tfmri.convex.ConvexFunctionLeastSquares

class ConvexFunctionLeastSquares(operator, rhs, gram_operator=None, scale=None, name=None)[source]

Bases: tensorflow_mri.python.ops.convex_ops.ConvexFunctionQuadratic

A ConvexFunction representing a least squares function.

Represents \(f(x) = \frac{1}{2} {\left \| A x - b \right \|}_{2}^{2}\).

Minimizing f(x) is equivalent to finding a solution to the linear system \(Ax - b\).

Parameters

  • operator – A tf.Tensor or a tfmri.linalg.LinearOperator representing a matrix \(A\) with shape [..., m, n]. The linear system operator.

  • rhs – A Tensor representing a vector b with shape [..., m]. The right-hand side of the linear system.

  • gram_operator –

    A tf.Tensor or a tfmri.linalg.LinearOperator representing the Gram matrix of operator. This may be used to provide a specialized implementation of the Gram matrix \(A^H A\). Defaults to None, in which case a naive implementation of the Gram matrix is derived from operator.

  • scale – A float. A scaling factor. Defaults to 1.0.

  • name – A name for this ConvexFunction.

Initialize this ConvexFunction.