Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: Free-form and sparse approach

Daniel U. Campos-Delgado; Omar Gutierrez-Navarro; Ricardo Salinas-Martinez; Elvis Duran; Aldo R. Mejia-Rodriguez; Miguel J. Velazquez-Duran; Javier A. Jo

doi:10.1371/journal.pone.0248301

Peer Review History

Original SubmissionSeptember 25, 2020
7 Dec 2020 Decision Letter - Hao Sun, Editor PONE-D-20-29880 Blind deconvolution estimation by multi-exponential models and alternated least squares approximations PLOS ONE Dear Dr. Campos-Delgado, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by Jan 21 2021 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. Please include the following items when submitting your revised manuscript: A rebuttal letter that responds to each point raised by the academic editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'. A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'. An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'. If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter. If applicable, we recommend that you deposit your laboratory protocols in protocols.io to enhance the reproducibility of your results. Protocols.io assigns your protocol its own identifier (DOI) so that it can be cited independently in the future. For instructions see: http://journals.plos.org/plosone/s/submission-guidelines#loc-laboratory-protocols We look forward to receiving your revised manuscript. Kind regards, Hao Sun Academic Editor PLOS ONE Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf 2. Thank you for stating the following in your Competing Interests section: 'No' a. Please complete your Competing Interests on the online submission form to state any Competing Interests. If you have no competing interests, please state "The authors have declared that no competing interests exist.", as detailed online in our guide for authors at http://journals.plos.org/plosone/s/submit-now b. This information should be included in your cover letter; we will change the online submission form on your behalf. Please know it is PLOS ONE policy for corresponding authors to declare, on behalf of all authors, all potential competing interests for the purposes of transparency. PLOS defines a competing interest as anything that interferes with, or could reasonably be perceived as interfering with, the full and objective presentation, peer review, editorial decision-making, or publication of research or non-research articles submitted to one of the journals. Competing interests can be financial or non-financial, professional, or personal. Competing interests can arise in relationship to an organization or another person. Please follow this link to our website for more details on competing interests: http://journals.plos.org/plosone/s/competing-interests Additional Editor Comments: I agree with the reviewer's comments. Please make sure to address them in the revised version. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes ******** 2. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: No ****** 3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes ****** 4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes ****** 5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: This work proposed a new method for solving blind deconvolution estimation (BDE) problem in fluorescence imaging microscopy, based on multi-exponential models and alternating least squares. Blind deconvolution is a well studied problem recently, and the idea of alternating minimization idea is not quite new. The reviewer does not find much technical novelty, but an application to a new problem. The work is well-organized overall, while the presentation can be improved. Below are some comments: The abbreviations for fluorescence impulse response (FIR) and instrument response (IR) might be a bit confusing for readers with signal processing background. In signal processing, FIR and IIR are typically for finite impulse response and infinite impulse response, respectively. The authors should consider how to differ from the traditional abbreviations, otherwise readers might got confused with the meaning of FIR and IR at the first glance. 2. There are a couple of recent papers are related and might be cited: [1] Joshua T Vogelstein, Adam M Packer, Tim A Machado, Tanya Sippy, Baktash Babadi, Rafael Yuste, Liam Paninski, Fast non-negative deconvolution for spike train inference from population calcium imaging [2] Johannes Friedrich, Pengcheng Zhou, Liam Paninski, Fast online deconvolution of calcium imaging data [3] Yenson Lau, Qing Qu, Han-wen Kuo, Pengcheng Zhou, Yuqian Zhang, John Wright. Short-and-Sparse Deconvolution – A Geometric Approach, ICLR’20. In particular, the reviewer finds the proposed method is quite close to those of [1,2], though [1,2] considered a different application in Calcium imaging. In [1,2], the authors assumed some sparsity structures on FIR, while the proposed method does not. Some more comments and detailed comparison discussions are needed. In particular, the method might be improved by imposing sparsity structure on FIRs similarly, or other structures. 