Special Issue "Inverse Problems and Imaging"

A special issue of Journal of Imaging (ISSN 2313-433X).

Deadline for manuscript submissions: 31 August 2021.

Special Issue Editors

Prof. Dr. Fabiana Zama
E-Mail Website
Guest Editor
Department of Mathematics, University of Bologna, 40127 Bologna, Italy
Interests: regularization algorithms; inverse problems in imaging; numerical optimization; parameter estimation; inversion algorithms for NMR relaxometry data; algorithms for sparse MRI
Prof. Dr. Elena Loli Piccolomini
E-Mail Website
Guest Editor
Department of Computer Science and Engineering, University of Bologna, 40127 Bologna, Italy
Interests: optimization and regularization algorithms; inverse problems in imaging; neural networks for deblurring and denoising problems; neural networks for image reconstruction from sparse data

Special Issue Information

Dear Colleagues,

Inverse problems represent the model of applications that has a crucial impact on human life. Such models are characteristic of applications where data coming from scanners or sensors are used to obtain information about objects that are not directly measurable. Visual representation of such objects is a fundamental tool in the decision and analysis in various applicative areas such as medicine, life sciences, and technology, in both the public and private sector. The development of new sensors and scanners leads to sophisticated mathematical models and requires efficient computational methods. Researchers are increasing their efforts to develop new variational algorithms, as well as learning algorithms based on neural networks to tackle the challenges of recent technological evolution.

We invite authors to submit original research papers related to modern challenges in the solution of inverse problems in imaging and data inversion with a focus on tomographic imaging, MRI, and NMR reconstruction problems. Papers with a focus on optimizations and regularization methods for inverse problems in imaging, computational optimization, and regularization methods and applications are equally welcome.

Prof. Dr. Fabiana Zama
Prof. Dr. Elena Loli Piccolomini
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Journal of Imaging is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • variational regularization algorithms
  • inverse problems
  • neural networks
  • learning algorithms in image processing
  • regularization algorithms for NMR data inversion
  • image deblurring
  • image denoising
  • tomographic imaging
  • MRI
  • optimization methods for image processing

Published Papers (5 papers)

