Pith. sign in

REVIEW 4 major objections 6 minor 1 cited by

Efficient Dynamic Image Reconstruction with motion estimation

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A new algorithm, MMGKS-OF, reconstructs moving objects in dynamic tomography by estimating optical flow between frames and using it as an extra temporal regularizer; across limited-angle and single-shot CT tests, the motion-aware…

desk verdict Useful and honest numerical paper on optical-flow-regularized dynamic CT, but the mismatch between the stated ℓ2 objective and the implemented ℓ1 subproblem must be resolved before the reported gains are taken at face value. read the letter →

arxiv 2501.12497 v1 pith:HJ6LWCCL submitted 2025-01-21 math.NA cs.NA

Toluwani Okunola , Mirjeta Pasha , Misha Kilmer , Melina Freitag This is my paper · ORCID
classification math.NAcs.NA MSC 65F2265F1065K10
keywords dynamicinverseproblemsgeneralizedKrylovsubspacecomputerizedtomographymotionestimationopticalflowspatio-temporalregularizationill-posedproblemparameterselection
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper proposes a way to handle dynamic inverse problems—where the object moves while projection data are collected—by estimating that motion with optical flow and using it as an additional temporal regularizer in the reconstruction. The central claim is that the motion-aware term, combined with an edge-preserving spatial regularizer and solved by a generalized Krylov subspace method, gives better reconstructions than the same solvers without motion information. The experiments cover limited-angle and single-shot computerized tomography, exactly the severely undersampled settings where temporal coherence should matter most. If the claim holds, the method offers a computationally practical route to reconstructing moving targets from sparse projection data, with regularization parameters selected automatically rather than tuned by hand.

What carries the argument

The load-bearing object is the linearized optical-flow regularization matrix $\bar{M}(s)$, a block matrix whose diagonal blocks are the identity and whose off-diagonal blocks are motion warping matrices $M(s(t))$; $M(s(t))$ is built either by rounding estimated velocities to integer pixel shifts (making it a permutation) or by bilinear warping weights. The identity that carries the argument is $\bar{M}(s)u = \Upsilon(u)s + u_t$, which says that applying the motion matrix to the image sequence is the same as evaluating the standard optical flow constraint. That identity turns a nonlinear motion model into a linear regularizer, which can be merged with the $\ell^1$ edge-preserving spatial operator into a single operator $\Theta^{(k)}$ and solved by majorization-minimization inside a growing Krylov subspace; the same MMGKS machinery solves the optical flow subproblem and selects its regularization parameter automatically.

What would settle it

Run the published algorithm on a dynamic phantom whose true per-frame displacement exceeds about one pixel, or whose motion rotates or shears the object so that brightness constancy fails, under the same limited-angle geometry; if the motion-augmented reconstructions do not beat the non-motion baseline in relative error and SSIM, the central claim fails.

Watch

Extended reading notes

Core claim

The paper's central claim is that the optical flow constraint can be encoded as a linear operator on the whole image sequence, so that motion information becomes a drop-in regularization term rather than a separate nonlinear model. Given estimated velocity fields, the matrix $\bar{M}(s)$ is a block bidiagonal operator built from image warping blocks $M(s(t))$, and the identity $\bar{M}(s)u \approx \Upsilon(u)s + u_t$ connects this matrix product to the classical optical flow equation. The paper solves the resulting functional by alternating between optical flow estimation and image reconstruction, using the MMGKS (majorization-minimization generalized Krylov subspace) method for both subproblems with automatic regularization parameter selection by discrepancy principle or generalized cross-validation. In the four test settings, the optical-flow variants consistently outperform their non-motion counterparts in relative error and structural similarity, with the largest gains in severely limited-angle and binned-angle scenarios and diminishing returns as more projection angles are added.

Load-bearing premise

The method assumes pixel intensities stay constant along motion paths and that frames are close enough in time for the first-order Taylor expansion of the optical flow equation to be accurate; if displacements are large, objects deform, or illumination changes, the temporal regularizer is mis-specified and can degrade the reconstruction.