3. Since the problem is highly nonconvex, can the authors provide some convergence guarantees of the proposed optimization method? Some numerical and even theoretical justification is needed. Additionally, for convolution, the implementation could be faster via FFTs. 4. In numerical comparisons, the authors only compared the previous method by the authors themselves. Comparing with blind deconvolution methods such as those mentioned [1-3], or other generic methods are needed. ****** 6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: Yes:** Qing Qu [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step. https://doi.org/10.1371/journal.pone.0248301.r001
Revision 1
23 Jan 2021 Author Response First, the authors would like to thank the reviewer and the Editor for their valuable comments. The main contribution on this new version is the inclusion of a deeper critical perspective to the manuscript. We really think that such comments helped to improve the quality of the manuscript. %%%%%%%%%%%%%%%%%%%%% Journal Requirements: When submitting your revision, we need you to address these additional requirements. 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf RESPONSE We have carefully revised the PLOS ONE template and we are following all the style requirements in this new version. For the manuscript, we have used the LaTeX template, so all the styles for the heading and fonts are followed. %%%%%%%%%% 2. Thank you for stating the following in your Competing Interests section: 'No' a. Please complete your Competing Interests on the online submission form to state any Competing Interests. If you have no competing interests, please state "The authors have declared that no competing interests exist.", as detailed online in our guide for authors at http://journals.plos.org/plosone/s/submit-now b. This information should be included in your cover letter; we will change the online submission form on your behalf. RESPONSE We have included in the cover letter for this new submission the statement "The authors have declared that no competing interests exist." %%%%%%%%%% Additional Editor Comments: I agree with the reviewer's comments. Please make sure to address them in the revised version. RESPONSE We sincerely thank the Editor for the evaluation of our manuscript. In the following, we have included a precise response to each reviewer comment. %%%%%%%%%%%%%%%%%%%%%%% Reviewer #1: Comments to the Author This work proposed a new method for solving blind deconvolution estimation (BDE) problem in fluorescence imaging microscopy, based on multi-exponential models and alternating least squares. Blind deconvolution is a well studied problem recently, and the idea of alternating minimization idea is not quite new. The reviewer does not find much technical novelty, but an application to a new problem. The work is well-organized overall, while the presentation can be improved. Below are some comments: 1. The abbreviations for fluorescence impulse response (FIR) and instrument response (IR) might be a bit confusing for readers with signal processing background. In signal processing, FIR and IIR are typically for finite impulse response and infinite impulse response, respectively. The authors should consider how to differ from the traditional abbreviations, otherwise readers might got confused with the meaning of FIR and IR at the first glance. RESPONSE We acknowledge this important remark by the reviewer, so we have updated the abbreviations for fluorescence impulse response and instrument response to FluoIR and InstR, respectively to avoid a possible confusion to the reader. For consistency, the abbreviation of fluorescence decay was also updated to FluoD in the whole manuscript (see page 20). %%%%%%%%%% 2. There are a couple of recent papers are related and might be cited: [1] Joshua T Vogelstein, Adam M Packer, Tim A Machado, Tanya Sippy, Baktash Babadi, Rafael Yuste, Liam Paninski, Fast non-negative deconvolution for spike train inference from population calcium imaging [2] Johannes Friedrich, Pengcheng Zhou, Liam Paninski, Fast online deconvolution of calcium imaging data [3] Yenson Lau, Qing Qu, Han-wen Kuo, Pengcheng Zhou, Yuqian Zhang, John Wright. Short-and-Sparse Deconvolution – A Geometric Approach, ICLR’20. In particular, the reviewer finds the proposed method is quite close to those of [1,2], though [1,2] considered a different application in Calcium imaging. In [1,2], the authors assumed some sparsity structures on FIR, while the proposed method does not. Some more comments and detailed comparison discussions are