Regularized Image Reconstruction Research Articles

Rapid quantitative magnetization transfer imaging: Utilizing the hybrid state and the generalized Bloch model.

To explore efficient encoding schemes for quantitative magnetization transfer (qMT) imaging with few constraints on model parameters. We combine two recently proposed models in a Bloch-McConnell equation: the dynamics of the free spin pool are confined to the hybrid state, and the dynamics of the semi-solid spin pool are described by the generalized Bloch model. We numerically optimize the flip angles and durations of a train of radio frequency pulses to enhance the encoding of three qMT parameters while accounting for all eight parameters of the two-pool model. We sparsely sample each time frame along this spin dynamics with a three-dimensional radial koosh-ball trajectory, reconstruct the data with subspace modeling, and fit the qMT model with a neural network for computational efficiency. We extracted qMT parameter maps of the whole brain with an effective resolution of 1.24 mm from a 12.6-min scan. In lesions of multiple sclerosis subjects, we observe a decreased size of the semi-solid spin pool and longer relaxation times, consistent with previous reports. The encoding power of the hybrid state, combined with regularized image reconstruction, and the accuracy of the generalized Bloch model provide an excellent basis for efficient quantitative magnetization transfer imaging with few constraints on model parameters.

Model-based image reconstruction with wavelet sparsity regularization for through-plane resolution restoration in T2 -weighted spin-echo prostate MRI.

The purpose is to develop a model-based image-reconstruction method using wavelet sparsity regularization for maintaining restoration of through-plane resolution but with improved retention of SNR versus linear reconstruction using Tikhonov (TK) regularization in high through-plane resolution (1 mm) T2 -weighted spin-echo (T2SE) images of the prostate. A wavelet sparsity (WS)-regularized image reconstruction was developed that takes as input a set of ≈80 overlapped 3-mm-thick slices acquired using a T2SE multislice scan and typically 30 coil elements. After testing in contrast and resolution phantoms and calibration in 6 subjects, the WS reconstruction was evaluated in 16 consecutive prostate T2SE MRI exams. Results reconstructed with nominal 1-mm thickness were compared with those from the TK reconstruction with the same raw data. Results were evaluated radiologically. The ratio of magnitude of prostate signal to periprostatic muscle signal was used to assess the presence of noise reduction. Technical performance was also compared with a commercial 3D-T2SE sequence. The new WS reconstruction was assessed as superior statistically to TK for overall SNR, contrast, and multiple evaluation criteria related to sharpness while retaining the high (1 mm) through-plane resolution. Wavelet sparsity tended to provide improved overall diagnostic quality versus TK, but not significantly so. In all 16 studies, the prostate-to-muscle signal ratio increased. Model-based WS-regularized reconstruction consistently provides improved SNR in high (1 mm) through-plane resolution images of prostate T2SE MRI versus linear reconstruction using TK regularization.

Dualization and Automatic Distributed Parameter Selection of Total Generalized Variation via Bilevel Optimization

Total Generalized Variation (TGV) regularization in image reconstruction relies on an infimal convolution type combination of generalized first- and second-order derivatives. This helps to avoid the staircasing effect of Total Variation (TV) regularization, while still preserving sharp contrasts in images. The associated regularization effect crucially hinges on two parameters whose proper adjustment represents a challenging task. In this work, a bilevel optimization framework with a suitable statistics-based upper level objective is proposed in order to automatically select these parameters. The framework allows for spatially varying parameters, thus enabling better recovery in high-detail image areas. A rigorous dualization framework is established, and for the numerical solution, a Newton type method for the solution of the lower level problem, i.e. the image reconstruction problem, and a bilevel TGV algorithm are introduced. Denoising tests confirm that automatically selected distributed regularization parameters lead in general to improved reconstructions when compared to results for scalar parameters.