Editorial extensions

If this is right

  • In severely limited-angle tomography, adding the optical-flow term produces substantially lower relative reconstruction error and higher SSIM than the same spatial regularizers alone; the advantage shrinks as more projection angles are available.
  • The method applies to single-shot tomography, where only one projection angle is measured per time step, recovering rigidly moving objects from extremely sparse data.
  • Regularization parameters for both the image and motion subproblems are selected automatically, either by the discrepancy principle or by generalized cross-validation, removing a manual tuning step that the paper shows is a sensitivity bottleneck in an alternating-method baseline.
  • The algorithm keeps computational cost comparable to existing joint motion-estimation methods by projecting onto a low-dimensional Krylov subspace, recomputing optical flow only every 20 iterations, downsampling images before flow estimation, and deriving reverse motion from forward motion rather than solving the backward problem.
  • The motion-aware regularizer is compatible with several spatial priors, and in every tested combination the optical-flow version beats the non-motion version.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Because the optical flow term is encoded as a fixed linear operator once velocities are estimated, the same $\bar{M}(s)$ matrix could be plugged into other variational solvers, not only Krylov-subspace ones; testing this would show whether the motion encoding itself or the MMGKS solver drives the reported gains.
  • The observed diminishing returns with more projection angles suggest the method's value is concentrated in extremely sparse sampling; a natural experiment is to apply it to gapped or non-uniform angular sampling patterns beyond the binning case studied here.
  • The reverse-flow approximation, which derives backward velocities from forward velocities instead of solving the optical flow problem in reverse, is a cost-saving shortcut whose accuracy should degrade as motion grows; measuring that degradation would define when the shortcut is safe.
  • A learned or parametric motion model could replace the brightness-constancy velocity field, potentially extending the approach to non-rigid deformation and larger time steps, which the paper names as future work.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper proposes MMGKS-OF, an alternating algorithm for dynamic image reconstruction in which the optical flow between consecutive frames is estimated from the current reconstruction, encoded as a linear warping operator M(s), and then used as a temporal regularization term alongside edge-enhancing spatial regularization. Both the optical flow subproblem and the image reconstruction subproblem are solved with a majorization-minimization generalized Krylov subspace method, with regularization parameters selected automatically by the discrepancy principle or generalized cross-validation. The numerical section reports consistent improvements in relative reconstruction error and SSIM for MMGKS-OF over non-optical-flow baselines on limited-angle CT (synthetic and real emoji data) and single-shot CT (two synthetic datasets).

Significance. If the method is correctly specified and the reported experiments are representative, MMGKS-OF is a useful and computationally attractive contribution to joint motion estimation and dynamic tomographic reconstruction: it avoids expensive inner proximal loops, uses a Krylov subspace reduction, and replaces manual tuning of the main regularization parameter by automatic DP/GCV selection. The paper also contains several practical engineering choices, such as periodic optical flow updates, downsampling, reverse-flow approximation, and parallelization, which are relevant for large-scale problems, and it mitigates inverse crime in the synthetic tests by using mismatched projectors and added noise. The main strengths are therefore the algorithmic design and the breadth of numerical comparisons. However, as detailed below, a load-bearing ambiguity about which objective was actually minimized, a post-hoc choice of the optical flow norm exponents, and the partially hand-set regularization ratios mean that the numerical evidence does not yet fully establish the central claims.

