cr.sparse.problems.Problem¶
- class cr.sparse.problems.Problem(name: str, Phi: cr.sparse._src.lop.lop.Operator, Psi: cr.sparse._src.lop.lop.Operator, A: cr.sparse._src.lop.lop.Operator, b: jax.Array, reconstruct: Callable, x: Optional[jax.Array] = None, y: Optional[jax.Array] = None, figures: List[str] = [], plot: Optional[Callable] = None, both: bool = False)[source]¶
A sparse signal recovery problem
The problem is given by \(\bb = \Phi \by\) where \(\by = \Psi \bx\). This can written as \(\bb = \Phi \Psi \bx\). We shorten \(\bA = \Phi \Psi\) and reformulate the problem as bb = bA bx. In the sparse reconstruction problem, we have access to \(\bb\) and \(\bA\) and we attempt to recover \(\bx\). We can reconstruct \(\by\) from \(\bx\) by using the
reconstruct
function provided.- __init__()¶
Initialize self. See help(type(self)) for accurate signature.
Methods
__init__
()Initialize self.
count
(value, /)Return number of occurrences of value.
index
(value[, start, stop])Return first index of value.
Attributes
A
The combined sensing matrix + sparsifying dictionary operator
Phi
A linear operator representing the sensing process
Psi
A sparsifying basis/dictionary
b
The observed signal
both
A flag to indicate if both Phi and Psi are non-trivial
figures
Titles of figures associated with the problem
name
Name of the problem
plot
A function to plot specific figures associated with the problem
reconstruct
Function handle to reconstruct a signal from coefficients in x
x
Expected sparse representation (if available for synthetic problems)
y
Original signal