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Objective.Deep learning has markedly enhanced the performance of sparse-view computed tomography reconstruction. However, the dependence of these methods on supervised training using high-quality paired datasets, and the necessity for retraining under varied physical acquisition conditions, constrain their generalizability across new imaging contexts and settings.Approach.To overcome these limitations, we propose an unsupervised approach grounded in the deep image prior framework. Our approach advances beyond the conventional single noise level input by incorporating multi-level linear diffusion noise, significantly mitigating the risk of overfitting. Furthermore, we embed non-local self-similarity as a deep implicit prior within a self-attention network structure, improving the model's capability to identify and utilize repetitive patterns throughout the image. Additionally, leveraging imaging physics, gradient backpropagation is performed between the image domain and projection data space to optimize network weights.Main Results.Evaluations with both simulated and clinical cases demonstrate our method's effective zero-shot adaptability across various projection views, highlighting its robustness and flexibility. Additionally, our approach effectively eliminates noise and streak artifacts while significantly restoring intricate image details.Significance. Our method aims to overcome the limitations in current supervised deep learning-based sparse-view CT reconstruction, offering improved generalizability and adaptability without the need for extensive paired training data.

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Deep learning, particularly convolutional neural networks (CNNs), has advanced positron emission tomography (PET) image reconstruction. However, it requires extensive, high-quality training datasets. Unsupervised learning methods, such as deep image prior (DIP), have shown promise for PET image reconstruction. Although DIP-based PET image reconstruction methods demonstrate superior performance, they involve highly time-consuming calculations. This study proposed a two-step optimization method to accelerate end-to-end DIP-based PET image reconstruction and improve PET image quality. The proposed two-step method comprised a pre-training step using conditional DIP denoising, followed by an end-to-end reconstruction step with fine-tuning. Evaluations using Monte Carlo simulation data demonstrated that the proposed two-step method significantly reduced the computation time and improved the image quality, thereby rendering it a practical and efficient approach for end-to-end DIP-based PET image reconstruction.

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PURPOSE: We present SCAMPI (Sparsity Constrained Application of deep Magnetic resonance Priors for Image reconstruction), an untrained deep Neural Network for MRI reconstruction without previous training on datasets. It expands the Deep Image Prior approach with a multidomain, sparsity-enforcing loss function to achieve higher image quality at a faster convergence speed than previously reported methods. METHODS: Two-dimensional MRI data from the FastMRI dataset with Cartesian undersampling in phase-encoding direction were reconstructed for different acceleration rates for single coil and multicoil data. RESULTS: The performance of our architecture was compared to state-of-the-art Compressed Sensing methods and ConvDecoder, another untrained Neural Network for two-dimensional MRI reconstruction. SCAMPI outperforms these by better reducing undersampling artifacts and yielding lower error metrics in multicoil imaging. In comparison to ConvDecoder, the U-Net architecture combined with an elaborated loss-function allows for much faster convergence at higher image quality. SCAMPI can reconstruct multicoil data without explicit knowledge of coil sensitivity profiles. Moreover, it is a novel tool for reconstructing undersampled single coil k-space data. CONCLUSION: Our approach avoids overfitting to dataset features, that can occur in Neural Networks trained on databases, because the network parameters are tuned only on the reconstruction data. It allows better results and faster reconstruction than the baseline untrained Neural Network approach.

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The high noise level of dynamic Positron Emission Tomography (PET) images degrades the quality of parametric images. In this study, we aim to improve the quality and quantitative accuracy of Ki images by utilizing deep learning techniques to reduce the noise in dynamic PET images. We propose a novel denoising technique, Population-based Deep Image Prior (PDIP), which integrates population-based prior information into the optimization process of Deep Image Prior (DIP). Specifically, the population-based prior image is generated from a supervised denoising model that is trained on a prompts-matched static PET dataset comprising 100 clinical studies. The 3D U-Net architecture is employed for both the supervised model and the following DIP optimization process. We evaluated the efficacy of PDIP for noise reduction in 25%-count and 100%-count dynamic PET images from 23 patients by comparing with two other baseline techniques: the Prompts-matched Supervised model (PS) and a conditional DIP (CDIP) model that employs the mean static PET image as the prior. Both the PS and CDIP models show effective noise reduction but result in smoothing and removal of small lesions. In addition, the utilization of a single static image as the prior in the CDIP model also introduces a similar tracer distribution to the denoised dynamic frames, leading to lower Ki in general as well as incorrect Ki in the descending aorta. By contrast, as the proposed PDIP model utilizes intrinsic image features from the dynamic dataset and a large clinical static dataset, it not only achieves comparable noise reduction as the supervised and CDIP models but also improves lesion Ki predictions.