major comments (4)
  1. [§4, Eq. (4.1) vs. §4.1.1, Eqs. (4.5), (4.7)] The formal joint objective and the algorithm actually described minimize different functionals. Equation (4.1) defines the motion-fidelity term as λ2 ||M_bar(s,s')u||_2 (an ℓ2 norm), but the image reconstruction subproblem in Eq. (4.5) and its combined form in Eq. (4.7) use the ℓ1 norm ||M_bar^(k)u||_1, and the MMGKS weighting used in Algorithm 4.1 step 8 and Appendix B is designed for the ℓ1 setting. Because the code is not yet public, a reader cannot determine which objective produced the results in Tables 5.2–5.5. This ambiguity is load-bearing: ℓ1 and ℓ2 regularization of the motion residual have different edge-preservation properties, and the reported reconstruction gains could depend on that choice. Please state explicitly which objective is minimized in the implementation and make the code available for review.
  2. [§4.1.2 and §5] The choice p=q=2 for the optical flow norm appears to be made after observing test performance. The text states that for a standalone optical flow problem p=q=1 gives optimal results, but that for the limited-angle and single-shot tomography problems "choosing p=q=2 resulted in more accurate reconstructed image sequence. Hence, for all the experiments we use the later." Since p and q are free parameters of the proposed method and were selected on the same experiments used to demonstrate improvement, the reported gains may be partially due to selection bias. The paper provides no error bars, no repeated-run statistics, and no held-out tuning set. Please report results for both (p,q) choices, or otherwise demonstrate that the conclusions are robust to this choice.
  3. [§4.1.1 and §4.1.3] The claim of automatic regularization parameter selection is overstated. Equation (4.5) contains two regularization parameters, and Section 4.1.1 fixes λ := λ1 = λ2, so the ratio of spatial to temporal regularization is a hand-set modeling choice; the optical flow subproblem (4.3) carries additional parameters γ and q, with (p,q) selected manually as noted above. Thus only a single effective λ is selected automatically, via DP or GCV, once these ratios and exponents are fixed. Please temper the abstract and contribution statements, or demonstrate that the reconstruction quality is insensitive to the fixed λ1/λ2 ratio and to the other hand-set choices.
  4. [§5, reproducibility] Section 5 states that all test problems and algorithm implementations "will be made publicly available... once the manuscript is accepted to the journal," which means the numerical experiments are not independently verifiable during review. Given that the reported improvements are entirely empirical and that the objective implemented is currently ambiguous (see the first major comment), a reviewer-accessible supplement or code archive is needed to confirm that the experiments correspond to the proposed algorithm as written.
minor comments (6)
  1. [§2.2, Eq. (2.4)] The sentence preceding Eq. (2.4) says the right-hand side of (2.3) is linearly approximated, but the expansion is performed on the left-hand side, u(x_i + s_x ∆t, y_i + s_y ∆t, t + ∆t); please correct this to "left-hand side."
  2. [§2.2, Eq. (2.7)] The phrase "γ ∈ R is and a regularization parameter" is garbled; it should read "γ > 0 is a regularization parameter."
  3. [§4, Eq. (4.4)] In Eq. (4.4), the left-hand side reads "s′(k) argmin" and is missing an equals sign; it should be "s′(k) = argmin."
  4. [§4.1.1, Algorithm 4.1, Appendix B] The definition of the weighting matrix P_ε is inconsistent across the paper: Eq. (4.8) uses P_ε = (diag(1/φ_ε(z)))^{1/2}, Algorithm 4.1 step 8 uses (diag((ν^(k))^2 + ε^2))^{-1/4}, and Algorithm B.1 step 6 uses (diag(w_ε))^{1/2} with w_ε = ((y^(k))^2 + ε^2)^{1/2}; please unify these definitions and relate them to the ℓ1 majorizer explicitly.
  5. [§5.1.1, Table 5.2] In Table 5.2, the SSIM rows for nviews = 5 and nviews = 7 are identical to the corresponding RRE rows, which is almost certainly a copy-paste error; the correct SSIM values should be reported.
  6. [§5.1.3] In Test 3, the evaluation is necessarily qualitative because no ground truth is available; the text says the OF methods "from observation... outperform" the others, but it would strengthen the comparison to quantify this, for example with a no-reference metric or by reporting the estimated optical flow quality.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the optical-flow regularizer is constructed from standard assumptions and external MMGKS machinery, and the alternating loop does not reduce to its inputs.

full rationale

The proposed derivation is self-contained and not circular. The optical flow model is a standard brightness-constancy assumption (Eq. 2.2) with a first-order Taylor expansion (Eq. 2.4), and the paper builds the linear motion operator M_bar(s) explicitly in Section 3; the key identity M_bar(s)u = Υ(u)s + u_t (Eq. 3.3) is a direct consequence of the definitions, not an imported or self-cited theorem. The alternating MMGKS-OF loop (Algorithm 4.1) estimates velocities from the current reconstruction and then uses the fixed operator M_bar(k) as a linear regularizer in the image subproblem (4.5)-(4.7); because the next iterate must still fit Hu ≈ b, the temporal regularizer acts as a prior rather than as a forced reproduction of its own input. Regularization parameters are selected by the discrepancy principle or GCV (Section 4.1.3), and the experiments report that DP is used when noise information is known, so the parameters are not fitted to the ground-truth RRE/SSIM values. Self-citations in the reference list (e.g., the authors' prior MMGKS recycling paper and Trips-Py toolbox) supply software, datasets, and background, but none carries the central claim; the MMGKS algorithm itself is cited to the external works [28,31]. No uniqueness theorem from the authors is invoked, and no known empirical pattern is repackaged under new coordinates. A separate consistency caveat should be noted but is not circularity: the formal objective (4.1) writes the motion-fidelity term with an ℓ2 norm, while the implemented subproblem (4.5)/(4.7) and the MMGKS weighting use the ℓ1 norm of the same term; that mismatch affects reproducibility of the numerical claims, not the logical equivalence of a result to its input.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method relies on standard assumptions of optical flow and a specific linear encoding of motion. The main free choices are model norms and algorithmic hyperparameters, several of which were tuned on the test problems rather than derived from first principles.

