Parallelized implementation of L1 CoSe with error tolerance

cose_noisy_parallel.py

#!/usr/bin/env python
# -*-coding:utf-8-*-


"""
This module contains 2 functions:

* ``cose_recovery``: Implements the L1 compressed sensing program, allowing
  for L2 error tolerance in the constraint.
* ``cose_recovery_mpp``: Parallelized version of ``cose_recovery`` that runs
  multiple recoveries in parallel, each recovery in a different process.
  
  
MIT License below.
--------------------------------------------------------------------------------
Copyright 2023 aferro (OrcID: 0000-0003-3830-3595)
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"""


from multiprocessing import Pool
from itertools import repeat
#
import numpy as np
import cvxpy as cp


# ##############################################################################
# #
# ##############################################################################
def cose_recovery(measurement, sensing_matrix, epsilon=0,
                  verbose=False, lp_solver="SCS", max_val=None):
    """
    The compressed sensing recovery consists in solving a linear program:
    find ``x`` with minimal L1 norm, such that the L2 norm of
    ``sensing_matrix @ x - measurements`` is less than epsilon. If epsilon is
    zero, this is a LP, otherwise it is a SOCP. Note that ``x`` is always
    assumed to be non-negative.

    :param measurement: Real-valued vector of size ``m`` containing the
      CoSe measurements
    :param sensing_matrix: Real-valued matrix of shape ``(ndim, m)``
      used to obtain measurements via ``matrix.T @ original = measurements``.
    :param max_val: If given, establishes an upper bound for the values in the
      solution ``x``.
    :returns: The estimated ``x`` sparse signal of ``ndim`` dimensions.
    """

    assert epsilon >= 0, "Epsilon must be nonnegative!"
    ndim = sensing_matrix.shape[0]
    coeffs = np.ones(ndim)
    x = cp.Variable(ndim)
    #
    constraints = [x >= 0]
    if max_val is not None:
        constraints.append(x <= max_val)
    if epsilon == 0:
        constraints.append(sensing_matrix.T @ x == measurement)
        prob = cp.Problem(cp.Minimize(coeffs.T @ x), constraints)
        prob.solve(solver=lp_solver, verbose=verbose)
    else:
        constraints.append(
            cp.SOC(epsilon, (sensing_matrix.T @ x) - measurement))
        prob = cp.Problem(cp.Minimize(coeffs.T @ x), constraints)
        prob.solve(verbose=verbose)
    #
    assert prob.status == "optimal", "Ill-posed LP?"
    return x.value


# ##############################################################################
# # PARALLEL
# ##############################################################################
def cose_recovery_mpp(measurements, matrices, epsilon=0, verbose=False,
                      lp_solver="SCS", max_val=None):
    """
    Parallelized version of ``cose_recovery`` that admits multiple measurements
    and sensing matrices, and runs one recovery for each, each recovery in a
    separate process.

    :param measurements: Collection of ``N`` real-valued vectors of size ``m_i``
      containing the CoSe measurements
    :param matrices: Collection of ``N`` real-valued matrices of shapes
      ``(ndim_i, m_i)``, used to obtain the given measurements via
      ``matrix.T @ original = measurements``.
    """

    with Pool() as mpp:
        epsilon = repeat(epsilon)
        verbose = repeat(verbose)
        lp_solver = repeat(lp_solver)
        max_val = repeat(max_val)
        result = np.stack(
            mpp.starmap(cose_recovery, zip(measurements, matrices, epsilon,
                                           verbose, lp_solver, max_val)))
        return result