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Solve AcceleratedPGM with multiple priors applied #465

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shnaqvi opened this issue Nov 8, 2023 · 2 comments · Fixed by #469
Closed

Solve AcceleratedPGM with multiple priors applied #465

shnaqvi opened this issue Nov 8, 2023 · 2 comments · Fixed by #469
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enhancement New feature or request

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@shnaqvi
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shnaqvi commented Nov 8, 2023

Currently AcceleratedPGM can only solve the problem with a single loss function and a single prior. We cannot solve the composite minimization problem defined like so:

$\min_x f(x) + \bar{g}(x),\ \text{where}\ \ \bar{g}(x) = \sum_i \alpha_i g_i(x),\ \text{and}\ \ \alpha_i \ge 0, \ \sum_i \alpha_i = 1$

This has been addressed by Yao-Liang, 2013 in Algorithm 1. This is an enhancement request to implement this Proximal-Averaged AcceleratedPGM where the proximal of the weighted priors is given by the average of their respective proximals.

This would be extremely useful when we want to restore the noisy image with say TV prior while also enforcing that the result be non-zero with NonNegativeIndicator prior.

@bwohlberg bwohlberg self-assigned this Nov 9, 2023
@bwohlberg bwohlberg added the enhancement New feature or request label Nov 9, 2023
@bwohlberg
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See branch brendt/proxavg for an approach to implementing the proximal average method that does not require a new solver class. Instead, it provides a ProximalAverage functional that uses the proximal average when passed to the existing PGM or AcceleratedPGM solvers.

@bwohlberg
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Resolved in #469.

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