free parameters (5)
  • Optical flow norm exponents p and q = 2, 2
    In Section 4.1.2, the authors report that p=q=1 works best for standalone OF but p=q=2 gives more accurate reconstructions in the limited-angle and single-shot tests; this choice was made after observing test performance, not a priori.
  • Optical flow update frequency tau = 20
    Section 5 states OF calculations were performed only every 20 iterations to manage resources, a heuristic choice with no sensitivity analysis.
  • Initial subspace dimension ell = 10
    Set to 10 for all experiments (Section 5), with no sensitivity analysis.
  • Downsampling factor = 4 or 2
    Images are downsampled before OF computation to below 50x50 pixels (Section 5); the factor is not specified per test, and it affects the accuracy of the estimated flow.
  • Smoothing parameter epsilon = unspecified
    Used in the MMGKS weighting matrix P_epsilon (Section 4.1.1); no value or selection rule is given.
assumptions (5)
  • domain assumption The optical flow constraint (brightness constancy) holds: pixel intensity is invariant along the motion trajectory (Eq. 2.2).
    The entire temporal regularization model is built on this assumption. If intensities change, the motion model is invalid. Stated in Section 2.2.
  • domain assumption Velocity is constant within each time interval and displacements between consecutive frames are small.
    The linear approximation in Eq. (2.4) uses a first-order Taylor expansion, which requires small time steps and small displacements. Acknowledged in Section 6 as a limitation.
  • domain assumption The objects undergo rigid motion with no deformation.
    The paper explicitly excludes diffeomorphic or shape-based methods, assuming no deformation (Section 1). This limits applicability to non-deforming objects.
  • ad hoc to paper The motion model can be represented as a linear warping operator M(s) via rounding or bilinear interpolation.
    The mapping from continuous velocities to a sparse matrix is an approximation designed for the MMGKS framework. It is not rigorously justified and may introduce errors for large or fractional displacements.
  • domain assumption The condition N(H^T H) ∩ N(Theta^T P Theta) = {0} holds, ensuring a unique solution to the normal equations.
    Assumed to hold 'in practice' in Section 4.1.1, but not verified for the test problems. If violated, the majorant minimization step is ill-posed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Efficient Dynamic Image Reconstruction with motion estimation." pith.science (2026). https://pith.science/paper/HJ6LWCCL

@misc{pith2026250112497,
  author       = {Pith},
  title        = {Pith review of: Efficient Dynamic Image Reconstruction with motion estimation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HJ6LWCCL}},
  note         = {Machine review of arXiv:2501.12497}
}
read the original abstract

Dynamic inverse problems are challenging to solve due to the need to identify and incorporate appropriate regularization in both space and time. Moreover, the very large scale nature of such problems in practice presents an enormous computational challenge. In this work, in addition to the use of edge-enhancing regularization of spatial features, we propose a new regularization method that incorporates a temporal model that estimates the motion of objects in time. In particular, we consider the optical flow model that simultaneously estimates the motion and provides an approximation for the desired image, and we incorporate this information into the cost functional as an additional form of temporal regularization. We propose a computationally efficient algorithm to solve the jointly regularized problem that leverages a generalized Krylov subspace method. We illustrate the effectiveness of the prescribed approach on a wide range of numerical experiments, including limited angle and single-shot computerized tomography.

Figures

Figures reproduced from arXiv: 2501.12497 by the authors.