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The data-driven approach of supervised learning methods has limited applicability in solving dipole inversion in Quantitative Susceptibility Mapping (QSM) with varying scan parameters across different objects. To address this generalization issue in supervised QSM methods, we propose a novel training-free model-based unsupervised method called MoDIP (Model-based Deep Image Prior). MoDIP comprises a small, untrained network and a Data Fidelity Optimization (DFO) module. The network converges to an interim state, acting as an implicit prior for image regularization, while the optimization process enforces the physical model of QSM dipole inversion. Experimental results demonstrate MoDIP's excellent generalizability in solving QSM dipole inversion across different scan parameters. It exhibits robustness against pathological brain QSM, achieving over 32 % accuracy improvement than supervised deep learning methods. It is also 33 % more computationally efficient and runs 4 times faster than conventional DIP-based approaches, enabling 3D high-resolution image reconstruction in under 4.5 min.

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Noninvasive extracellular pH (pHe) mapping with Biosensor Imaging of Redundant Deviation in Shifts (BIRDS) using MR spectroscopic imaging (MRSI) has been demonstrated on 3T clinical MR scanners at 8 × 8 × 10 mm3 spatial resolution and applied to study various liver cancer treatments. Although pHe imaging at higher resolution can be achieved by extending the acquisition time, a postprocessing method to increase the resolution is preferable, to minimize the duration spent by the subject in the MR scanner. In this work, we propose to improve the spatial resolution of pHe mapping with BIRDS by incorporating anatomical information in the form of multiparametric MRI and using an unsupervised deep-learning technique, Deep Image Prior (DIP). Specifically, we used high-resolution T 1 , T 2 , and diffusion-weighted imaging (DWI) MR images of rabbits with VX2 liver tumors as inputs to a U-Net architecture to provide anatomical information. U-Net parameters were optimized to minimize the difference between the output super-resolution image and the experimentally acquired low-resolution pHe image using the mean-absolute error. In this way, the super-resolution pHe image would be consistent with both anatomical MR images and the low-resolution pHe measurement from the scanner. The method was developed based on data from 49 rabbits implanted with VX2 liver tumors. For evaluation, we also acquired high-resolution pHe images from two rabbits, which were used as ground truth. The results indicate a good match between the spatial characteristics of the super-resolution images and the high-resolution ground truth, supported by the low pixelwise absolute error.

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Objective.In recent years, convolutional neural networks (CNNs) have shown great potential in positron emission tomography (PET) image reconstruction. However, most of them rely on many low-quality and high-quality reference PET image pairs for training, which are not always feasible in clinical practice. On the other hand, many works improve the quality of PET image reconstruction by adding explicit regularization or optimizing the network structure, which may lead to complex optimization problems.Approach.In this paper, we develop a novel iterative reconstruction algorithm by integrating the deep image prior (DIP) framework, which only needs the prior information (e.g. MRI) and sinogram data of patients. To be specific, we construct the objective function as a constrained optimization problem and utilize the existing PET image reconstruction packages to streamline calculations. Moreover, to further improve both the reconstruction quality and speed, we introduce the Nesterov's acceleration part and the restart mechanism in each iteration.Main results.2D experiments on PET data sets based on computer simulations and real patients demonstrate that our proposed algorithm can outperform existing MLEM-GF, KEM and DIPRecon methods.Significance.Unlike traditional CNN methods, the proposed algorithm does not rely on large data sets, but only leverages inter-patient information. Furthermore, we enhance reconstruction performance by optimizing the iterative algorithm. Notably, the proposed method does not require much modification of the basic algorithm, allowing for easy integration into standard implementations.

