tfmri.convex.ConvexFunctionTikhonov

class ConvexFunctionTikhonov(transform=None, prior=None, domain_dimension=None, scale=None, dtype=tf.float32, name=None)

Bases: tensorflow_mri.python.ops.convex_ops.ConvexFunctionAffineMappingComposition

A ConvexFunction representing a Tikhonov regularization term.

For a given input \(x\), computes \(\lambda \left\| T(x - x_0) \right\|_2^2\), where \(\lambda\) is a scaling factor, \(T\) is any linear operator and \(x_0\) is a prior estimate.

Parameters

• transform – A tf.linalg.LinearOperator. The Tikhonov operator \(T\). Defaults to the identity operator.

• prior – A tf.Tensor. The prior estimate \(x_0\). Defaults to 0.

• domain_dimension –

  A scalar integer tf.Tensor. The dimension of the domain.

• scale – A float. The scaling factor.

• dtype – A tf.DType. The dtype of the inputs. Defaults to float32.

• name – A name for this ConvexFunction.

Initialize this ConvexFunction.