Fix #906: inati should be iterative and walsh should phase align

[fzimmermann89]

This fixes #906
Inati should be the iterative inati method (2014), not walsh + phase alignment.
Also, it adds phase alignment (can be disabled for pure walsh) to walsh, making it inati 2013.

[github-actions]

Coverage Report

File	Stmts	Miss	Cover	Missing
src/mrpro
_version.py	6	2	67%	7–8
src/mrpro/algorithms/csm
inati.py	26	1	96%	76
src/mrpro/algorithms/dcf
dcf_voronoi.py	55	4	93%	15, 55–56, 89
src/mrpro/algorithms/optimizers
adam.py	30	6	80%	108, 125–129
cg.py	52	1	98%	139
pdhg.py	82	3	96%	187–188, 194
pgd.py	53	4	92%	110, 158–161
src/mrpro/algorithms/reconstruction
DirectReconstruction.py	30	2	93%	64, 80
Reconstruction.py	56	8	86%	57–59, 123–126, 128, 136
RegularizedIterativeSENSEReconstruction.py	52	2	96%	125, 153
TotalVariationRegularizedReconstruction.py	54	4	93%	106, 112, 129, 132
src/mrpro/data
AcqInfo.py	165	7	96%	49, 56, 134–135, 137, 243, 367
Dataclass.py	311	26	92%	58, 319, 335, 401, 465–467, 480, 575, 595–596, 598, 613–614, 616, 663–664, 669–670, 855–856, 881, 888, 893–894, 896
DcfData.py	33	1	97%	62
EncodingLimits.py	97	3	97%	37, 127, 130
IData.py	178	12	93%	138, 155–156, 217–225, 258, 304, 322
IHeader.py	174	8	95%	49, 98–101, 284, 288, 292, 296
KData.py	226	24	89%	121–122, 137, 144, 155–166, 177, 185, 196, 235, 257–259, 306–307, 372, 538, 540, 612
KHeader.py	171	13	92%	119–125, 152, 200, 207–208, 240–247
KNoise.py	22	1	95%	44
KTrajectory.py	95	3	97%	163, 165, 185
Rotation.py	737	42	94%	104, 202, 339, 437, 481, 499, 586, 588, 597, 634, 636, 699, 776, 781, 784, 799, 816, 821, 897, 1085, 1090, 1093, 1117, 1121, 1145, 1265, 1267, 1275–1276, 1340, 1422, 1626, 1633–1635, 1694, 1790, 1942, 1977, 1981, 2156, 2177
SpatialDimension.py	150	19	87%	34, 103, 146, 158, 278–280, 293–295, 329, 347, 360, 373, 386, 399, 408–409, 437
src/mrpro/data/traj_calculators
KTrajectoryCalculator.py	26	2	92%	84, 95
KTrajectoryCartesian.py	31	4	87%	129–132, 136
KTrajectoryIsmrmrd.py	19	1	95%	57
KTrajectorySpiral2D.py	57	13	77%	63–66, 69, 71, 73, 75, 77, 105, 107, 134–136
src/mrpro/operators
AveragingOp.py	38	2	95%	73, 115
B0InformedFourierOp.py	75	2	97%	151–154
CartesianSamplingOp.py	112	4	96%	152, 191, 266, 387
ConjugateGradientOp.py	89	7	92%	62, 64, 100, 106, 228, 230, 233
ConstraintsOp.py	85	4	95%	78, 80, 250, 255
EndomorphOperator.py	28	2	93%	71, 77
FiniteDifferenceOp.py	29	2	93%	40, 126
FourierOp.py	105	9	91%	85–87, 192–193, 212, 257, 321, 326
Functional.py	70	2	97%	116, 118
GridSamplingOp.py	165	15	91%	72–73, 82–83, 90–91, 94, 96, 98, 282, 290–291, 306, 312–313
LinearOperator.py	202	6	97%	217, 255, 296, 305, 313, 330
LinearOperatorMatrix.py	174	19	89%	99, 136, 169, 178, 183, 192–195, 208–211, 219–220, 225–226, 238, 347, 377, 404
MultiIdentityOp.py	16	2	88%	58, 63
NonUniformFastFourierOp.py	198	10	95%	72, 99, 221, 223, 261, 263, 340, 397, 471, 476
Operator.py	88	3	97%	82, 115, 125
PatchOp.py	49	3	94%	93, 129, 144
ProximableFunctionalSeparableSum.py	42	3	93%	118, 213, 224
SliceProjectionOp.py	178	10	94%	45, 62, 64, 70, 154, 180, 216, 253, 290, 330
WaveletOp.py	119	3	97%	184, 228, 254
ZeroPadOp.py	18	1	94%	30
src/mrpro/operators/functionals
SSIM.py	73	4	95%	82, 86, 114, 147
src/mrpro/operators/models
EPG.py	256	19	93%	31–32, 283, 288, 304–306, 326–327, 332, 356, 361, 386, 391, 545, 599, 738, 755, 782
src/mrpro/phantoms
EllipsePhantom.py	43	2	95%	66, 131
b0map.py	26	21	19%	37–63
brainweb.py	297	40	87%	276, 290–294, 349–359, 398, 454–457, 479–480, 485–486, 488–489, 493, 501, 508–509, 550, 621, 624–625, 644, 653–656, 667, 669, 700–701, 715, 723
fastmri.py	106	10	91%	50–51, 59, 65, 162, 169–171, 174–175, 189
m4raw.py	74	4	95%	58–59, 74, 76
mdcnn.py	71	7	90%	58, 62–63, 70, 82, 88, 135
src/mrpro/utils
RandomGenerator.py	155	15	90%	23–24, 36, 38, 188, 212, 428, 446, 528, 799, 829–832, 895, 898
ema.py	42	4	90%	49, 74, 78, 82
filters.py	61	1	98%	46
indexing.py	177	1	99%	321
pad_or_crop.py	39	6	85%	40, 43, 46, 49, 66, 73
reshape.py	153	10	93%	176, 370, 482–484, 505, 508–509, 515, 530
slice_profiles.py	49	6	88%	21, 37, 119–122, 155
split_idx.py	10	2	80%	43, 47
summarize.py	57	6	89%	40–41, 70–73, 81
unit_conversion.py	72	15	79%	34, 44, 51, 53, 62, 69, 71, 78, 80, 89, 100, 121, 123, 144, 146
TOTAL	8110	498	94%

Tests	Skipped	Failures	Errors	Time
3304	0 💤	0 ❌	0 🔥	2m 34s ⏱️

[github-actions]

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[schuenke]

The implementation, tests and documentation look good to me.

Maybe @ckolbPTB wants to have a quick look as well?!

[fzimmermann89]

It would also be great to test it on another challenging dataset.
For the mrf data I did this change for, all three codes result in slightly different csms but unfortunately none seems clearly superior.
Nevertheless, I think this would be the proper csm Walsh and Inati variants to use

[ckolbPTB]

I compared the old and the new methods on a few datasets and all show a similar behaviour as this:

The new Walsh implementation with phase alignment leads to a reasonable homogenous phase.

Nevertheless, the new Inati now leads to the same results as Walsh. I could not find a dataset where there was any noticeable difference and the number of iterations also does not seem to have an effect (i.e. no difference between first and last iteration). The result do not have a flat phase (more pronounced in cardiac datasets) whereas the old implementation leads to a completely constant phase.

I could not find a bug so my suggestion would be to only change the Walsh implementation but leave the old Inati method and clearly label it as non-iterative. @fzimmermann89 @schuenke what are your thoughs on this?

We should really work on the ESPIRT coil estimation...