needed. In particular, the method might be improved by imposing sparsity structure on FIRs similarly, or other structures. RESPONSE We thank deeply the reviewer for bringing to our attention these three relevant works [1,2,3] related to blind deconvolution estimation (BDE). We reviewed carefully the three previous contributions and we detected key differences with our BDE formulation. Contrary to [1,2], in our approach, the excitation signal does not have a spike train shape, and our observation model relies on a convolution with a multi-exponential kernel, compared to the autoregressive structure in the references. Furthermore, the main goal in our work is to reconstruct the fluorescence impulse response in each pixel of the FLIM measurement, nor to identify the spike train of the excitation signal, as in [1,2]. In addition, our formulation considers a free-form for the excitation signal, which is common to all pixels in the FLIM image, but with some sparsity condition as well. Hence, for FLIM datasets, the excitation signal is one narrow pulse without repetitions. Meanwhile, the fluorescence impulse responses have a smooth monotonic exponential decay over the whole measurement interval, so we cannot assume for them a sparsity condition, as suggested by the reviewer. With respect to [3], our formulation does not assume a short kernel and a sparse activation map. In addition, our multi-exponential kernel is not restricted to a sphere constraint, as in [3]. Also, the extension in [3] to convolutional dictionary learning considers multiple unknown kernels/motifs, i.e., multiple input signals, which is not consistent with the studied BDE formulation. Nonetheless, references [1,2,3] ([33], [34] and [35] in our manuscript) are described in the introduction and the main differences to our formulation are also discussed there (see page 2). %%%%%%%%%% 3. Since the problem is highly nonconvex, can the authors provide some convergence guarantees of the proposed optimization method? Some numerical and even theoretical justification is needed. Additionally, for convolution, the implementation could be faster via FFTs. RESPONSE We acknowledge the detailed and precise evaluation of our work by the reviewer. Since in our formulation for FLIM datasets, we assume a narrow pulse without repetitions as excitation, and each measured fluorescence decay will exhibit a sharp increase to its peak value, followed by a monotonic decrease. Moreover, all the measurements are scaled to sum-to-one, and also the instrument response is limited to sum-to-one. As a result, the scaled shift symmetry described in [3] will not hold in our BDE formulation. In addition, at each stage of the alternated least squares (ALS) scheme in the local and global approaches, a quadratic approximation problem is solved by either a non-linear least squares or linear least squares. So, at each stage, the estimation error is reduced or at least maintained. Consequently, convergence is guaranteed in the iterative scheme, but only to a local minimum. For this reason, the initialization based on processing the FLIM dataset is a crucial step in our formulation to obtain meaningful results. We include this discussion in third section, while describing the alternated least squares structure (see page 7). In this new version, we have added a numerical convergence evaluation of the BDE schemes (BDELME and BDEGME) with synthetic FLIM datasets for different noise levels (SNR,PSNR) ∈{(10,40),(15,45),(20,50),(25,55)} dB, and orders in the multi-exponential model of the synthetic impulse response (2nd, 3rd and 4th). The stopping threshold is set to ϵ_3=1×10^(-3) . The resulting normalized metric in the alternated least squares iterations is described below in Fig. 4 of the new version, where it is observed that in either BDE scheme, the convergence is always monotonic for any noise combination and model order, and just its final steady-state value depends on the noise level. From this figure, we conclude that the local approach (BDELME) converges slower than the global scheme (BDEGME), which could be intuitively expected, since BDELME has roughly twice the free parameters to optimize. For BDELME, the most drastic reductions are achieved in the first five iterations, and for BDEGME, in the first two. In this way, our previous convergence analysis is validated numerically. This previous analysis and discussion is included in page 12. Now, with respect to the suggestion of implementing the convolution via FFTs, we have chosen to use a time-domain perspective to allow a direct optimization by nonlinear and linear least squares of the parameters in the impulse and instrument responses, nor for the computation of the estimated fluorescence decays. Also, our formulation considers a linear convolution for the observation model. Nonetheless, we thank the reviewer