Higher Structural Similarity Index Research Articles

Improving the image quality and quantitative accuracy of arterial spin labeling based on generative adversarial network

Objective: To investigate the use of deep learning approaches to improve the image quality of arterial spin labeling (ASL) and optimize its quantitative accuracy for cerebral blood flow (CBF). Methods: The clinical and imaging data of 101 patients with cerebrovascular disease in Tianjin Huanhu Hospital from May 2018 to August 2019 were retrospectively collected. Patients were divided into a training set (71 cases) and a validation set (30 cases). In training set, there were 53 cases of male,18 cases of female,with age of 55.0 (41.3, 64.5), and in validation set, there were 23 cases of male,7 cases of female,with age of57.5 (49.0, 65.0). Quantitative perfusion weighted imaging was used as the reference standard, and the original ASL-CBF images were reconstructed by training a deep learning generative adversarial network (GAN). The image quality of original ASL-CBF and GAN-CBF was compared by the structural similarity index and the normalized root mean square error. Pearson correlation coefficient was used to analyze the correlation between ASL-CBF, GAN-CBF and quantitative perfusion in different cerebral vascular blood supply areas and stroke areas, and to verify the improvement effect of GAN on the image quality and quantitative accuracy of ASL. Results: There were significant differences in gender, age, disease type, site and size between training set and validation set (all P>0.05). Compared with ASL-CBF, GAN-CBF had a higher structural similarity index (0.888 vs 0.801, P<0.001), and a lower normalized root mean square error (0.628 vs 0.775, P<0.001). The correlation between GAN-CBF and quantitative perfusion in different blood vessel supply areas and stroke lesion areas was improved compared with the original ASL-CBF, in which the perforating branch of the middle artery (r=0.853) and stroke lesion areas (r=0.765) were the most obvious (all P<0.001). Conclusion: The generative adversarial network could improve the image quality and quantization accuracy of ASL without increasing the scanning time, and expand the clinical application value of ASL.

Microwave Imaging of Breast Skin Utilizing Elliptical UWB Antenna and Reverse Problems Algorithm.

Skin cancer is one of the most widespread and fast growing of all kinds of cancer since it affects the human body easily due to exposure to the Sun’s rays. Microwave imaging has shown better outcomes with higher resolution, faster processing time, mobility, and less cutter and artifact effects. A miniaturized elliptical ultra-wideband (UWB) antenna and its semi-spherical array arrangement were used for signal transmission and reception from the defected locations in the breast skin. Several conditions such as various arrays of three, six, and nine antenna elements, smaller tumor, multi-tumors, and skin on a larger breast sample of 30 cm were considered. To assess the ability of the system, a breast shape container with a diameter of 130 mm and height of 60 mm was 3D printed and then filled with fabricated skin and breast fat to perform the experimental investigation. An improved modified time-reversal algorithm (IMTR) was used to recreate 2D images of tumors with the smallest radius of 1.75 mm in any location within the breast skin. The reconstructed images using both simulated and experimental data verified that the system can be a reliable imaging system for skin cancer diagnosis having a high structural similarity index and resolution.

Image noise removal using optimal deep learning-based noisy pixel identification and image enhancement

ABSTRACT Image restoration is utilised to discard image noise without demolishing edge information. A new optimisation based deep model is devised for image enhancement with restoration. Here, the noisy pixel map is detected with Deep Residual Network (DRN). DRN training is carried out using the JayaBat algorithm, which was created by combining the Jaya optimisation method and the Bat algorithm (BA). The statistical model is then used to restore the noisy pixels. The neuro fuzzy model and the Image Enhancement Conditional Generative Adversarial Network (IE-CGAN) are taken into account while enhancing images. Here, the IE-CGAN training is performed with designed CAViaRJayaBat. The CAViaRJayaBat is designed newly by combining the CAViaR and JayaBat algorithms. The proposed CAViaRJayaBat-based IE-CGAN offered improved performance with the best Peak signal to noise ratio (PSNR) of 49.049 dB, the highest Second derivative measure of enhancement (SDME), 62.570 dB, and the highest structural similarity index (SSIM), 0.858.

