Source code for cr.sparse._src.problems.spec

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"""Basic definitions for problems
"""

import math

from typing import NamedTuple, Callable,Tuple, List

from jax import lax, jit

import jax.numpy as jnp


import cr.nimble as crn
import cr.sparse as crs
import cr.sparse.lop as crlop

class Problem(NamedTuple):
    r"""A sparse signal recovery problem

    The problem is given by
    :math:`\bb = \Phi \by`
    where :math:`\by = \Psi \bx`.
    This can written as :math:`\bb = \Phi \Psi \bx`.
    We shorten :math:`\bA = \Phi \Psi` and
    reformulate the problem as `\bb = \bA \bx`.
    In the sparse reconstruction problem, we have
    access to :math:`\bb` and :math:`\bA`
    and we attempt to recover :math:`\bx`.
    We can reconstruct :math:`\by` from :math:`\bx`
    by using the ``reconstruct`` function provided.
    """
    name: str
    "Name of the problem"
    Phi: crlop.Operator
    "A linear operator representing the sensing process"
    Psi: crlop.Operator
    "A sparsifying basis/dictionary"
    A: crlop.Operator
    "The combined sensing matrix + sparsifying dictionary operator"
    b: jnp.ndarray
    "The observed signal"
    reconstruct: Callable
    "Function handle to reconstruct a signal from coefficients in x"
    x: jnp.ndarray = None
    "Expected sparse representation (if available for synthetic problems)"
    y: jnp.ndarray = None
    "Original signal"
    figures : List[str] = []
    "Titles of figures associated with the problem"
    plot: Callable = None
    "A function to plot specific figures associated with the problem"
    both: bool = False
    "A flag to indicate if both Phi and Psi are non-trivial"