Application of Particle Swarm Optimization with Simulated Annealing in MIT Regularization Image Reconstruction

Background and Objectives: Due to the soft-field effect of the electromagnetic field and the limit of detection, image reconstruction of magnetic induction tomography has to recover more complex electrical characteristics from very few signals. These cause a problem which have underdetermination, nonlinearity, and ill-posed characteristics, and therefore lead to many difficulties in finding its solution. Although many regularization image reconstruction methods exist, they are not suitable for MIT applications due to regularization parameter selection. The purpose of this paper is to study the principle of particle swarm optimization with simulated annealing, and to propose a regularization method for reconstruction, which will provide a new way to solve the MIT image problems. Methods and Models: Firstly, the regularization principle of image reconstruction of MIT will be analyzed. Then the hybrid regularization algorithm, including Tikhonov and NOSER regularization, will be developed, using the dimension of the Hessian matrix as a penalty term respecting the prior knowledge. PSO-SA algorithm will be applied to obtain an optimal solution for regularization parameters. Finally, six typical numerical models and approximately symmetrical cerebral hemorrhage models by COMSOL will be carried out, and the voltage signals obtained from the simulation will be used to verify the proposed reconstruction method. Results: Through the simulation results, the proposed imaging method has the average CC values of 0.9932, 0.8286 and the average RE values of 0.4982, 0.8320 for simple and complex models, respectively. Moreover, when the SNR changes from 55 dB to 35 dB, the CC value of the cerebral hemorrhage model reduced by 0.1034. The results demonstrate the effectiveness and high theoretical feasibility of the proposed method in MIT image reconstruction. Conclusions: This study indicates the potential application of PSO-SA algorithm in regularization imaging problem. Compared with traditional regularization imaging methods, the proposed method has the advantages of better accuracy, robustness and noise resistance, showing the certain application value in other similar ill-ness imaging problems.

Group-Based Sparse Representation for Compressed Sensing Image Reconstruction with Joint Regularization

Achieving high-quality reconstructions of images is the focus of research in image compressed sensing. Group sparse representation improves the quality of reconstructed images by exploiting the non-local similarity of images; however, block-matching and dictionary learning in the image group construction process leads to a long reconstruction time and artifacts in the reconstructed images. To solve the above problems, a joint regularized image reconstruction model based on group sparse representation (GSR-JR) is proposed. A group sparse coefficients regularization term ensures the sparsity of the group coefficients and reduces the complexity of the model. The group sparse residual regularization term introduces the prior information of the image to improve the quality of the reconstructed image. The alternating direction multiplier method and iterative thresholding algorithm are applied to solve the optimization problem. Simulation experiments confirm that the optimized GSR-JR model is superior to other advanced image reconstruction models in reconstructed image quality and visual effects. When the sensing rate is 0.1, compared to the group sparse residual constraint with a nonlocal prior (GSRC-NLR) model, the gain of the peak signal-to-noise ratio (PSNR) and structural similarity (SSIM) is up to 4.86 dB and 0.1189, respectively.

Penalized-Likelihood PET Image Reconstruction Using Similarity-Driven Median Regularization.

In this paper, we present a new regularized image reconstruction method for positron emission tomography (PET), where an adaptive weighted median regularizer is used in the context of a penalized-likelihood framework. The motivation of our work is to overcome the limitation of the conventional median regularizer, which has proven useful for tomographic reconstruction but suffers from the negative effect of removing fine details in the underlying image when the edges occupy less than half of the window elements. The crux of our method is inspired by the well-known non-local means denoising approach, which exploits the measure of similarity between the image patches for weighted smoothing. However, our method is different from the non-local means denoising approach in that the similarity measure between the patches is used for the median weights rather than for the smoothing weights. As the median weights, in this case, are spatially variant, they provide adaptive median regularization achieving high-quality reconstructions. The experimental results indicate that our similarity-driven median regularization method not only improves the reconstruction accuracy, but also has great potential for super-resolution reconstruction for PET.

REXPACO: An algorithm for high contrast reconstruction of the circumstellar environment by angular differential imaging

