Building iterative methods

SigPy provides four abstraction classes (Linop, Prox, Alg, and App) for optimization based iterative methods. Such abstraction is inspired by similar structure in BART.

The Linop class abstracts a linear operator, and supports adjoint, addition, composing, and stacking. Prepackaged Linops include FFT, NUFFT, and wavelet, and common array manipulation functions. In particular, given a Linop A, the following operations can be performed:

>>> A.H  # adjoint
>>> A.H * A  # compose
>>> A.H * A + lamda * I  # addition and scalar multiplication
>>> Hstack([A, B])  # horizontal stack
>>> Vstack([A, B])  # vertical stack
>>> Diag([A, B])  # diagonal stack

The Prox class abstracts a proximal operator, and can do stacking and conjugation. Prepackaged Proxs include L1/L2 regularization and projection functions. In particular, given a proximal operator proxg, the following operations can be performed:

>>> Conj(proxg)  # convex conjugate
>>> UnitaryTransform(proxg, A)  # A.H * proxg * A
>>> Stack([proxg1, proxg2])  # diagonal stack

The Alg class abstracts iterative algorithms. Prepackaged Algs include conjugate gradient, (accelerated/proximal) gradient method, and primal dual hybrid gradient. A typical usage is as follows:

>>> while not alg.done():
>>>     alg.update()

Finally, the App class wraps the above three classes into a final deliverable application. Users can run an App without knowing the internal implementation. A typical usage of an App is as follows:

>>> out = app.run()