Add SymmetrizedGradientOp and TGV image reconstruction demonstration

[trung-vt]

(This PR is a fix for the previous PR #894 and a direct continuation from #903.)

Summary

• Add SymmetrizedGradientOp as a linear operator in mrpro.operators. Supports $k$-dimensional spatial dimensions for arbitrary number of dimensions $k$. Add unit tests tests/operators/test_symmetrized_gradient_op.py for correctness and adjointness.
• Add example notebook demonstrating Total Generalized Variation image reconstruction for radial undersampled MRI reconstruction using SymmetrizedGradientOp.

Motivation

The symmetrized gradient is required for total generalised variation (TGV) type regularisation, in particular for
second-order TGV as in Bredies (2014). Having a dedicated operator in mrpro makes it easier to implement TGV-based
reconstruction methods in a consistent way with the rest of the library,
as demonstrated in the example notebook.

Notes

No breaking changes expected; existing APIs remain unchanged.

[github-actions]

Coverage Report

File	Stmts	Miss	Cover	Missing
src/mrpro
_version.py	6	2	67%	7–8
src/mrpro/algorithms/csm
inati.py	25	1	96%	43
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	81	3	96%	180–181, 187
pgd.py	53	4	92%	107, 152–155
src/mrpro/algorithms/reconstruction
DirectReconstruction.py	28	6	79%	62, 65, 70, 77–79
IterativeSENSEReconstruction.py	13	1	92%	79
Reconstruction.py	50	13	74%	54–56, 80–87, 109, 112
RegularizedIterativeSENSEReconstruction.py	51	26	49%	104–108, 122–161
src/mrpro/data
AcqInfo.py	165	7	96%	49, 56, 134–135, 137, 243, 367
CsmData.py	43	2	95%	233–235
Dataclass.py	312	26	92%	59, 320, 336, 402, 460–462, 475, 570, 590–591, 593, 608–609, 611, 658–659, 664–665, 852–853, 878, 885, 890–891, 893
DcfData.py	33	1	97%	62
EncodingLimits.py	97	3	97%	37, 127, 130
IData.py	138	6	96%	125, 185, 231, 244, 249, 293
IHeader.py	130	7	95%	69–72, 255, 259, 263, 267
KData.py	228	24	89%	122–123, 138, 145, 156–167, 178, 186, 197, 236, 258–260, 304–305, 377, 543, 545, 617
KHeader.py	176	13	93%	115–121, 148, 196, 203–204, 231–238
KNoise.py	22	1	95%	44
KTrajectory.py	95	3	97%	163, 165, 185
QData.py	32	1	97%	43
Rotation.py	735	42	94%	104, 202, 339, 437, 481, 499, 586, 588, 597, 631, 633, 696, 773, 778, 781, 796, 813, 818, 894, 1082, 1087, 1090, 1114, 1118, 1142, 1262, 1264, 1272–1273, 1337, 1419, 1623, 1630–1632, 1691, 1787, 1939, 1974, 1978, 2154, 2175
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	36	2	94%	72, 113
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	101	6	94%	186–187, 206, 251, 315, 320
Functional.py	70	2	97%	116, 118
GridSamplingOp.py	165	15	91%	72–73, 82–83, 90–91, 94, 96, 98, 282, 290–291, 303, 309–310
LinearOperator.py	202	6	97%	217, 255, 296, 305, 313, 330
LinearOperatorMatrix.py	174	19	89%	98, 135, 168, 177, 182, 191–194, 207–210, 218–219, 224–225, 237, 346, 376, 403
MultiIdentityOp.py	16	2	88%	58, 63
NonUniformFastFourierOp.py	195	10	95%	68, 95, 217, 219, 257, 259, 336, 393, 467, 472
Operator.py	88	3	97%	82, 115, 125
PatchOp.py	49	3	94%	93, 129, 144
ProximableFunctionalSeparableSum.py	44	3	93%	117, 208, 219
SliceProjectionOp.py	178	10	94%	45, 62, 64, 70, 154, 180, 216, 253, 290, 330
WaveletOp.py	121	5	96%	168, 186, 230, 235, 258
ZeroPadOp.py	18	1	94%	30
src/mrpro/operators/functionals
SSIM.py	73	7	90%	60–80, 82, 86, 114, 147
src/mrpro/operators/models
EPG.py	212	44	79%	31–32, 105–120, 168–172, 192–195, 216–221, 284, 289, 305–307, 327–328, 333, 357, 362, 387, 392, 508, 609, 636
src/mrpro/phantoms
EllipsePhantom.py	43	2	95%	66, 131
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	156	15	90%	23–24, 36, 38, 188, 212, 428, 446, 528, 799, 829–832, 895, 898
filters.py	62	2	97%	44, 49
indexing.py	177	1	99%	321
pad_or_crop.py	32	6	81%	27, 31, 62, 65, 68, 71
reshape.py	139	9	94%	112, 308, 420–422, 443, 445, 452, 467
slice_profiles.py	49	6	88%	21, 37, 119–122, 155
split_idx.py	10	2	80%	43, 47
summarize.py	57	7	88%	40–41, 70–73, 77, 81
unit_conversion.py	72	15	79%	34, 44, 51, 53, 62, 69, 71, 78, 80, 89, 100, 121, 123, 144, 146
TOTAL	7655	525	93%

Tests	Skipped	Failures	Errors	Time
3057	0 💤	0 ❌	0 🔥	2m 7s ⏱️

[github-actions]

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