
print("===Done!")
return X
if __name__ == '__main__':
import pysparse as pys
M = 3
N = 4
x = np.array([-0.5, 0.01, 3.1, 0.8])
A = pys.gaussian((M, N))
# A = pys.odctdict((M, N))
y = np.matmul(A, x)
print("---A (Mesurement Matrix): ", A)
print("---y (Mesurement Vector): ", y)
print("---x (Orignal Signal): ", x)
x = pys.romp(y, A, k=2, alpha=0.0001, verbose=False)
print("---x (Reconstructed Signal): ", x)
x = pys.omp(y, A, k=3, verbose=False)
print("---x (Reconstructed Signal): ", x)