Figure 5.1
Figure 5.1. Slices of ground truth images of (a) Test 1 at [PITH_FULL_IMAGE:figures/full_fig_p016_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Test 1: RRE convergence plots 5.1.2 Test 2: MNIST Moving Numbers Dataset In this example we con￾sider the MNIST dataset found in [48] which consists of 10,000 video sequences of length 20. Each frame in the sequence is of resolution 64×64 pixels and contains two moving digits. From this dataset, we select a single sequence as our ground truth. This manuscript is for review purposes only [PITH_FULL_IMAGE:figures/ful… view at source ↗
Figure 5.3
Figure 5.3. Test 1: Estimated optical flow when nviews = 3 at t = 1, 5, 10. nviews RRE M M-OF D1 D1-OF D2 D2-OF D3 D3-OF 3 0.528 0.167 0.251 0.177 0.491 0.409 0.644 0.423 5 0.590 0.341 0.376 0.319 0.430 0.376 0.607 0.405 7 0.582 0.330 0.370 0.313 0.424 0.371 0.595 0.402 SSIM 3 0.608 0.358 0.388 0.336 0.443 0.398 0.629 0.433 5 0.590 0.341 0.376 0.319 0.430 0.376 0.607 0.405 7 0.582 0.330 0.370 0.313 0.424 0.371 0.595 0.402 [PIT… view at source ↗
Figures from the paper (9 more)
Figure 5.4
Figure 5.4. Figure 5.4: Test 1: Reconstructed images at t = {2, 6, 10} when nviews = 3. Results and Discussion We evaluate the performance of all eight methods under each of the three angle selection scenarios. In all scenarios, we observe that the OF methods consistently outperform their n…
Figure 5.5
Figure 5.5. Figure 5.5: Test 2: RRE convergence plots for MMGKS, MMGKS-OF, ANISO, ANISO-OF, [PITH_FULL_IMAGE:figures/full_fig_p019_5_5.png]
Figure 5.6
Figure 5.6. Figure 5.6: Test 2: Reconstructed images at t = {2, 11, 18} when angles are selected according to Case a. giving the best results this time. 5.2 Computerized Single-shot Tomography 5.2.1 Test 4: Single-shot tomography of synthetic rigid motion For this example, we consider the s…
Figure 5
Figure 5. Figure 5 [PITH_FULL_IMAGE:figures/full_fig_p019_5.png]
Figure 5.7
Figure 5.7. Figure 5.7: Test 3: Reconstructed Images at t = {2, 17, 31} shows the ground-truth images at a selection of time steps. Forward Model and Projection Geometry From the dataset provided, we generate the problems Htu(t) + γ t = b t , t = 1, 2, . . . , 33 where Ht ∈ R 75×2500 , b t …
Figure 5.8
Figure 5.8. Figure 5.8: Slices of ground truth images of (a) Test 4 at [PITH_FULL_IMAGE:figures/full_fig_p021_5_8.png]
Figure 5.9
Figure 5.9. Figure 5.9: Test 4: Reconstructed Images at at t = {30, 64, 98} constancy. We therefore aim to generalize our motion models beyond optical flow to encompass nonlinear deformations, as explored in works such as [12, 11], and to develop more sophisticated models capable of handlin…
Figure 5.10
Figure 5.10. Figure 5.10: Test 4 (L) and Test 5 (R): RRE convergence plots. [PITH_FULL_IMAGE:figures/full_fig_p022_5_10.png]
Figure 5.11
Figure 5.11. Figure 5.11: Test 5: Reconstructed Images at t = 2, 14, 28. M M-OF D1 D1-OF D2 D2-OF D3 D3-OF RRE 0.815 0.314 0.418 0.323 0.489 0.399 0.777 0.368 SSIM 0.301 0.926 0.863 0.922 0.806 0.880 0.384 0.896 [PITH_FULL_IMAGE:figures/full_fig_p023_5_11.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Randomized Tucker-Sketched GMRES

    math.NA 2026-08 conditional novelty 6.0 of 10

    Two sketched GMRES variants in Tucker format, using randomized HOSVD and multilinear Nyström compression, solve tensor linear systems with reduced memory and time, and low-rank compression regularizes inverse problems.

Reference graph

Works this paper leans on

54 extracted references · 47 canonical work pages · cited by 1 Pith paper

  1. [1]

    Alfarano, L

    A. Alfarano, L. Maiano, L. Papa, and I. Amerini , Estimating optical flow: A comprehen- sive review of the state of the art , Computer Vision and Image Understanding, (2024), p. 104160

    work page 2024

  2. [2]

    Arridge, P

    S. Arridge, P. Fernsel, and A. Hauptmann , Joint reconstruction and low-rank decomposi- tion for dynamic inverse problems , Inverse Problems and Imaging, 16 (2022), pp. 483–523

    work page 2022

  3. [3]

    J. M. Bardsley, A. Parker, A. Solonen, and M. Howard , Krylov space approximate Kalman filtering , Numerical Linear Algebra with Applications, 20 (2013), pp. 171–184

    work page 2013

  4. [4]

    Buccini, M

    A. Buccini, M. Pasha, and L. Reichel , Modulus-based iterative methods for constrained ℓp − ℓq minimization, Inverse Problems, 36 (2020), p. 084001

    work page 2020

  5. [5]

    Buccini, M

    A. Buccini, M. Pasha, and L. Reichel , Linearized Krylov subspace Bregman iteration with nonnegativity constraint, Numerical Algorithms, 87 (2021), pp. 1177–1200

    work page 2021

  6. [6]