Context.Direct imaging is a method of choice for probing the close environment of young stars. Even with the coupling of adaptive optics and coronagraphy, the direct detection of off-axis sources such as circumstellar disks and exoplanets remains challenging due to the required high contrast and small angular resolution. Angular differential imaging (ADI) is an observational technique that introduces an angular diversity to help disentangle the signal of off-axis sources from the residual signal of the star in a post-processing step.Aims.While various detection algorithms have been proposed in the last decade to process ADI sequences and reach high contrast for the detection of point-like sources, very few methods are available to reconstruct meaningful images of extended features such as circumstellar disks. The purpose of this paper is to describe a new post-processing algorithm dedicated to the reconstruction of the spatial distribution of light (total intensity) received from off-axis sources, in particular from circumstellar disks.Methods.Built on the recentPACOalgorithm dedicated to the detection of point-like sources, the proposed method is based on the local learning of patch covariances capturing the spatial fluctuations of the stellar leakages. From this statistical modeling, we develop a regularized image reconstruction algorithm (REXPACO) following an inverse problems approach based on a forward image formation model of the off-axis sources in the ADI sequences.Results.Injections of fake circumstellar disks in ADI sequences from the VLT/SPHERE-IRDIS instrument show that both the morphology and the photometry of the disks are better preserved byREXPACOcompared to standard post-processing methods such as cADI. In particular, the modeling of the spatial covariances proves useful in reducing typical ADI artifacts and in better disentangling the signal of these sources from the residual stellar contamination. The application to stars hosting circumstellar disks with various morphologies confirms the ability ofREXPACOto produce images of the light distribution with reduced artifacts. Finally, we show howREXPACOcan be combined withPACOto disentangle the signal of circumstellar disks from the signal of candidate point-like sources.Conclusions.REXPACOis a novel post-processing algorithm for reconstructing images of the circumstellar environment from high contrast ADI sequences. It produces numerically deblurred images and exploits the spatial covariances of the stellar leakages and of the noise to efficiently eliminate this nuisance term. The processing is fully unsupervised, all tuning parameters being directly estimated from the data themselves.

Anatomy-guided PET reconstruction using l 1 bowsher prior

Advances in simultaneous positron emission tomography/magnetic resonance imaging (PET/MRI) technology have led to an active investigation of the anatomy-guided regularized PET image reconstruction algorithm based on MR images. Among the various priors proposed for anatomy-guided regularized PET image reconstruction, Bowsher’s method based on second-order smoothing priors sometimes suffers from over-smoothing of detailed structures. Therefore, in this study, we propose a Bowsher prior based on the -norm and an iteratively reweighting scheme to overcome the limitation of the original Bowsher method. In addition, we have derived a closed solution for iterative image reconstruction based on this non-smooth prior. A comparison study between the original and proposed Bowsher priors was conducted using computer simulation and real human data. In the simulation and real data application, small lesions with abnormal PET uptake were better detected by the proposed Bowsher prior methods than the original Bowsher prior. The original Bowsher leads to a decreased PET intensity in small lesions when there is no clear separation between the lesions and surrounding tissue in the anatomical prior. However, the proposed Bowsher prior methods showed better contrast between the tumors and surrounding tissues owing to the intrinsic edge-preserving property of the prior which is attributed to the sparseness induced by -norm, especially in the iterative reweighting scheme. Besides, the proposed methods demonstrated lower bias and less hyper-parameter dependency on PET intensity estimation in the regions with matched anatomical boundaries in PET and MRI. Therefore, these methods will be useful for improving the PET image quality based on the anatomical side information.

Generative adversarial network based regularized image reconstruction for PET

Positron emission tomography (PET) is an ill-posed inverse problem and suffers high noise due to limited number of detected events. Prior information can be used to improve the quality of reconstructed PET images. Deep neural networks have also been applied to regularized image reconstruction. One method is to use a pretrained denoising neural network to represent the PET image and to perform a constrained maximum likelihood estimation. In this work, we propose to use a generative adversarial network (GAN) to further improve the network performance. We also modify the objective function to include a data-matching term on the network input. Experimental studies using computer-based Monte Carlo simulations and real patient datasets demonstrate that the proposed method leads to noticeable improvements over the kernel-based and U-net-based regularization methods in terms of lesion contrast recovery versus background noise trade-offs.

Provable Convergence of Plug-and-Play Priors With MMSE Denoisers

Plug-and-play priors (PnP) is a methodology for regularized image reconstruction that specifies the prior through an image denoiser. While PnP algorithms are well understood for denoisers performing maximum a posteriori probability (MAP) estimation, they have not been analyzed for the minimum mean squared error (MMSE) denoisers. This letter addresses this gap by establishing the first theoretical convergence result for the iterative shrinkage/thresholding algorithm (ISTA) variant of PnP for MMSE denoisers. We show that the iterates produced by PnP-ISTA with an MMSE denoiser converge to a stationary point of some global cost function. We validate our analysis on sparse signal recovery in compressive sensing by comparing two types of denoisers, namely the exact MMSE denoiser and the approximate MMSE denoiser obtained by training a deep neural net.