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PURPOSE: In MRI, motion artifacts can significantly degrade image quality. Motion artifact correction methods using deep neural networks usually required extensive training on large datasets, making them time-consuming and resource-intensive. In this paper, an unsupervised deep learning-based motion artifact correction method for turbo-spin echo MRI is proposed using the deep image prior framework. THEORY AND METHODS: The proposed approach takes advantage of the high impedance to motion artifacts offered by the neural network parameterization to remove motion artifacts in MR images. The framework consists of parameterization of MR image, automatic spatial transformation, and motion simulation model. The proposed method synthesizes motion-corrupted images from the motion-corrected images generated by the convolutional neural network, where an optimization process minimizes the objective function between the synthesized images and the acquired images. RESULTS: In the simulation study of 280 slices from 14 subjects, the proposed method showed a significant increase in the averaged structural similarity index measure by 0.2737 in individual coil images and by 0.4550 in the root-sum-of-square images. In addition, the ablation study demonstrated the effectiveness of each proposed component in correcting motion artifacts compared to the corrected images produced by the baseline method. The experiments on real motion dataset has shown its clinical potential. CONCLUSION: The proposed method exhibited significant quantitative and qualitative improvements in correcting rigid and in-plane motion artifacts in MR images acquired using turbo spin-echo sequence.

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PURPOSE: To develop a deep image prior (DIP) reconstruction for B1 + -corrected 2D cine MR fingerprinting (MRF). METHODS: The proposed method combines low-rank (LR) modeling with a DIP to generate cardiac phase-resolved parameter maps without motion correction, employing self-supervised training to enforce consistency with undersampled spiral k-space data. Two implementations were tested: one approach (DIP) for cine T1 , T2 , and M0 mapping, and a second approach (DIP with effective B1 + estimation [DIP-B1]) that also generated an effective B1 + map to correct for errors due to RF transmit inhomogeneities, through-plane motion, and blood flow. Cine MRF data were acquired in 14 healthy subjects and four reconstructions were compared: LR, low-rank motion-corrected (LRMC), DIP, and DIP-B1. Results were compared to diastolic ECG-triggered MRF, MOLLI, and T2 -prep bSSFP. Additionally, bright-blood and dark-blood images calculated from cine MRF maps were used to quantify ventricular function and compared to reference cine measurements. RESULTS: DIP and DIP-B1 outperformed other cine MRF reconstructions with improved noise suppression and delineation of high-resolution details. Within-segment variability in the myocardium (reported as the coefficient of variation for T1 /T2 ) was lowest for DIP-B1 (2.3/8.3%) followed by DIP (2.7/8.7%), LRMC (3.5/10.5%), and LR (15.3/39.6%). Spatial homogeneity improved with DIP-B1 having the lowest intersegment variability (2.6/4.1%). The mean bias in ejection fraction was -1.1% compared to reference cine scans. CONCLUSION: A DIP reconstruction for 2D cine MRF enabled cardiac phase-resolved mapping of T1 , T2 , M0 , and the effective B1 + with improved noise suppression and precision compared to LR and LRMC.

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Material decomposition (MD) is an application of dual-energy computed tomography (DECT) that decomposes DECT images into specific material images. However, the direct inversion method used in MD often amplifies noise in the decomposed material images, resulting in lower image quality. To address this issue, we propose an image-domain MD method based on the concept of deep image prior (DIP). DIP is an unsupervised learning method that can perform different tasks without using a large training dataset with known targets (i.e., basis material images). We retrospectively recruited patients who underwent non-contrast brain DECT scans and investigated the feasibility of using the proposed DIP-based method to decompose DECT images into two (i.e., bone and soft tissue) and three (i.e., bone, soft tissue, and fat) basis materials. We evaluated the decomposed material images in terms of signal-to-noise ratio (SNR) and modulation transfer function (MTF). The proposed DIP-based method showed greater improvement in SNR in the decomposed soft-tissue images compared to the direct inversion method and the iterative method. Moreover, the proposed method produced similar MTF curves in both two- and three-material decompositions. Additionally, the proposed DIP-based method demonstrated better separation ability than the other two studied methods in the case of three-material decomposition. Our results suggest that the proposed DIP-based method is capable of unsupervisedly generating high-quality basis material images from DECT images.