    On Optical Flow Models for Variational Motion Estimation

    M. Burger, H. Dirks, and L. Frerking , On optical flow models for variational mo- tion estimation, ArXiv, abs/1512.00298 (2015), https://api.semanticscholar.org/CorpusID: 2469758

    work page Pith review arXiv 2015

  7. [7]

    Burger, H

    M. Burger, H. Dirks, L. Frerking, A. Hauptmann, T. Helin, and S. Siltanen , A varia- tional reconstruction method for undersampled dynamic X-ray tomography based on phys- ical motion models , Inverse Problems, 33 (2017), p. 124008

    work page 2017

  8. [8]

    Burger, H

    M. Burger, H. Dirks, and C.-B. Sch¨onlieb, A variational model for joint motion estimation and image reconstruction , SIAM Journal on Imaging Sciences, 11 (2018), pp. 94–128, https://doi.org/10.1137/16M1084183, https://doi.org/10.1137/16M1084183

    work page doi:10.1137/16m1084183 2018

Show all 54 references
  1. [9]

    Burger, A

    M. Burger, A. Sawatzky, and G. Steidl , First order algorithms in variational image pro- cessing, 2014, https://arxiv.org/abs/1412.4237, https://arxiv.org/abs/1412.4237

    2014 arXiv

  2. [10]

    Chambolle and T

    A. Chambolle and T. Pock , An introduction to continuous optimization for imaging , Acta Numerica, 25 (2016), p. 161–319, https://doi.org/10.1017/S096249291600009X

    2016 doi

  3. [11]

    Chen, Spatiotemporal imaging with diffeomorphic optimal transportation, Inverse Problems, 37 (2021), p

    C. Chen, Spatiotemporal imaging with diffeomorphic optimal transportation, Inverse Problems, 37 (2021), p. 115004

    2021

  4. [12]

    C. Chen, B. Gris, and O. Oktem , A new variational model for joint image reconstruction and motion estimation in spatiotemporal imaging , SIAM Journal on Imaging Sciences, 12 (2019), pp. 1686–1719

    2019

  5. [13]

    Chung, M

    J. Chung, M. Chung, S. Gazzola, and M. Pasha , Efficient learning methods for large-scale optimal inversion design , Numerical Algebra, Control and Optimization, (2022), https: //doi.org/10.3934/naco.2022036

    2022 doi

  6. [14]

    Chung and S

    J. Chung and S. Gazzola , Flexible Krylov methods for \ell p regularization, SIAM Journal on Scientific Computing, 41 (2019), pp. S149–S171

    2019

  7. [15]

    Chung and A

    J. Chung and A. K. Saibaba , Generalized hybrid iterative methods for large-scale Bayesian inverse problems, SIAM Journal on Scientific Computing, 39 (2017), pp. S24–S46

    2017

  8. [16]

    Chung, A

    J. Chung, A. K. Saibaba, M. Brown, and E. Westman , Efficient generalized Golub–Kahan based methods for dynamic inverse problems , Inverse Problems, 34 (2018), p. 024005

    2018

  9. [17]

    H. Dirks, Variational Methods for Joint Motion Estimation and Image Reconstruction , PhD thesis, Institute for Computational and Applied Mathematics University of Muenster, june 2015, /2015/Dir15

    2015

  10. [18]

    Djurabekova, A

    N. Djurabekova, A. Goldberg, A. Hauptmann, D. Hawkes, G. Long, F. Lucka, and M. Betcke , Application of proximal alternating linearized minimization (palm) and in- This manuscript is for review purposes only. 26 OKUNOLA T., PASHA M., KILMER M., FREITAG M. ertial palm to dynami...

    2019 doi

  11. [19]

    Donatelli and L

    M. Donatelli and L. Reichel, Square smoothing regularization matrices with accurate bound- ary conditions, Journal of Computational and Applied Mathematics, 272 (2014), pp. 334– 349

    2014

  12. [20]

    H. W. Engl, M. Hanke, and A. Neubauer , Regularization of Inverse Problems , Kluwer, Dordrecht, 1996

    1996

  13. [21]

    M. A. Figueiredo and R. D. Nowak , An EM algorithm for wavelet-based image restoration , IEEE Transactions on Image Processing, 12 (2003), pp. 906–916

    2003

  14. [22]

    Gao, J.-F

    H. Gao, J.-F. Cai, Z. Shen, and H. Zhao , Robust principal component analysis-based four- dimensional computed tomography, Physics in Medicine & Biology, 56 (2011), p. 3181

    2011

  15. [23]