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Research

Article
Calibration-Less Multi-Coil Compressed Sensing Magnetic Resonance Image Reconstruction Based on OSCAR Regularization
J. Imaging 2021, 7(3), 58; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging7030058 - 19 Mar 2021
Viewed by 378
Abstract
Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the [...] Read more.
Over the last decade, the combination of compressed sensing (CS) with acquisition over multiple receiver coils in magnetic resonance imaging (MRI) has allowed the emergence of faster scans while maintaining a good signal-to-noise ratio (SNR). Self-calibrating techniques, such as ESPiRIT, have become the standard approach to estimating the coil sensitivity maps prior to the reconstruction stage. In this work, we proceed differently and introduce a new calibration-less multi-coil CS reconstruction method. Calibration-less techniques no longer require the prior extraction of sensitivity maps to perform multi-coil image reconstruction but usually alternate estimation sensitivity map estimation and image reconstruction. Here, to get rid of the nonconvexity of the latter approach we reconstruct as many MR images as the number of coils. To compensate for the ill-posedness of this inverse problem, we leverage structured sparsity of the multi-coil images in a wavelet transform domain while adapting to variations in SNR across coils owing to the OSCAR (octagonal shrinkage and clustering algorithm for regression) regularization. Coil-specific complex-valued MR images are thus obtained by minimizing a convex but nonsmooth objective function using the proximal primal-dual Condat-Vù algorithm. Comparison and validation on retrospective Cartesian and non-Cartesian studies based on the Brain fastMRI data set demonstrate that the proposed reconstruction method outperforms the state-of-the-art (1-ESPIRiT, calibration-less AC-LORAKS and CaLM methods) significantly on magnitude images for the T1 and FLAIR contrasts. Additionally, further validation operated on 8 to 20-fold prospectively accelerated high-resolution ex vivo human brain MRI data collected at 7 Tesla confirms the retrospective results. Overall, OSCAR-based regularization preserves phase information more accurately (both visually and quantitatively) compared to other approaches, an asset that can only be assessed on real prospective experiments. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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Article
Data-Driven Regularization Parameter Selection in Dynamic MRI
J. Imaging 2021, 7(2), 38; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging7020038 - 20 Feb 2021
Viewed by 399
Abstract
In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One problem in CS approaches is [...] Read more.
In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One problem in CS approaches is determining the regularization parameters, which control the balance between data fidelity and regularization. We propose a data-driven approach for the total variation regularization parameter selection, where reconstructions yield expected sparsity levels in the regularization domains. The expected sparsity levels are obtained from the measurement data for temporal regularization and from a reference image for spatial regularization. Two formulations are proposed. Simultaneous search for a parameter pair yielding expected sparsity in both domains (S-surface), and a sequential parameter selection using the S-curve method (Sequential S-curve). The approaches are evaluated using simulated and experimental DCE-MRI. In the simulated test case, both methods produce a parameter pair and reconstruction that is close to the root mean square error (RMSE) optimal pair and reconstruction. In the experimental test case, the methods produce almost equal parameter selection, and the reconstructions are of high perceived quality. Both methods lead to a highly feasible selection of the regularization parameters in both test cases while the sequential method is computationally more efficient. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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Article
A Model-Based Optimization Framework for Iterative Digital Breast Tomosynthesis Image Reconstruction
J. Imaging 2021, 7(2), 36; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging7020036 - 13 Feb 2021
Viewed by 464
Abstract
Digital Breast Tomosynthesis is an X-ray imaging technique that allows a volumetric reconstruction of the breast, from a small number of low-dose two-dimensional projections. Although it is already used in the clinical setting, enhancing the quality of the recovered images is still a [...] Read more.
Digital Breast Tomosynthesis is an X-ray imaging technique that allows a volumetric reconstruction of the breast, from a small number of low-dose two-dimensional projections. Although it is already used in the clinical setting, enhancing the quality of the recovered images is still a subject of research. The aim of this paper was to propose and compare, in a general optimization framework, three slightly different models and corresponding accurate iterative algorithms for Digital Breast Tomosynthesis image reconstruction, characterized by a convergent behavior. The suggested model-based implementations are specifically aligned to Digital Breast Tomosynthesis clinical requirements and take advantage of a Total Variation regularizer. We also tune a fully-automatic strategy to set a proper regularization parameter. We assess our proposals on real data, acquired from a breast accreditation phantom and a clinical case. The results confirm the effectiveness of the presented framework in reconstructing breast volumes, with particular focus on the masses and microcalcifications, in few iterations and in enhancing the image quality in a prolonged execution. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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Article
A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization
J. Imaging 2021, 7(2), 18; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging7020018 - 28 Jan 2021
Viewed by 420
Abstract
This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and [...] Read more.
This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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Article
A Computationally Efficient Reconstruction Algorithm for Circular Cone-Beam Computed Tomography Using Shallow Neural Networks
J. Imaging 2020, 6(12), 135; https://0-doi-org.brum.beds.ac.uk/10.3390/jimaging6120135 - 08 Dec 2020
Viewed by 807
Abstract
Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a [...] Read more.
Circular cone-beam (CCB) Computed Tomography (CT) has become an integral part of industrial quality control, materials science and medical imaging. The need to acquire and process each scan in a short time naturally leads to trade-offs between speed and reconstruction quality, creating a need for fast reconstruction algorithms capable of creating accurate reconstructions from limited data. In this paper, we introduce the Neural Network Feldkamp–Davis–Kress (NN-FDK) algorithm. This algorithm adds a machine learning component to the FDK algorithm to improve its reconstruction accuracy while maintaining its computational efficiency. Moreover, the NN-FDK algorithm is designed such that it has low training data requirements and is fast to train. This ensures that the proposed algorithm can be used to improve image quality in high-throughput CT scanning settings, where FDK is currently used to keep pace with the acquisition speed using readily available computational resources. We compare the NN-FDK algorithm to two standard CT reconstruction algorithms and to two popular deep neural networks trained to remove reconstruction artifacts from the 2D slices of an FDK reconstruction. We show that the NN-FDK reconstruction algorithm is substantially faster in computing a reconstruction than all the tested alternative methods except for the standard FDK algorithm and we show it can compute accurate CCB CT reconstructions in cases of high noise, a low number of projection angles or large cone angles. Moreover, we show that the training time of an NN-FDK network is orders of magnitude lower than the considered deep neural networks, with only a slight reduction in reconstruction accuracy. Full article
(This article belongs to the Special Issue Inverse Problems and Imaging)
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