cr.sparse.RecoveryPerformance¶
- class cr.sparse.RecoveryPerformance(Phi, y, x, x_hat=None, sol=None)[source]¶
Performance of a sparse signal recovery operation
Synthesis \(y = \Phi x + e\)
Recovery: \(y = \Phi \hat{x} + r\)
Representation error: \(h = x - \hat{x}\)
Residual: \(y - \Phi \hat{x}\)
- __init__(Phi, y, x, x_hat=None, sol=None)[source]¶
Computes all parameters related to the quality of reconstruction
Methods
__init__
(Phi, y, x[, x_hat, sol])Computes all parameters related to the quality of reconstruction
print
([details])Prints metrics related to reconstruction quality
Attributes
K
Number of non-zero entries in \(x\)
M
Signal/Measurement space dimension, number of rows in \(\Phi\)
N
Representation space dimension, number of atoms/columns in \(\Phi\)
R0
Index set of K largest (magnitude) entries in the reconstruction \(\hat{x}\)
T0
The index set of K non-zero coefficients in \(x\)
h
Recovery/reconstruction error \(h = x - \hat{x}\)
h_norm
Norm of reconstruction error \(h\)
measurement_snr
Measurement SNR (dB) in measurement/signal space \(20 \log (\| y \|_2 / \| r \|_2)\)
num_correct_atoms
Number of entries in the overlap, i.e. number of indices of the support correctly recovered.
overlap
Indices overlapping between T0 and R0 \(T_0 \cap R_0\)
perfect_support_recovery
Returns if the support has been recovered perfectly
r
The residual \(r = y - \Phi \hat{x}\)
r_norm
Norm of the residual
recovery_snr
Reconstruction/recovery SNR (dB) in representation space \(20 \log (\| x \|_2 / \| h \|_2)\)
success
Returns True if more than 75% indices are correctly identified and recovery SNR is high (> 30 dB)
support_recovery_ratio
Returns the ratio of correctly recovered atoms
x_dr
Dynamic range of x
x_hat_dr
Dynamic range of x_hat
x_hat_norm
norm of the reconstruction \(\hat{x}\)
x_norm
norm of representation \(x\)
y_dr
Dynamic range of y
y_norm
norm of measurement/signal \(y\)