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pyproximal/proximal/SingularValuePenalty.py

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@@ -20,18 +20,19 @@ class SingularValuePenalty(ProxOperator):
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----------
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dim : :obj:`tuple`
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Size of matrix :math:`\mathbf{X}`.
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penalty : :class:`pylops.ProxOperator`
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penalty : :class:`pyproximal.ProxOperator`
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Function acting on the singular values.
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Notes
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-----
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The pyproximal implementation allows ``penalty`` to be any function on the singular
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values; however, not all penalties will have an accurate proximal operator defined
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this way. Given a penalty :math:`f`, the proximal operator is assumed to be
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The pyproximal implementation allows ``penalty`` to be any
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:class:`pyproximal.ProxOperator` acting on the singular values; however, not all
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penalties will result in a mathematically accurate proximal operator defined this
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way. Given a penalty :math:`f`, the proximal operator is assumed to be
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.. math::
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\prox_{\tau f}(\mathbf{X}) =
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\prox_{\tau \mathcal{R}_f}(\mathbf{X}) =
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\mathbf{U} \diag\left( \prox_{\tau f}(\boldsymbol\lambda)\right) \mathbf{V}^H
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where :math:`\mathbf{X} = \mathbf{U}\diag(\boldsymbol\lambda)\mathbf{V}^H`, is an

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