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PURPOSE: To mitigate the problem of noisy parameter maps with high uncertainties by casting parameter mapping as a denoising task based on Deep Image Priors. METHODS: We extend the concept of denoising with Deep Image Prior (DIP) into parameter mapping by treating the output of an image-generating network as a parametrization of tissue parameter maps. The method implicitly denoises the parameter mapping process by filtering low-level image features with an untrained convolutional neural network (CNN). Our implementation includes uncertainty estimation from Bernoulli approximate variational inference, implemented with MC dropout, which provides model uncertainty in each voxel of the denoised parameter maps. The method is modular, so the specifics of different applications (e.g., T1 mapping) separate into application-specific signal equation blocks. We evaluate the method on variable flip angle T1 mapping, multi-echo T2 mapping, and apparent diffusion coefficient mapping. RESULTS: We found that deep image prior adapts successfully to several applications in parameter mapping. In all evaluations, the method produces noise-reduced parameter maps with decreased uncertainty compared to conventional methods. The downsides of the proposed method are the long computational time and the introduction of some bias from the denoising prior. CONCLUSION: DIP successfully denoise the parameter mapping process and applies to several applications with limited hyperparameter tuning. Further, it is easy to implement since DIP methods do not use network training data. Although time-consuming, uncertainty information from MC dropout makes the method more robust and provides useful information when properly calibrated.

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Objective.Unsupervised learning-based methods have been proven to be an effective way to improve the image quality of positron emission tomography (PET) images when a large dataset is not available. However, when the gap between the input image and the target PET image is large, direct unsupervised learning can be challenging and easily lead to reduced lesion detectability. We aim to develop a new unsupervised learning method to improve lesion detectability in patient studies.Approach.We applied the deep progressive learning strategy to bridge the gap between the input image and the target image. The one-step unsupervised learning is decomposed into two unsupervised learning steps. The input image of the first network is an anatomical image and the input image of the second network is a PET image with a low noise level. The output of the first network is also used as the prior image to generate the target image of the second network by iterative reconstruction method.Results.The performance of the proposed method was evaluated through the phantom and patient studies and compared with non-deep learning, supervised learning and unsupervised learning methods. The results showed that the proposed method was superior to non-deep learning and unsupervised methods, and was comparable to the supervised method.Significance.A progressive unsupervised learning method was proposed, which can improve image noise performance and lesion detectability.

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Two-dimensional observation of biological samples at hundreds of nanometers resolution or even below is of high interest for many sensitive medical applications. Recent advances have been obtained over the last ten years with computational imaging. Among them, Fourier Ptychographic Microscopy is of particular interest because of its important super-resolution factor. In complement to traditional intensity images, phase images are also produced. A large set of N raw images (with typically N = 225) is, however, required because of the reconstruction process that is involved. In this paper, we address the problem of FPM image reconstruction using a few raw images only (here, N = 37) as is highly desirable to increase microscope throughput. In contrast to previous approaches, we develop an algorithmic approach based on a physics-informed optimization deep neural network and statistical reconstruction learning. We demonstrate its efficiency with the help of simulations. The forward microscope image formation model is explicitly introduced in the deep neural network model to optimize its weights starting from an initialization that is based on statistical learning. The simulation results that are presented demonstrate the conceptual benefits of the approach. We show that high-quality images are effectively reconstructed without any appreciable resolution degradation. The learning step is also shown to be mandatory.

