Implement Gram Shortcut for FourierOp

[fzimmermann89]

Add Gram Operator to the FourierOp and CartesianSamplingOp

FourierOp:
written as convolution with kernel, making use of toeplitz structure of nufft. kernel is calculated with 2^n_dim adjoint nuffs, instead of one nufft with twice the size in all dimensions, saving on memory. same approach as done by tensorflow MRI, but with a loop over he combinations instead of recursion. The torchkbnufft adjoint nufft can at some point be replaced by a different nufft operation. Currently, the code prodces the same results as https://torchkbnufft.readthedocs.io/en/stable/_modules/torchkbnufft/_nufft/toep.html#calc_toeplitz_kernel
If we slit nufft op out of FourierOp, we can also move the nufft-related stuff from init and forward 1:1 to new nufft op.

CartesianSamplingOp
does forward and adjoint pass on an all-ones mask. this could be optimized to instead just set ones in a all-zero mask. but the current form works and is simple.
If we add CartesianSamplingOp to FourierOp, we would also have to include it in FourierOp.gram on the cartesian dimensions.

Tests compare against Operator.H@Operator as ground-truth.

[github-actions]

Coverage Report

File	Stmts	Miss	Cover	Missing
src/mrpro/algorithms/csm
inati.py	24	1	96%	44
walsh.py	16	1	94%	34
src/mrpro/algorithms/dcf
dcf_voronoi.py	53	4	92%	15, 48–49, 76
src/mrpro/algorithms/optimizers
adam.py	20	1	95%	69
src/mrpro/algorithms/reconstruction
DirectReconstruction.py	28	16	43%	51–71, 85
IterativeSENSEReconstruction.py	13	1	92%	76
Reconstruction.py	50	22	56%	42, 54–56, 80–87, 104–113
RegularizedIterativeSENSEReconstruction.py	41	17	59%	96–100, 114–139
src/mrpro/data
AcqInfo.py	128	3	98%	26, 169, 207
CsmData.py	29	3	90%	15, 82–84
DcfData.py	45	8	82%	18, 66, 78–83
IData.py	67	9	87%	119, 125, 129, 159–167
IHeader.py	75	7	91%	75, 109, 127–131
KHeader.py	153	17	89%	25, 119–123, 150, 199, 210, 217–218, 221, 228, 260–271
KNoise.py	31	15	52%	39–52, 56–61
KTrajectory.py	69	5	93%	178–182
MoveDataMixin.py	137	18	87%	15, 113, 129, 143–145, 207, 305–307, 320, 399, 419–420, 422, 437–438, 440
QData.py	39	7	82%	42, 65–73
Rotation.py	674	35	95%	100, 198, 335, 433, 477, 495, 581, 583, 592, 626, 628, 691, 768, 773, 776, 791, 808, 813, 889, 1077, 1082, 1085, 1109, 1113, 1240, 1242, 1250–1251, 1315, 1397, 1690, 1846, 1881, 1885, 1996
SpatialDimension.py	230	21	91%	33, 103, 128, 135, 141, 261–263, 276–278, 312, 330, 343, 356, 369, 382, 391–392, 407, 416
acq_filters.py	12	1	92%	47
src/mrpro/data/_kdata
KData.py	134	18	87%	109–110, 125, 132, 142, 150, 204–205, 243, 248–249, 268–279
KDataRemoveOsMixin.py	29	2	93%	44, 46
KDataSelectMixin.py	19	2	89%	48, 63
KDataSplitMixin.py	48	3	94%	53, 84, 93
src/mrpro/data/traj_calculators
KTrajectoryCalculator.py	25	2	92%	23, 45
KTrajectoryIsmrmrd.py	13	2	85%	41, 50
KTrajectoryPulseq.py	29	1	97%	54
src/mrpro/operators
CartesianSamplingOp.py	89	3	97%	118, 157, 280
ConstraintsOp.py	60	2	97%	46, 48
EndomorphOperator.py	65	2	97%	228, 234
FiniteDifferenceOp.py	27	2	93%	40, 105
FourierOp.py	157	3	98%	263, 381, 386
Functional.py	71	5	93%	20–22, 117, 119
GridSamplingOp.py	136	9	93%	72–73, 82–83, 90–91, 94, 96, 98
LinearOperator.py	171	12	93%	55, 91, 190, 220, 261, 270, 278, 287, 295, 320, 418, 423
LinearOperatorMatrix.py	158	16	90%	82, 119, 152, 161, 166, 175–178, 191–194, 203, 215, 304, 331, 359
MultiIdentityOp.py	13	2	85%	43, 48
Operator.py	78	2	97%	25, 74
ProximableFunctionalSeparableSum.py	39	3	92%	50, 103, 110
SliceProjectionOp.py	173	8	95%	44, 61, 63, 69, 206, 227, 260, 300
WaveletOp.py	120	5	96%	152, 170, 205, 210, 233
ZeroPadOp.py	16	1	94%	30
src/mrpro/utils
filters.py	62	2	97%	44, 49
slice_profiles.py	46	6	87%	20, 36, 113–116, 149
sliding_window.py	34	1	97%	34
split_idx.py	10	2	80%	43, 47
summarize_tensorvalues.py	11	9	18%	20–29
typing.py	18	11	39%	8–23
zero_pad_or_crop.py	31	6	81%	26, 30, 54, 57, 60, 63
TOTAL	4865	354	93%

Tests	Skipped	Failures	Errors	Time
2009	0 💤	0 ❌	0 🔥	2m 15s ⏱️

[github-actions]

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[fzimmermann89]

This will need an adjustment once the CartesianSamplingOp is added to FourierOp. ✔️

Should we keep the helper function that creates the convolution kernel next to the Operators or should we move it into algorithms somewhere?

It is IMHO not really an algorithm, just a tiny bit smarter way to do a Nufft with doubled images size in each dimension..

[fzimmermann89]

needs #517 ..

[fzimmermann89]

We could remove the Gram Operators and instead return directly the composition of the other operators.
But this might be a bit confusing, that FourierOp.gram results in a composition of 2 FourierOps, two multiplications, ...

[fzimmermann89]

Also, it could be made a bit more efficient if we add a normalize and fftshift flag to the fftop, we can avoid both by scaling/shifting the kernel instead.

[koflera]

looks good to me

[Stef-Martin]

Looks good to me as well, Toeplitz Kernel from tkbnufft and Gram also give very similar results