Applying image registration algorithm combined with CNN model to video image stitching

The purposes are to explore the video image stitching technique of Unmanned Aerial Vehicles (UAVs), expand the application of image registration algorithms and new sensing equipment in video image stitching, and improve the development of video remote sensing image processing. First, how to remotely stitch UAV video images is analyzed. Second, the Scale Invariant Feature Transform (SIFT) algorithm is improved by re-dividing the pixel region and incorporating the vector correlation coefficient. Then, the matching results of the improved SIFT algorithm are compared with those of the traditional SIFT algorithm and Speed Up Robust Feature algorithm. Second, the Random Sample Consensus algorithm is introduced to match the video images accurately, and the matching accuracy of the converted images is verified. Finally, the improved image registration algorithm, the homography matrix estimation model based on convolutional neural network, and the conformation equation of the video sensor are combined to complete the video image stitching of UAVs. Also, the stitching quality of the video image is analyzed. The results show that the improved SIFT algorithm is better than the traditional SIFT algorithm in terms of correct matching and matching time. The visually transformed finely-matched image has a higher matching accuracy rate, and the combination of the two registration algorithms eliminates mismatch points effectively. Compared with the traditional stitching method, the video image stitching method proposed in this study has a higher structural similarity index and edge difference spectrum index, which is feasible and effective. The combination of image registration algorithm with new sensors and deep learning has great application potential in video image stitching.

A Deep Learning Approach to Re-create Raw Full-Field Digital Mammograms for Breast Density and Texture Analysis.

To develop a computational approach to re-create rarely stored for-processing (raw) digital mammograms from routinely stored for-presentation (processed) mammograms. In this retrospective study, pairs of raw and processed mammograms collected in 884 women (mean age, 57 years ± 10 [standard deviation]; 3713 mammograms) from October 5, 2017, to August 1, 2018, were examined. Mammograms were split 3088 for training and 625 for testing. A deep learning approach based on a U-Net convolutional network and kernel regression was developed to estimate the raw images. The estimated raw images were compared with the originals by four image error and similarity metrics, breast density calculations, and 29 widely used texture features. In the testing dataset, the estimated raw images had small normalized mean absolute error (0.022 ± 0.015), scaled mean absolute error (0.134 ± 0.078) and mean absolute percentage error (0.115 ± 0.059), and a high structural similarity index (0.986 ± 0.007) for the breast portion compared with the original raw images. The estimated and original raw images had a strong correlation in breast density percentage (Pearson r = 0.946) and a strong agreement in breast density grade (Cohen κ = 0.875). The estimated images had satisfactory correlations with the originals in 23 texture features (Pearson r ≥ 0.503 or Spearman ρ ≥ 0.705) and were well complemented by processed images for the other six features. This deep learning approach performed well in re-creating raw mammograms with strong agreement in four image evaluation metrics, breast density, and the majority of 29 widely used texture features.Keywords: Mammography, Breast, Supervised Learning, Convolutional Neural Network (CNN), Deep learning algorithms, Machine Learning AlgorithmsSee also the commentary by Chan in this issue.Supplemental material is available for this article.©RSNA, 2021.

Refinement of spectra using a deep neural network: Fully automated removal of noise and background

AbstractWe report the potential of U‐Net deep neural network for the efficient removal of noise and background from raw Raman spectra. The U‐Net method was first trained on simulated spectra and then tested with experimental spectra. The quality of the test results was quantified via different signal‐to‐noise ratios and the structural similarity index metric. The U‐Net recovered Raman spectra feature a high structural similarity index, even for raw spectra that were dominated by background. The U‐Net model does not rely on any human intervention.