    Gazzola, M

    S. Gazzola, M. E. Kilmer, J. G. Nagy, O. Semerci, and E. L. Miller , An inner–outer iterative method for edge preservation in image restoration and reconstruction , Inverse Problems, 36 (2020), p. 124004

    2020

  16. [24]

    Hakkarainen, Z

    J. Hakkarainen, Z. Purisha, A. Solonen, and S. Siltanen , Undersampled dynamic X-ray tomography with dimension reduction Kalman filter, IEEE Transactions on Computational Imaging, 5 (2019), pp. 492–501

    2019

  17. [25]

    P. C. Hansen , Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion, SIAM, Philadelphia, 1998

    1998

  18. [26]

    Hauptmann, O

    A. Hauptmann, O. ¨Oktem, and C. Sch ¨onlieb, Image reconstruction in dynamic inverse problems with temporal models , Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging: Mathematical Imaging and Vision, (2021), pp. 1–31

    2021

  19. [27]

    B. K. Horn and B. G. Schunck , Determining optical flow , Artificial Intelligence, 17 (1981), pp. 185–203, https://doi.org/https://doi.org/10.1016/0004-3702(81)90024-2, https://www.sciencedirect.com/science/article/pii/0004370281900242

    1981

  20. [28]

    Huang, A

    G. Huang, A. Lanza, S. Morigi, L. Reichel, and F. Sgallari , Majorization–minimization generalized Krylov subspace methods for ℓp − ℓq optimization applied to image restoration , BIT Numerical Mathematics, 57 (2017), pp. 351–378

    2017

  21. [29]

    A. Kadu, F. Lucka, and K. J. Batenburg , Single-shot tomography of discrete dynamic objects, IEEE Transactions on Computational Imaging, (2024)

    2024

  22. [30]

    S. Lan, M. Pasha, and S. Li , Spatiotemporal Besov priors for bayesian inverse problems , arXiv preprint arXiv:2306.16378, (2023)

    2023

  23. [31]

    Lanza, S

    A. Lanza, S. Morigi, L. Reichel, and F. Sgallari , A generalized Krylov subspace method for ℓp − ℓq minimization, SIAM Journal on Scientific Computing, 37 (2015), pp. S30–S50

    2015

  24. [32]

    Lucka, N

    F. Lucka, N. Huynh, M. Betcke, E. Zhang, P. Beard, B. Cox, and S. Arridge , Enhanc- ing compressed sensing 4D photoacoustic tomography by simultaneous motion estimation , SIAM Journal on Imaging Sciences, 11 (2018), pp. 2224–2253

    2018

  25. [33]

    Maboudi Afkham, N

    B. Maboudi Afkham, N. A. B. Riis, Y. Dong, and P. C. Hansen, Inferring object boundaries and their roughness with uncertainty quantification , Journal of Mathematical Imaging and Vision, (2024), pp. 1–16

    2024

  26. [34]

    Milanfar, A model of the effect of image motion in the radon transform domain , IEEE Transactions on Image processing, 8 (1999), pp

    P. Milanfar, A model of the effect of image motion in the radon transform domain , IEEE Transactions on Image processing, 8 (1999), pp. 1276–1281

    1999

  27. [35]

    Y. D. Mutaf, J. A. Antolak, and D. H. Brinkmann , The impact of temporal inaccuracies on 4dct image quality , Medical physics, 34 (2007), pp. 1615–1622

    2007

  28. [36]

    Niemi, M

    E. Niemi, M. Lassas, A. Kallonen, L. Harhanen, K. H ¨am¨al¨ainen, and S. Siltanen , Dy- namic multi-source X-ray tomography using a spacetime level set method , Journal of Com- putational Physics, 291 (2015), pp. 218–237

    2015

  29. [37]

    Nolte and C

    D. Nolte and C. Bertoglio, Inverse problems in blood flow modeling: A review , International journal for numerical methods in biomedical engineering, 38 (2022), p. e3613

    2022

  30. [38]

    Ozsar, M

    E. Ozsar, M. Kilmer, E. de Sturler, A. Saibaba, and E. L. Miller , Parametric level-sets enhanced to improve reconstruction (palentir), Inverse Problems, (2025)

    2025

  31. [39]

    Papoutsellis, E

    E. Papoutsellis, E. Ametova, C. Delplancke, G. F ardell, J. S. Jørgensen, E. Pasca, M. Turner, R. W arr, W. R. Lionheart, and P. J. Withers , Core imaging library- part ii: multichannel reconstruction for dynamic and spectral tomography , Philosophical Transactions of the Roya...