Improved acceleration of phase-contrast flow imaging with magnitude difference regularization

PurposeTo develop a regularized image reconstruction algorithm for improved scan acceleration of phase-contrast (PC) flow MRI. MethodsBased on the magnitude similarity between bipolar-encoded k-space data, magnitude-difference regularization was incorporated into the conventional compressed sensing (CS) reconstruction. The gradient of the magnitude regularization was derived so the reconstruction problem can be solved using non-linear conjugate gradient with backtracking line search. Phase contrast flow data obtained in the peripheral arteries of healthy and patient subjects were retrospectively undersampled for testing the proposed reconstruction method. Three-dimensional velocity-encoded PC flow MRI was performed with prospective 4-fold undersampling for measuring arotic flow velocity in a healthy volunteer. ResultsIn the femoral arteries of healthy volunteers, the root-mean-square (RMS) errors of mean velocities were 0.56 ± 0.09 cm/s with CS-only reconstruction and 0.46 ± 0.08 cm/s with addition of magnitude regularization for three-fold acceleration; 1.34 ± 0.17 cm/s (CS only) and 1.08 ± 0.15 cm/s (magnitude regularized) for four-fold acceleration. In the iliac arteries of the patient, the RMS errors of mean velocities were 0.72 ± 0.12 cm/s and 0.56 ± 0.10 for three-fold acceleration, and 1.75 ± 0.21 and 1.24 ± 0.19 cm/s for four-fold acceleration (in the order of CS-only and magnitude regularized reconstructions). In the popliteal arteries, the RMS errors were 0.61 ± 0.10 cm/s and 0.42 ± 0.11 for three-fold acceleration, and 1.41 ± 0.19 and 1.12 ± 0.17 cm/s for four-fold acceleration. The maximum through-plane mean flow velocities were measured as 63.2 cm/s and 84.5 cm/s in ascending and descending aortas, respectively. ConclusionThe addition of magnitude-difference regularization into conventional CS reconstruction improves the accuracy of image reconstruction using highly undersampled phase-contrast flow MR data.

Conjugate gradient variants for {ell}_{p}-regularized image reconstruction in low-field MRI

We consider the MRI physics in a low-field MRI scanner, in which permanent magnets are used to generate a magnetic field in the millitesla range. A model describing the relationship between measured signal and image is derived, resulting in an ill-posed inverse problem. In order to solve it, a regularization penalty is added to the least-squares minimization problem. We generalize the conjugate gradient minimal error (CGME) algorithm to the weighted and regularized least-squares problem. Analysis of the convergence of generalized CGME (GCGME) and the classical generalized conjugate gradient least squares (GCGLS) shows that GCGME can be expected to converge faster for ill-conditioned regularization matrices. The {ell}_{p}-regularized problem is solved using iterative reweighted least squares for p=1 and p=frac{1}{2}, with both cases leading to an increasingly ill-conditioned regularization matrix. Numerical results show that GCGME needs a significantly lower number of iterations to converge than GCGLS.

Hyperspectral Image Restoration via Local Low-Rank Matrix Recovery and Moreau-Enhanced Total Variation

In this letter, we present a hyperspectral image (HSI) mixed-noise removal method named Moreau-enhanced total variation (TV) regularized local low-rank matrix recovery (LLRMTV). The rank-fixed matrix recovery is first adopted to separate the low-rank clean HSI patches from the sparse noise. Then, a Moreau-enhanced TV regularized image reconstruction strategy is utilized to ensure the piecewise smoothness of the reconstructed image from the low-rank patches. The proposed Moreau-enhanced TV restoration method involves a nonconvex penalty designed to maintain the convexity of the objective function. Moreover, the proposed model is integrated into an augmented Lagrange multiplier (ALM) algorithm to produce final results, leading to a complete HSI restoration framework. Examples of restoration illustrate the improvement over the typical TV regularization.