U-ASD Net: Supervised Crowd Counting Based on Semantic Segmentation and Adaptive Scenario Discovery

Crowd counting considers one of the most significant and challenging issues in computer vision and deep learning communities, whose applications are being utilized for various tasks. While this issue is well studied, it remains an open challenge to manage perspective distortions and scale variations. How well these problems are resolved has a huge impact on predicting a high-quality crowd density map. In this study, a hybrid and modified deep neural network (U-ASD Net), based on U-Net and adaptive scenario discovery (ASD), is proposed to get precise and effective crowd counting. The U part is produced by replacing the nearest upsampling in the encoder of U-Net with max-unpooling. This modification provides a better crowd counting performance by capturing more spatial information. The max-unpooling layers upsample the feature maps based on the max locations held from the downsampling process. The ASD part is constructed with three light pathways, two of which have been learned to reflect various densities of the crowd and define the appropriate geometric configuration employing various sizes of the receptive field. The third pathway is an adaptation path, which implicitly discovers and models complex scenarios to recalibrate pathway-wise responses adaptively. ASD has no additional branches to avoid increasing the complexity. The designed model is end-to-end trainable. This integration provides an effective model to count crowds in both dense and sparse datasets. It also predicts an elevated quality density map with a high structural similarity index and a high peak signal-to-noise ratio. Several comprehensive experiments on four popular datasets for crowd counting have been carried out to demonstrate the proposed method’s promising performance compared to other state-of-the-art approaches. The proposed model achieves the lowest count error in terms of the MAE in ShanghaiTech Part A, Part B, and Mall datasets with 64.6, 7.5, and 1.8, respectively. Moreover, it achieves the lowest count error in terms of the MSE in ShanghaiTech Part B, UCF CC 50, UCSD, and Mall datasets with 12.4, 217.8, 2.1, 2.2, respectively. In addition, the proposed model accomplishes the best quality density maps on all the utilized datasets. Furthermore, a new dataset with its manual annotations, called Haramain with three different scenes and different densities, is introduced and used for evaluating the U-ASD Net.

Boosting Magnetic Resonance Image Denoising With Generative Adversarial Networks

Denoising plays an important role in the Magnetic Resonance Imaging (MRI) applications for medical diagnosis. MRI images usually contain undesired noises which would negatively affect the exactitude of pathological diagnosis. Recently, many models for MRI denoising have been developed from deep learning networks. In this paper, we propose a novel MRI image denoising method using the conditional Generative Adversarial Networks (GANs). Specifically, a Convolutional Neural Network (CNN) is utilized as the discriminator in the process to distinguish whether the image pair obtained from the conditional GAN is a real pair which consists of a noisy image and a noise-free image or a fake pair which, on the other hand, contains a noisy image and a denoised image. In our design, the convolutional encoder-decoder networks-based generator is used to remove the noise in the noisy MRI images as much as possible. The whole architecture is trained by adversarial learning. Experiments using both synthetic and real clinical MRI datasets are conducted. When tested on the synthetic T1w images with 10% noise level, our method performed better in terms of reaching a high structural similarity index (SSIM) at 0.9489 while that of the next best method was only 0.7485. Moreover, when the image noise level was increased from 1% to 10%, our method was more stable that the SSIM only dropped about 3.2% while that of the next best method dropped about 23.7%. Simulation results demonstrate that the proposed method is more robust and outperforms the conventional methods in both the denoising level and preservation of the anatomical structures and defined contrast.