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OBJECTIVE: Non-blinded image deblurring with deep learning was performed on blurred numerical brain images without point spread function (PSF) reconstruction to obtain edge artifacts (EA)-free images. This study uses numerical simulation to investigate the mechanism of EA in PSF reconstruction based on the spatial frequency characteristics of EA-free images. METHODS: In 256 × 256 matrix brain images, the signal values of gray matter (GM), white matter, and cerebrospinal fluid were set to 1, 0.25, and 0.05, respectively. We assumed ideal projection data of a two-dimensional (2D) parallel beam with no degradation factors other than detector response blur to precisely grasp EA using the PSF reconstruction algorithm from blurred projection data. The detector response was assumed to be a shift-invariant and one-dimensional (1D) Gaussian function with 2-5 mm full width at half maximum (FWHM). Images without PSF reconstruction (non-PSF), PSF reconstruction without regularization (PSF) and with regularization of relative difference function (PSF-RD) were generated by ordered subset expectation maximization (OSEM). For non-PSF, the image deblurring with a deep image prior (DIP) was applied using a 2D Gaussian function with 2-5 mm FWHM. The 1D object-specific modulation transfer function (1D-OMTF), which is the ratio of 1D amplitude spectrum of the original and reconstructed images, was used as the index of spatial frequency characteristics. RESULTS: When the detector response was greater than 3 mm FWHM, EA in PSF was observed in GM borders and narrow GM. No remarkable EA was observed in the DIP, and the FWHM estimated from the recovery coefficient for the deblurred image of non-PSF at 5 mm FWHM was reduced to 3 mm or less. PSF of 5 mm FWHM showed higher spatial frequency characteristics than that of DIP up to around 2.2 cycles/cm but was lower than the latter after 3 cycles/cm. PSF-RD showed almost the same spatial frequency characteristics as that of DIP above 3 cycles/cm but was inferior below 3 cycles/cm. PSF-RD has a lower spatial resolution than DIP. CONCLUSIONS: Unlike DIP, PSF lacks high-frequency components around the Nyquist frequency, generating EA. PSF-RD mitigates EA while simultaneously suppressing the signal, diminishing spatial resolution.

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Objective. Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction method, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function.Approach. A practical implementation of a fully 3D PET image reconstruction could not be performed at present because of a graphics processing unit memory limitation. Consequently, we modify the DIP optimization to a block iteration and sequential learning of an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term is added to the loss function to enhance the quantitative accuracy of the PET image.Main results. We evaluated our proposed method using Monte Carlo simulation with [18F]FDG PET data of a human brain and a preclinical study on monkey-brain [18F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximuma posterioriEM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that, compared with other algorithms, the proposed method improved the PET image quality by reducing statistical noise and better preserved the contrast of brain structures and inserted tumors. In the preclinical experiment, finer structures and better contrast recovery were obtained with the proposed method.Significance.The results indicated that the proposed method could produce high-quality images without a prior training dataset. Thus, the proposed method could be a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

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PURPOSE: Personalized synthetic MRI (syn-MRI) uses MR images of an individual subject acquired at a few design parameters (echo time, repetition time, flip angle) to obtain underlying parametric ( ρ , T 1 , T 2 ) $$ \left(\rho, {\mathrm{T}}_1,{\mathrm{T}}_2\right) $$ maps, from where MR images of that individual at other design parameter settings are synthesized. However, classical methods that use least-squares (LS) or maximum likelihood estimators (MLE) are unsatisfactory at higher noise levels because the underlying inverse problem is ill-posed. This article provides a pipeline to enhance the synthesis of such images in three-dimensional (3D) using a deep learning (DL) neural network architecture for spatial regularization in a personalized setting where having more than a few training images is impractical. METHODS: Our DL enhancements employ a Deep Image Prior (DIP) with a U-net type denoising architecture that includes situations with minimal training data, such as personalized syn-MRI. We provide a general workflow for syn-MRI from three or more training images. Our workflow, called DIPsyn-MRI, uses DIP to enhance training images, then obtains parametric images using LS or MLE before synthesizing images at desired design parameter settings. DIPsyn-MRI is implemented in our publicly available Python package DeepSynMRI available at: https://github.com/StatPal/DeepSynMRI. RESULTS: We demonstrate feasibility and improved performance of DIPsyn-MRI on 3D datasets acquired using the Brainweb interface for spin-echo and FLASH imaging sequences, at different noise levels. Our DL enhancements improve syn-MRI in the presence of different intensity nonuniformity levels of the magnetic field, for all but very low noise levels. CONCLUSION: This article provides recipes and software to realistically facilitate DL-enhanced personalized syn-MRI.

