The operfact package enables the modeling and solution of structured low-rank operator recovery problems using nuclear norms.
My thesis discusses these problems in more detail. Reference:
Bruer, John J. (2017) Recovering structured low-rank operators using nuclear norms. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/Z9F18WQS. http://resolver.caltech.edu/CaltechTHESIS:02082017-062956314
The following code demonstrates the creation and solution of a synthetic operator denoising problem.
import numpy as np
from operfact import operators, measurements, solvers
from operfact import regularizers as regs
shape = (m, n, p, q)
nfactors = r
sigma = 0.1
# Create the true operator and noisy measurements
oper = operators.RandomDyadsOperator(shape, nfactors)
measobj = measurements.IdentityMeasurement(shape)
measvec = measobj.apply(oper) + sigma*np.random.normal(size=measobj.nmeas)
# Create the problem instance
prob = solvers.Problem()
prob.shape = shape
prob.measurementobj = measobj
prob.measurementvec = measvec
prob.norm = regs.NucNorm_Prod(regs.norm_l2, regs.norm_l2)
prob.penconst = regs.penconst_denoise(shape, sigma, prob.norm)
prob.solver = cvxpy.SCS
prob.rank = r # altminsolve only
# Solve the problem
out = solvers.altminsolve(prob)The easiest way to obtain this package is from PyPI:
pip install operfact
It requires CVXPY, NumPy, and SciPy.
Documentation is included in the doc folder (autogenerated from docstrings). Background information is available in my thesis.
While appropriate licensing to this software is pending, the author reserves all rights.