Microwave Imaging of Voids in Oil Palm Trunk Applying UWB Antenna and Robust Time-Reversal Algorithm

The oil palm trees in Southeast Asia face a great challenge due to voids within tree trunks. Besides, both plantations and the palm oil industry suffered considerable losses due to ineffective inspection of defective trees. Several techniques such as ultrasound, X-ray, capacitive volume, gamma computed tomography, and microwave tomography were applied to detect and control the decay of a trunk. However, all the techniques showed substantial drawbacks (such as limited resolution, tedious processing time, and use of bulky equipment with limited mobility) except for microwave tomography which overtook the other techniques by using a method that distinguishes the dielectric properties of healthy and diseased trunks. This work proposes ultra-wide-band (UWB) signal transmission and reception using antenna sensor arrays that record reflections from affected regions in the trunk. Various factors have been considered, such as different cylindrical arrays of 4, 8, 12, and 16 antennas; different positions of hollows; a heterogeneous trunk; multiple targets; and larger trunk samples (16–30 cm). To validate the system’s capabilities, two cylindrical wood samples with different diameters of 100 mm and 140 mm and with one hollow and three hollows within are 3D-printed, investigated, and then measured. The authors recommended a robust time-reversal algorithm (RTR) to reconstruct 2D images that successfully identified and localized cavities with the smallest diameter of 3.5 mm. Furthermore, reconstructed images of measured data verified a practical and reliable oil palm trunk imaging and sensing system with a high structural similarity index and resolution.

Unsupervised learning for deformable registration of thoracic CT and cone-beam CT based on multiscale features matching with spatially adaptive weighting.

Cone-beam computed tomography (CBCT) is a common on-treatment imaging widely used in image-guided radiotherapy. Fast and accurate registration between the on-treatment CBCT and planning CT is significant for and precise adaptive radiotherapy treatment (ART). However, existing CT-CBCT registration methods, which are mostly affine or time-consuming intensity- based deformation registration, still need further study due to the considerable CT-CBCT intensity discrepancy and the artifacts in low-quality CBCT images. In this paper, we propose a deep learning-based CT-CBCT registration model to promote rapid and accurate CT-CBCT registration for radiotherapy. The proposed CT-CBCT registration model consists of a registration network and an innovative deep similarity metric network. The registration network is a novel fully convolution network adapted specially for patch-wise CT-CBCT registration. The metric network, going beyond intensity, automatically evaluates the high-dimensional attribute-based dissimilarity between the registered CT and CBCT images. In addition, consideringthe artifacts in low-quality CBCT images, we add spatial weighting (SW) block to adaptively attach more importance to those informative voxels while inhibit the interference of artifact regions. Such SW-based metric network is expected to extract the most meaningful and discriminative deep features, and form a more reliable CT-CBCT similarity measure to train the registration network. We evaluate the proposed method on clinical thoracic CBCT and CT dataset, and compare the registration results with some other common image similarity metrics and some state-of-the-art registration algorithms. The proposed method provides the highest Structural Similarity index (86.17±5.09), minimum Target Registration Error of landmarks (2.37±0.32mm), and the best DSC coefficient (78.71±10.95) of tumor volumes. Moreover, our model also obtains comparable distance error of lung surfaces (1.75±0.35mm). The proposed model shows both efficiency and efficacy for reliable thoracic CT-CBCT registration, and can generate the matched CT and CBCT images within few seconds, which is of great significance to clinical radiotherapy.

RUN-UP: Accelerated multishot diffusion-weighted MRI reconstruction using an unrolled network with U-Net as priors.

To accelerate and improve multishot diffusion-weighted MRI reconstruction using deep learning. An unrolled pipeline containing recurrences of model-based gradient updates and neural networks was introduced for accelerating multishot DWI reconstruction with shot-to-shot phase correction. The network was trained to predict results of jointly reconstructed multidirection data using single-direction data as input. In vivo brain and breast experiments were performed for evaluation. The proposed method achieves a reconstruction time of 0.1 second per image, over 100-fold faster than a shot locally low-rank reconstruction. The resultant image quality is comparable to the target from the joint reconstruction with a peak signal-to-noise ratio of 35.3 dB, a normalized root-mean-square error of 0.0177, and a structural similarity index of 0.944. The proposed method also improves upon the locally low-rank reconstruction (2.9 dB higher peak signal-to-noise ratio, 29% lower normalized root-mean-square error, and 0.037 higher structural similarity index). With training data from the brain, this method also generalizes well to breast diffusion-weighted imaging, and fine-tuning further reduces aliasing artifacts. A proposed data-driven approach enables almost real-time reconstruction with improved image quality, which improves the feasibility of multishot DWI in a wide range of clinical and neuroscientific studies.