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Objective.Magnetic particle imaging (MPI) is an emerging tomography imaging technique with high specificity and temporal-spatial resolution. MPI reconstruction based on the system matrix (SM) is an important research content in MPI. However, SM is usually obtained by measuring the response of an MPI scanner at all positions in the field of view. This process is very time-consuming, and the scanner will overheat in a long period of continuous operation, which is easy to generate thermal noise and affects MPI imaging performance.Approach.In this study, we propose a deep image prior-based method that prominently decreases the time of SM calibration. It is an unsupervised method that utilizes the neural network structure itself to recover a high-resolution SM from a downsampled SM without the need to train the network using a large amount of training data.Main results.Experiments on the Open MPI data show that the time of SM calibration can be greatly reduced with only slight degradation of image quality.Significance.This study provides a novel method for obtaining SM in MPI, which shows the potential to achieve SM recovery at a high downsampling rate. It is expected that this study will increase the practicability of MPI in biomedical applications and promote the development of MPI in the future.

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Deep Image Prior (DIP) is currently among the most efficient unsupervised deep learning based methods for ill-posed inverse problems in imaging. This novel framework relies on the implicit regularization provided by representing images as the output of generative Convolutional Neural Network (CNN) architectures. So far, DIP has been shown to be an effective approach when combined with classical and novel regularizers. Unfortunately, to obtain appropriate solutions, all the models proposed up to now require an accurate estimate of the regularization parameter. To overcome this difficulty, we consider a locally adapted regularized unconstrained model whose local regularization parameters are automatically estimated for additively separable regularizers. Moreover, we propose a novel constrained formulation in analogy to Morozov's discrepancy principle which enables the application of a broader range of regularizers. Both the unconstrained and the constrained models are solved via the proximal gradient descent-ascent method. Numerical results demonstrate the robustness with respect to image content, noise levels and hyperparameters of the proposed models on both denoising and deblurring of simulated as well as real natural and medical images.

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Remote sensing is increasingly recognized as a convenient tool with a wide variety of uses in agriculture. Landsat-7 has supplied multi-spectral imagery of the Earth's surface for more than 4 years and has become an important data source for a large number of research and policy-making initiatives. Unfortunately, a scan line corrector (SLC) on Landsat-7 broke down in May 2003, which caused the loss of up to 22 percent of any given scene. We present a single-image approach based on leveraging the abilities of the deep image prior method to fill in gaps using only the corrupt image. We test the ability of deep image prior to reconstruct remote sensing scenes with different levels of corruption in them. Additionally, we compare the performance of our approach with the performance of classical single-image gap-filling methods. We demonstrate a quantitative advantage of the proposed approach compared with classical gap-filling methods. The lowest-performing restoration made by the deep image prior approach reaches 0.812 in r2, while the best value for the classical approaches is 0.685. We also present the robustness of deep image prior in comparing the influence of the number of corrupted pixels on the restoration results. The usage of this approach could expand the possibilities for a wide variety of agricultural studies and applications.

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A Multiple-Input Multiple-Output (MIMO) Frequency-Modulated Continuous Wave (FMCW) radar can provide a range-angle map that expresses the signal power against each range and angle. It is possible to estimate object locations by detecting the signal power that exceeds a threshold using an algorithm, such as Constant False Alarm Rate (CFAR). However, noise and multipath components often exist over the range-angle map, which could produce false alarms for an undesired location depending on the threshold setting. In other words, the threshold setting is sensitive in noisy range-angle maps. Therefore, if the noise is reduced, the threshold can be easily set to reduce the number of false alarms. In this paper, we propose a method that improves the CFAR threshold tolerance by denoising a range-angle map using Deep Image Prior (DIP). DIP is an unsupervised deep-learning technique that enables image denoising. In the proposed method, DIP is applied to the range-angle map calculated by the Curve-Length (CL) method, and then the object location is detected over the denoised range-angle map based on Cell-Averaging CFAR (CA-CFAR), which is a typical threshold setting algorithm. Through the experiments to estimate human locations in indoor environments, we confirmed that the proposed method with DIP reduced the number of false alarms and estimated the human location accurately while improving the tolerance of the threshold setting, compared to the method without DIP.

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