Improved statistical efficiency of simultaneous multi-slice fMRI by reconstruction with spatially adaptive temporal smoothing

We introduce an approach to reconstruction of simultaneous multi-slice (SMS)-fMRI data that improves statistical efficiency. The method incorporates regularization to adjust temporal smoothness in a spatially varying, encoding-dependent manner, reducing the g-factor noise amplification per temporal degree of freedom. This results in a net improvement in tSNR and GLM efficiency, where the efficiency gain can be derived analytically as a function of the encoding and reconstruction parameters. Residual slice leakage and aliasing is limited when fMRI signal energy is dominated by low frequencies. Analytical predictions, simulated and experimental results demonstrate a marked improvement in statistical efficiency in the temporally regularized reconstructions compared to conventional slice-GRAPPA reconstructions, particularly in central brain regions. Furthermore, experimental results confirm that residual slice leakage and aliasing errors are not noticeably increased compared to slice-GRAPPA reconstruction. This approach to temporally regularized image reconstruction in SMS-fMRI improves statistical power, and allows for explicit choice of reconstruction parameters by directly assessing their impact on noise variance per degree of freedom.

A New Recurrent Plug-and-Play Prior Based on the Multiple Self-Similarity Network

Recent work has shown the effectiveness of the plug-and-play priors (PnP) framework for regularized image reconstruction. However, the performance of PnP depends on the quality of the denoisers used as priors. In this letter, we design a novel PnP denoising prior, called multiple self-similarity net (MSSN), based on the recurrent neural network (RNN) with self-similarity matching using multi-head attention mechanism. Unlike traditional neural net denoisers, MSSN exploits different types of relationships among non-local and repeating features to remove the noise in the input image. We numerically evaluate the performance of MSSN as a module within PnP for solving magnetic resonance (MR) image reconstruction. Experimental results show the stable convergence and excellent performance of MSSN for reconstructing images from highly compressive Fourier measurements.

Microwave tomography sensing for potential agarwood trees imaging

Agarwood or its scientific name, Aquilaria is an expensive and precious non-timber forest product. The problems faced by the agarwood industry are the indiscriminate harvesting of agarwood and ineffective identification and inspection process of Aquilaria tree by agarwood prospectors and researchers. Hence, microwave tomography (MWT) is proposed to evaluate agarwood in order to encounter these problems. This technique operates in a safe, non-invasive and insensitive to environmental impacts. A simulation-based study had been performed in which 16 antennas microwave tomography system was modelled using the finite element analysis. In this study, six profiles were being tested and simulated at 1 GHz. An electric field was simulated based on transverse electric mode to be emitted into the modelled wood with agarwood. Besides, electric field at the receiving antennas was also simulated when the simulated incident field was emitted into the modelled wood. The readings of the electric field for both incidents and receiving antennas were recorded to find the difference of electric field which will be used for image reconstruction. The images for the six profiles were reconstructed using Linear Back Projection (LBP), Filtered Back Projection (FBP), Newton’s One-Step Error Reconstruction (NOSER) and Tikhonov Regularization (TR) image reconstruction algorithms. The reconstructed images were then analysed using the Mean Structural Similarity (MSSIM) index. The phantom and reconstructed images were analysed qualitatively and quantitatively. The findings showed promising results as the proposed MWT was able to distinguish and identify agarwood in Aquilaria tree.

Simultaneous multi‐slice cardiac cine with Fourier‐encoded self‐calibration at 7 Tesla

To accelerate cardiac cine at 7 tesla using simultaneous multi-slice (SMS) acquisition with self-calibration to resolve misalignment between calibration and imaging data due to breathing motion. A spoiled-gradient echo cine sequence was modified with radiofrequency phase-cycled SMS excitations. A Fourier encoding strategy was applied along the cardiac phase dimension to allow for slice untangling and split-slice GRAPPA calibration. Split-slice GRAPPA was coupled with regular GRAPPA (SMS-GRAPPA) and L1-SPIRiT (SMS-L1SPIRiT) for image reconstruction. 3-slice SMS cine MRI was evaluated in ten subjects against single-slice cine MRI in terms of SNR and contrast-to-noise ratio and slice leakage. SNR decreased significantly from 10.1 ± 7.1 for single-slice cine to 7.4 ± 2.8 for SMS-GRAPPA (P = 0.02) and was recovered to 9.0 ± 4.5 with SMS-L1SPIRiT (P = 0.02). Contrast to noise ratio decreased significantly from 14.5 ± 8.1 for single-slice cine to 5.6 ± 3.6 for SMS-GRAPPA (P < 0.0001) and increased slightly but significantly back to 6.7 ± 4.4 for SMS-L1SPIRiT (P = 0.03). Specific absorption rate restrictions imposed a reduced nominal flip angle (-37 ± 7%, P = 0.02) for 3-slice SMS excitations compared to single-slice acquisitions. SMS slice leakage increased significantly from apex (8.6 ± 6.5 %) to base (13.1 ± 4.1 %, P = 0.03) in the left ventricle. Three-fold acceleration of cine at 7T was achieved using the proposed SMS technique. Fourier encoding self-calibration and regularized image reconstruction enabled simultaneous acquisition of three slices without significant SNR decrease but significant CNR decrease linked to the reduced nominal excitation flip angle.