Accelerating Prostate Diffusion-weighted MRI Using a Guided Denoising Convolutional Neural Network: Retrospective Feasibility Study

To investigate the feasibility of accelerating prostate diffusion-weighted imaging (DWI) by reducing the number of acquired averages and denoising the resulting image using a proposed guided denoising convolutional neural network (DnCNN). Raw data from the prostate DWI scans were retrospectively gathered between July 2018 and July 2019 from six single-vendor MRI scanners. There were 103 datasets used for training (median age, 64 years; interquartile range [IQR], 11), 15 for validation (median age, 68 years; IQR, 12), and 37 for testing (median age, 64 years; IQR, 12). High b-value diffusion-weighted (hb DW) data were reconstructed into noisy images using two averages and reference images using all 16 averages. A conventional DnCNN was modified into a guided DnCNN, which uses the low b-value DW image as a guidance input. Quantitative and qualitative reader evaluations were performed on the denoised hb DW images. A cumulative link mixed regression model was used to compare the readers' scores. The agreement between the apparent diffusion coefficient (ADC) maps (denoised vs reference) was analyzed using Bland-Altman analysis. Compared with the original DnCNN, the guided DnCNN produced denoised hb DW images with higher peak signal-to-noise ratio (32.79 ± 3.64 [standard deviation] vs 33.74 ± 3.64), higher structural similarity index (0.92 ± 0.05 vs 0.93 ± 0.04), and lower normalized mean square error (3.9% ± 10 vs 1.6% ± 1.5) (P < .001 for all). Compared with the reference images, the denoised images received higher image quality scores from the readers (P < .0001). The ADC values based on the denoised hb DW images were in good agreement with the reference ADC values (mean ADC difference ranged from -0.04 to 0.02 × 10-3 mm2/sec). Accelerating prostate DWI by reducing the number of acquired averages and denoising the resulting image using the proposed guided DnCNN is technically feasible. Supplemental material is available for this article. © RSNA, 2020.

Detecting changes in multitemporal multispectral Landsat images using spatial frequency-based undecimated wavelet transform fusion

Changes in surface water are normally detected by extracting the water features from individual multispectral (MS) images. We present an approach based on pixel fusion of MS and panchromatic (PAN) bands of multitemporal Landsat images to detect the changes in surface water. Spatial frequency and the maximum amplitude selection-based fusion rule on multiresolution undecimated wavelet transform (UDWT) coefficients for extracting and injecting the spatial and spectral content from MS and PAN images is introduced. Landsat Thematic Mapper (TM) and Landsat Enhanced Thematic Mapper (ETM+) of 2010 and 2000 images acquired from the US Geological Survey were fused to investigate the potential of the proposed spatial frequency-based UDWT in highlighting the changes. Various component substitution and multiresolution analysis-based fusion algorithms were also applied. It was observed that UDWT with spatial frequency effectively extracts the spectral information from MS images and the spatial information from PAN images. The performance was evaluated based on visual interpretation and spatial and spectral quality assessment metrics. A high correlation coefficient (0.9992), high contrast similarity (0.99937), high structural similarity index measure (0.9884), less relative average spectral error (23.6426), less root mean squared error (2.2256), relatively less blind referenceless image spatial quality evaluator, natural image quality evaluator, and perception-based image quality evaluator significantly support the proposed fusion technique in yielding the pansharpened image, making it more suitable for detecting the multitemporal changes in remote sensing applications.

