L1Norm().proximal() is incorrect for complex-valued data

[fmwatson]

The current implementation of L1Norm().proximal will always return a real-valued array, because the implementation of soft_shrinkage(x,tau) is not valid for complex x.

the last line should be: out *= numpy.exp(1j*numpy.angle(x))

(this is the same as x.sign() for x real, up to data type)

I'm reminded I need to submit a pull request for proximal of some functions applied to the magnitude image (which would provide the fix), although I think L1Norm().proximal() ought to be correct itself for complex x since || numpy.abs(x) ||_1 = || x ||_1 for complex valued x.

[jakobsj]

Many thanks for submitting this! Would you be up for - in the first instance - submitting a small pull request to address just this? That would be wonderful!

On Wed, 26 Jul 2023, 16.51 fmwatson, @.***> wrote:

The current implementation of L1Norm().proximal will always return a real-valued array, because the implementation of soft_shrinkage(x,tau) is not valid for complex x.

the last line should be: out = numpy.exp(1jnumpy.angle(x))

(this is the same as x.sign() for x real, up to data type)

I'm reminded I need to submit a pull request for proximal of some functions applied to the magnitude image (which would provide the fix), although I think L1Norm().proximal() ought to be correct itself for complex x since || numpy.abs(x) ||_1 = || x ||_1 for complex valued x.

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[fmwatson]

@jakobsj I can do that when I get a minute!

[paskino]

It would be useful to think about a unit test too, please