Block-Matching Local SVD Operator-Based Sparsity and TV Regularization for Image Reconstruction in Computed Tomography

Iterative image reconstruction methods based on conventional total variation (TV) for computed tomography imaging may have limitations for specific applications or situations, such as images with non-sparse gradient parts, complicated textures, or severely contaminated data sets. For these cases, encoders in optimization programs with only TV-based terms may not be sufficient for high-precision image reconstruction. Here, we incorporate a new regularization method, which is based on a block matching local SVD operator, in the reconstruction program. In addition, we develop the corresponding algorithm, which is based on projection onto convex sets and the alternating direction method of multipliers. Theoretically, the proposed method indicates improved sparse representations for complicated textures. Necessary description and discussion on the design of the proposed algorithm are provided. Preliminary results obtained using the simulation data set and the real CT projection verify the capabilities of the proposed algorithm.

Hyperspectral Image Denoising Using Local Low-Rank Matrix Recovery and Global Spatial–Spectral Total Variation

Hyperspectral images (HSIs) are usually contaminated by various kinds of noise, such as stripes, deadlines, impulse noise, Gaussian noise, and so on, which significantly limits their subsequent application. In this paper, we model the stripes, deadlines, and impulse noise as sparse noise, and propose a unified mixed Gaussian noise and sparse noise removal framework named spatial–spectral total variation regularized local low-rank matrix recovery (LLRSSTV). The HSI is first divided into local overlapping patches, and rank-constrained low-rank matrix recovery is adopted to effectively separate the low-rank clean HSI patches from the sparse noise. Differing from the previous low-rank-based HSI denoising approaches, which process all the patches individually, a global spatial–spectral total variation regularized image reconstruction strategy is utilized to ensure the global spatial–spectral smoothness of the reconstructed image from the low-rank patches. In return, the globally reconstructed HSI further promotes the separation of the local low-rank components from the sparse noise. An augmented Lagrange multiplier method is adopted to solve the proposed LLRSSTV model, which simultaneously explores both the local low-rank property and the global spatial–spectral smoothness of the HSI. Both simulated and real HSI experiments were conducted to illustrate the advantage of the proposed method in HSI denoising, from visual/quantitative evaluations and time cost.

Simultaneous multi-slice inverse imaging of the human brain

Ultrafast functional magnetic resonance imaging (fMRI) can measure blood oxygen level dependent (BOLD) signals with high sensitivity and specificity. Here we propose a novel method: simultaneous multi-slice inverse imaging (SMS-InI) — a combination of simultaneous multi-slice excitation, simultaneous echo refocusing (SER), blipped controlled aliasing in parallel imaging echo-planar imaging (EPI), and regularized image reconstruction. Using a 32-channel head coil array on a 3 T scanner, SMS-InI achieves nominal isotropic 5-mm spatial resolution and 10 Hz sampling rate at the whole-brain level. Compared with traditional inverse imaging, we found that SMS-InI has higher spatial resolution with lower signal leakage and higher time-domain signal-to-noise ratio with the optimized regularization parameter in the reconstruction. SMS-InI achieved higher effective resolution and higher detection power in detecting visual cortex activity than InI. SMS-InI also detected subcortical fMRI signals with the similar sensitivity and localization accuracy like EPI. The spatiotemporal resolution of SMS-InI was used to reveal that presenting visual stimuli with 0.2 s latency between left and right visual hemifield led to 0.2 s relative hemodynamic response latency between the left and right visual cortices. Together, these results indicate that SMS-InI is a useful tool in measuring cortical and subcortical hemodynamic responses with high spatiotemporal resolution.