RETRACTED: A compensating total variation image denoising model combining L1 and L2 norm

To overcome the “staircase effect” while preserving the structural information such as image edges and textures quickly and effectively, we propose a compensating total variation image denoising model combining L1 and L2 norm. A new compensating regular term is designed, which can perform anisotropic and isotropic diffusion in image denoising, thus making up for insufficient diffusion in the total variation model. The algorithm first uses local standard deviation to distinguish neighborhood types. Then, the anisotropic diffusion based on L1 norm plays the role of edge protection in the strong edge region. The anisotropic and the isotropic diffusion simultaneously exist in the smooth region, so that the weak textures can be protected while overcoming the “staircase effect” effectively. The simulation experiments show that this method can effectively improve the peak signal-to-noise ratio and obtain the higher structural similarity index and the shorter running time.

An Improved Enhancement Algorithm Based on CNN Applicable for Weak Contrast Images

Image enhancement is commonly used in digital image processing applications. Through image enhancement, the features of the target object are enhanced to make it easier to identify. In order to realize image enhancement, a neural network with a trapezoidal convolution kernel is proposed in this paper. First, weak contrast images are generated using the images in SIDD, DND and RENOIR, which are public datasets used for image denoising. On this basis, pixel distribution characteristics of the R, G and B channels of the weak contrast images are analyzed, and the histogram distribution of the images is given, which can be used to determine the size of the network convolution kernels. Then, a multi-layer convolution neural network is constructed, which uses the original image as an input and outputs the noise map. This network includes convolution kernels of different sizes for the three channels of the original images, and the convolution kernel size is determined by calculating the mean square deviation of the pixels of the corresponding channel. The proposed algorithm provides visually pleasing contrast enhancement. In this paper, a public dataset for image enhancement and actual captured images are separately assessed, both the contrast experiment and ablation experiment results show that the algorithm proposed in this paper can achieve a higher Peak Signal to Noise Ratio (PSNR) and a higher Structural Similarity Index (SSIM) than other image enhancement algorithms.

An Improved Multithreshold Segmentation Algorithm Based on Graph Cuts Applicable for Irregular Image

In order to realize the multithreshold segmentation of images, an improved segmentation algorithm based on graph cut theory using artificial bee colony is proposed. A new weight function based on gray level and the location of pixels is constructed in this paper to calculate the probability that each pixel belongs to the same region. On this basis, a new cost function is reconstructed that can use both square and nonsquare images. Then the optimal threshold of the image is obtained through searching for the minimum value of the cost function using artificial bee colony algorithm. In this paper, public dataset for segmentation and widely used images were measured separately. Experimental results show that the algorithm proposed in this paper can achieve larger Information Entropy (IE), higher Peak Signal to Noise Ratio (PSNR), higher Structural Similarity Index (SSIM), smaller Root Mean Squared Error (RMSE), and shorter time than other image segmentation algorithms.

Sparsity adaptive reconstruction for highly accelerated cardiac MRI.

To enable parameter-free, accelerated cardiovascular magnetic resonance (CMR). Regularized reconstruction methods, such as compressed sensing (CS), can significantly accelerate MRI data acquisition but require tuning of regularization weights. In this work, a technique, called Sparsity adaptive Composite Recovery (SCoRe) that exploits sparsity in multiple, disparate sparsifying transforms is presented. A data-driven adjustment of the relative contributions of different transforms yields a parameter-free CS recovery process. SCoRe is validated in a dynamic digital phantom as well as in retrospectively and prospectively undersampled cine CMR data. The results from simulation and 6 retrospectively undersampled datasets indicate that SCoRe with auto-tuned regularization weights yields lower root-mean-square error (RMSE) and higher structural similarity index (SSIM) compared to state-of-the-art CS methods. In 45 prospectively undersampled datasets acquired from 15 volunteers, the image quality was scored by 2 expert reviewers, with SCoRe receiving a higher average score (p<0.01) compared to other CS methods. SCoRe enables accelerated cine CMR from highly undersampled data. In contrast to other acceleration techniques, SCoRe adapts regularization weights based on noise power and level of sparsity in each transform, yielding superior performance without admitting any free parameters.