    2021

  32. [40]

    Pasha, E

    M. Pasha, E. de Sturler, and M. E. Kilmer , Recycling MMGKS for large-scale dynamic and streaming data , arXiv preprint arXiv:2309.15759, (2023)

    2023 arXiv

  33. [41]

    Pasha, S

    M. Pasha, S. Gazzola, C. Sanderford, and U. O. Ugwu , Trips-py: Techniques for regular- ization of inverse problems in python , Numerical Algorithms, (2024), pp. 1–38

    2024

  34. [42]

    Pasha, A

    M. Pasha, A. K. Saibaba, S. Gazzola, M. I. Espa ˜nol, and E. de Sturler , A computa- tional framework for edge-preserving regularization in dynamic inverse problems , Elec- This manuscript is for review purposes only. DYNAMIC INVERSE PROBLEMS WITH OPTICAL FLOW 27 tronic Transa...

    2023

  35. [43]

    Schmitt and A

    U. Schmitt and A. Louis , Efficient algorithms for the regularization of dynamic inverse problems: I. theory , Inverse Problems, 18 (2002), pp. 645–658, https://doi.org/10.1088/ 0266-5611/18/3/308

    2002

  36. [44]

    Schmitt, A

    U. Schmitt, A. K. Louis, C. Wolters, and M. V auhkonen , Efficient algorithms for the regularization of dynamic inverse problems: Ii. applications , Inverse Problems, 18 (2002), p. 659, https://doi.org/10.1088/0266-5611/18/3/309, https://dx.doi.org/10.1088/ 0266-5611/18/3/309

    2002 doi

  37. [45]

    Schuster, B

    T. Schuster, B. Hahn, and M. Burger , Dynamic inverse problems: mod- elling—regularization—numerics, Inverse Problems, 34 (2018), p. 040301, https://doi.org/ 10.1088/1361-6420/aab0f5, https://dx.doi.org/10.1088/1361-6420/aab0f5

    2018 doi

  38. [46]

    Solonen, T

    A. Solonen, T. Cui, J. Hakkarainen, and Y. Marzouk, On dimension reduction in Gaussian filters, Inverse Problems, 32 (2016), p. 045003

    2016

  39. [47]

    Spantini, D

    A. Spantini, D. Bigoni, and Y. Marzouk, Inference via Low-Dimensional Couplings, Journal of Machine Learning Research, 19 (2018), pp. 1–71, http://jmlr.org/papers/v19/17-747. html

    2018

  40. [48]

    Srivastava, E

    N. Srivastava, E. Mansimov, and R. Salakhutdinov, Unsupervised learning of video repre- sentations using lstms, International Conference on Machine Learning, (2015), pp. 843–852

    2015

  41. [49]

    A. M. Stuart , Inverse problems: A bayesian perspective , Acta Numerica, 19 (2010), p. 451–559, https://doi.org/10.1017/S0962492910000061

    2010 doi

  42. [50]

    W ang, Y

    Q. W ang, Y. Tang, Y. Ge, H. Xie, X. Tong, and P. M. Atkinson, A comprehensive review of spatial-temporal-spectral information reconstruction techniques, Science of Remote Sensing, (2023), p. 100102

    2023

  43. [51]

    W ang, A

    Z. W ang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli , Image quality assessment: From error visibility to structural similarity , IEEE Transactions on Image Processing, 13 (2004), pp. 600–612

    2004

  44. [52]

    Westman, K

    E. Westman, K. Luxbacher, and S. Schafrik , Passive seismic tomography for three- dimensional time-lapse imaging of mining-induced rock mass changes , The Leading Edge, 31 (2012), pp. 338–345, https://doi.org/10.1190/1.3694902, https://doi.org/10.1190/1. 3694902, https://arxiv...

    2012 doi

  45. [53]

    Zhang, S

    H. Zhang, S. Sarkar, M. N. Toks ¨oz, H. S. Kuleli, and F. Al-Kindy , Passive seismic tomography using induced seismicity at a petroleum field in oman , Geophysics, 74 (2009), https://api.semanticscholar.org/CorpusID:129522435

    2009

  46. [54]

    N. Zhao, D. O’Connor, A. Basarab, D. Ruan, and K. Sheng, Motion compensated dynamic mri reconstruction with local affine optical flow estimation, IEEE Transactions on Biomed- ical Engineering, 66 (2019), pp. 3050–3059, https://doi.org/10.1109/TBME.2019.2900037. This manuscript...

    2019

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.