for this interesting suggestion. %%%%%%%%%% 4. In numerical comparisons, the authors only compared the previous method by the authors themselves. Comparing with blind deconvolution methods such as those mentioned [1-3], or other generic methods are needed. RESPONSE We thank this important observation by the reviewer. Nonetheless, the numerical comparison must be under the same mathematical formulation for the deconvolution process. Hence, as we argued in response 2), the performance comparisons with [1], [2], and [3] are not possible, since they address a different estimation problem. In the “Synthetic and experimental validation” section (see pages 10 to 16), we are comparing the performance of our proposed BDE schemes, BDELME and BDEGME, first to two standard deconvolution methodologies that assume known a priori the instrument response: DELME and DEGME (Pelet et al, 2004 & Warren et al., 2013) [17,18]. These two strategies are the common standards in the numerical analysis of FLIM datasets. Next, we use two previous BDE proposals of our same research group: BDELB and BDEEL. In this way, the proposed methodologies, BDELME and BDEGME, are compared against four schemes from the literature, where their advantages are illustrated in synthetic and experimental datasets (see page 11). We hope that the reviewer could identify our effort to compare our proposals, and to evaluate their performance without bias. [17] Pelet S, Previte M, Laiho L, So P. A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation. Biophysical Journal. 2004;87(4):2807–2817. doi:10.1529/biophysj.104.045492. [18] Warren SC, Margineanu A, Alibhai D, Kelly DJ, Talbot C, Alexandrov Y, et al. Rapid global fitting of large fluorescence lifetime imaging microscopy datasets. PLoS One. 2013;8(8):e70687. doi:10.1371/journal.pone.0070687. Attachments Attachment Submitted filename: Response_to_Reviewers_PONE-D-20-29880.pdf https://doi.org/10.1371/journal.pone.0248301.r002
24 Feb 2021 Decision Letter - Hao Sun, Editor Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: free-form and sparse approach PONE-D-20-29880R1 Dear Dr. Campos-Delgado, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice for payment will follow shortly after the formal acceptance. To ensure an efficient process, please log into Editorial Manager at http://www.editorialmanager.com/pone/, click the 'Update My Information' link at the top of the page, and double check that your user information is up-to-date. If you have any billing related questions, please contact our Author Billing department directly at authorbilling@plos.org. If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they’ll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. Kind regards, Hao Sun Academic Editor PLOS ONE Reviewers' comments: Reviewer's Responses to Questions Comments to the Author 1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation. Reviewer #1: All comments have been addressed ******** 2. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. Reviewer #1: Yes ****** 3. Has the statistical analysis been performed appropriately and rigorously? Reviewer #1: Yes ****** 4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified. Reviewer #1: Yes ****** 5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: The authors have successfully addressed all my concerns, that I recommend for acceptance in the current form. ****** 7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review?** For information about this choice, including consent withdrawal, please see our Privacy Policy. Reviewer #1: No https://doi.org/10.1371/journal.pone.0248301.r003
Formally Accepted
8 Mar 2021 Acceptance Letter - Hao Sun, Editor PONE-D-20-29880R1 Blind deconvolution estimation by multi-exponential models and alternated least squares approximations: free-form and sparse approach Dear Dr. Campos-Delgado: I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department. If your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information please contact onepress@plos.org. If we can help with anything else, please email us at plosone@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Professor Hao Sun Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0248301.r004

Open letter on the publication of peer review reports

PLOS recognizes the benefits of transparency in the peer review process. Therefore, we enable the publication of all of the content of peer review and author responses alongside final, published articles. Reviewers remain anonymous, unless they choose to reveal their names.

We encourage other journals to join us in this initiative. We hope that our action inspires the community, including researchers, research funders, and research institutions, to recognize the benefits of published peer review reports for all parts of the research system.

Learn more at ASAPbio .