cr.sparse.RecoveryPerformance

class cr.sparse.RecoveryPerformance(Phi, y, x, x_hat=None, sol=None)

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)

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()	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 \(y\)