operators
module¶
Implements high level interface to manipulate linear operators. This module is not required by QMM, is basic, but can serve as guide or for reuse.

dft2
(obj)¶ Return the orthogonal real 2D fft.
 Parameters
obj (arraylike) – The array on which to perform the 2D DFT.
 Returns
out
 Return type
array
Notes
This function is a wrapper of numpy.fft.rfft2. The DFT is made on the two last axis.

idft2
(obj, shape)¶ Return the orthogonal real 2D ifft.
 Parameters
obj (arraylike) – The array on which to perform the inverse 2D DFT.
shape (tuple) – The output shape.
 Returns
out
 Return type
array
Notes
This function is a wrapper of numpy.fft.irfft2. The DFT is made on the two last axis.

class
Operator
¶ An abstract base class for linear operators.

abstract
forward
(point)¶ Return H·x

abstract
adjoint
(point)¶ Return Hᵀ·e

fwback
(point)¶ Return HᵀH·x

T
(point)¶ Return Hᵀ·e

abstract

class
Conv2
(ir, shape)¶ 2D convolution on image.
Does not suppose periodic or circular condition.

imp_resp
¶ The impulse response.
 Type
array

shape
¶ The shape of the input image.
 Type
tuple of int

freq_resp
¶ The frequency response of shape shape.
 Type
array
Notes
Use fft internally for fast computation. The
forward
methods is equivalent to convolve2d with “valid” boudary condition andadjoint
is equivalent to convolve2d with “full” boundary condition with zero filling.
__init__
(ir, shape)¶ 2D convolution on image.
 Parameters
ir (array) – The impulse response.
shape (tuple of int) – The shape of the input image.

forward
(point)¶ Return H·x

adjoint
(point)¶ Return Hᵀ·e

fwback
(point)¶ Return HᵀH·x


class
Diff
(axis)¶ Difference operator.
Compute the firstorder differences along an axis.

axis
¶ The axis along which the differences is performed.
 Type
int
Notes
Use numpy.diff and implement the correct adjoint, with numpy.diff also.

__init__
(axis)¶ Firstorder differences operator.
 Parameters
axis (int) – the axis along which to perform the diff.

response
(ndim)¶ Return the equivalent impulse response.
The result of forward method is equivalent with “valid” convolution with this impulse response. The adjoint operator corresponds the “full” convolution with the flipped impulse response.

freq_response
(ndim, shape)¶ The frequency response.

forward
(point)¶ Return H·x

adjoint
(point)¶ Return Hᵀ·e


ir2fr
(imp_resp, shape, center=None, real=True)¶ Return the frequency response from impulse responses.
This function make the necessary correct zeropadding, zero convention, correct DFT etc. to compute the frequency response from impulse responses (IR).
The IR array is supposed to have the origin in the middle of the array.
The Fourier transform is performed on the last len(shape) dimensions.
 Parameters
imp_resp (array) – The impulse responses.
shape (tuple of int) – A tuple of integer corresponding to the target shape of the frequency responses, without hermitian property. len(shape) >= ndarray.ndim. The DFT is performed on the len(shape) last axis of ndarray.
center (tuple of int, optional) – The origin index of the impulse response. The middle by default.
real (boolean, optional) – If True, imp_resp is supposed real, the hermitian property is used with rfftn DFT and the output has shape[1] / 2 + 1 elements on the last axis.
 Returns
out – The frequency responses of shape shape on the last len(shape) dimensions.
 Return type
array
Notes
The output is returned as Ccontiguous array.
For convolution, the result have to be used with unitary discrete Fourier transform for the signal (norm=”ortho” of fft).
DFT are always performed on last axis for efficiency (Corder array).