Multi-Strategy Emperor Penguin Optimizer for RGB Histogram-Based Color Satellite Image Segmentation Using Masi Entropy

In order to realize the multilevel thresholding segmentation of color satellite images, a multi-strategy emperor penguin optimizer (called MSEPO) is proposed to find the optimal threshold values for three channels of RGB images. Masi entropy is utilized as the objective function. Meanwhile, three strategies are introduced, namely highly disruptive polynomial mutation, Levy flight, and thermal exchange operator. Through these, the MSEPO is able to properly balance the exploration and exploitation mechanisms. Moreover, the convergence, accuracy and stability performance have been significantly enhanced. Tests are carried out on color Berkeley images and color satellite images at various threshold levels. The experimental results show that the proposed method achieves higher Peak Signal to Noise Ratio (PSNR), higher Structural Similarity Index (SSIM), higher Feature Similarity Index (FSIM), and shorter CPU time than seven state-of-the-art optimization techniques. To present in a comprehensive manner, the computational complexity has also been analyzed in terms of time and space complexity. Wilcoxon rank sum test and Friedman test are also applied to statistical analysis. To sum up, MSEPO algorithm has achieved significant improvement and superior performance. What's more, the proposed technique is more suitable for high-dimensional segmentation of complex satellite images.

An Irregular-Shaped Inward-Outward Ring-Pair Magnet Array With a Monotonic Field Gradient for 2D Head Imaging in Low-Field Portable MRI

We present a design and the optimization of an irregular-shaped inward-outward (IO) ring-pair magnet array that generates a 1D monotonic field pattern for 2D head imaging in a low-field portable magnetic resonance imaging (MRI) system. The magnet rings are discretized into fan-shaped ring segments with varying outer radii for the design and optimization. Besides, the inner radii of ring-pairs are tapered from outside in to provide the controlled field inhomogeneity. Genetic algorithm (GA) was used, and a current model for a fan-shaped ring segment was derived to have a fast forward calculation in the optimization. A monotonic field pattern is successfully obtained along the x-direction in a cylindrical field of view (FoV), with a relatively strong magnetic field (132.98 mT) and the homogeneity of 151840 ppm. The proposed array was further evaluated by applying its field as a spatial encoding magnetic field (SEM) for imaging by using simulation. Due to the field monotonicity, the reconstructed image by applying the fields of the proposed array shows clearer features (a higher structural similarity index) with a reduced error rate compared to that using a sparse dipolar Halbach array. The proposed magnet array is a promising alternative to supply SEM for imaging in a permanent-magnet-based low-field portable MRI system.

Imaging through scattering media using semidefinite programming.

A clear image of an observed object may deteriorate into unrecognizable speckle when encountering heterogeneous scattering media, thus it is necessary to recover the object image from the speckle. A method combining least square and semidefinite programming is proposed, which can be used for imaging through scattering media. The proposed method consists of two main stages, that is, media scattering characteristics (SCs) estimation and image reconstruction. SCs estimation is accomplished through LS concept after establishing a database of known object-and-speckle pairs. Image reconstruction is realized by solving an SDP problem to obtain the product of the unknown object image and its Hermitian transposition. Finally, the unknown object image can be reconstructed by extracting the largest rank-1 component of the product. Structural similarity (SSIM) index is employed as a performance indicator in speckle prediction and image reconstruction. Numerical simulations and physical experiments are performed to verify the feasibility and practicality of the proposed method. Compared with the existing phase shift interferometry mean square optimization method and the single-shot phase retrieval algorithm, the proposed method is the most precise to obtain the best reconstruction results with highest SSIM index value. The work can be used for exploring the potential applications of scattering media, especially for imaging through turbid media in biomedical, scattering property measurement, and optical image encryption.