ProxNest.operators.proximal_operators.hard_thresh(x, T)

Compute the element-wise hard-thresholding of \(x\).

Parameters

• x (np.ndarray) – Array to threshold.

• T (float) – Hard-thresholding level (regularisation parameter)

• delta (float) – Weighting parameter.

Returns

Thresholded coefficients of \(x\).

Return type

np.ndarray

ProxNest.operators.proximal_operators.l1_projection(x, T, delta, Psi=<ProxNest.operators.sensing_operators.Identity object>)

Compute the l1 proximal operator wrt dictionary \(\Psi\).

Parameters

• x (np.ndarray) – Array to threshold.

• T (float) – Soft-thresholding level (regularisation parameter)

• delta (float) – Weighting parameter.

• Psi (LinearOperator) – Prior dictionary (default = Identity)

Returns

Thresholded coefficients of \(x\).

Return type

np.ndarray

ProxNest.operators.proximal_operators.l2_projection(x, T, delta, Psi=<ProxNest.operators.sensing_operators.Identity object>)

Compute the l2 gradient step wrt dictionary \(\Psi\).

Parameters

• x (np.ndarray) – Array to threshold.

• T (float) – Soft-thresholding level (regularisation parameter)

• delta (float) – Weighting parameter.

• Psi (LinearOperator) – Prior dictionary (default = Identity)

Returns

Thresholded coefficients of \(x\).

Return type

np.ndarray

ProxNest.operators.proximal_operators.soft_thresh(x, T, delta=2)

Compute the element-wise soft-thresholding of \(x\).

Parameters

• x (np.ndarray) – Array to threshold.

• T (float) – Soft-thresholding level (regularisation parameter)

• delta (float) – Weighting parameter (default = 2).

Returns

Thresholded coefficients of \(x\).

Return type

np.ndarray