Complex-valued Images Research Articles

Denoising complex-valued diffusion MR images using a two-step non-local principal component analysis approach.

to propose a two-step non-local principal component analysis (PCA) method and demonstrate its utility for denoising diffusion tensor MRI (DTI) with a few diffusion directions. A two-step denoising pipeline was implemented to ensure accurate patch selection even with high noise levels and was coupled with data preprocessing for g-factor normalization and phase stabilization before data denoising with a non-local PCA algorithm. At the heart of our proposed pipeline was the use of a data-driven optimal shrinkage algorithm to manipulate the singular values in a way that would optimally estimate the noise-free signal. Our approach's denoising performances were evaluated using simulation and in-vivo human data experiments. The results were compared to those obtained with existing local-PCA-based methods. In both simulation and human data experiments, our approach substantially enhanced image quality relative to the noisy counterpart, yielding improved performances for estimation of relevant DTI metrics. It also outperformed existing local-PCA-based methods in reducing noise while preserving anatomic details. It also led to improved whole-brain tractography relative to the noisy counterpart. The proposed denoising method has the utility for improving image quality for DTI with reduced diffusion directions and is believed to benefit many applications especially those aiming to achieve quality parametric mapping using only a few image volumes.

Complex-valued image reconstruction for compressed sensing MRI using hierarchical constraint

In Magnetic Resonance Imaging (MRI), the sequential acquisition of raw complex-valued image data in Fourier space, also known as k-space, results in extended examination times. To speed up the MRI scans, k-space data are usually undersampled and processed using numerical techniques such as compressed sensing (CS). While the majority of CS-MRI algorithms primarily focus on magnitude images due to their significant diagnostic value, the phase components of complex-valued MRI images also hold substantial importance for clinical diagnosis, including neurodegenerative diseases. In this work, complex-valued MRI reconstruction is studied with a focus on the simultaneous reconstruction of both magnitude and phase images. The proposed algorithm is based on the nonsubsampled contourlet transform (NSCT) technique, which offers shift invariance in images. Instead of directly transforming the complex-valued image into the NSCT domain, we introduce a wavelet transform within the NSCT domain, reducing the size of the sparsity of coefficients. This two-level hierarchical constraint (HC) enforces sparse representation of complex-valued images for CS-MRI implementation. The proposed HC is seamlessly integrated into a proximal algorithm simultaneously. Additionally, to effectively minimize the artifacts caused by sub-sampling, thresholds related to different sub-bands in the HC are applied through an alternating optimization process. Experimental results show that the novel method outperforms existing CS-MRI techniques in phase-regularized complex-valued image reconstructions.

Reliability of quantitative magnetic susceptibility imaging metrics for cerebral cortex and major subcortical structures.

Susceptibility estimates derived from quantitative susceptibility mapping (QSM) images for the cerebral cortex and major subcortical structures are variably reported in brain magnetic resonance imaging (MRI) studies, as average of all ( ), absolute ( ), or positive- ( ) and negative-only ( ) susceptibility values using a region of interest (ROI) approach. This pilot study presents a reliability analysis of currently used ROI-QSM metrics and an alternative ROI-based approach to obtain voxel-weighted ROI-QSM metrics ( and ). Ten healthy subjects underwent repeated (test-retest) 3-dimensional multi-echo gradient-echo (3DMEGE) 3 Tesla MRI measurements. Complex-valued 3DMEGE images were acquired and reconstructed with slice thicknesses of 1 and 2mm (3DMEGE1, 3DMEGE2) along with 3DT1-weighted isometric (voxel 1 mm3) images for independent registration and ROI segmentation. Agreement, consistency, and reproducibility of ROI-QSM metrics were assessed through Bland-Altman analysis, intraclass correlation coefficient, and interscan and intersubject coefficient of variation (CoV). All ROI-QSM metrics exhibited good to excellent consistency and test-retest agreement with no proportional bias. Interscan CoV was higher for in comparison to the other metrics where it was below 15%, in both 3DMEGE1 and 3DMEGE2 datasets. Intersubject CoV for and exceeded 50% in all ROIs. Among the evaluated ROI-QSM metrics, and estimates were less reliable, whereas separating positive and negative values (using ) improved the reproducibility within, and the comparability between, subjects, even when reducing the slice thickness. These preliminary findings may offer valuable insights toward standardizing ROI-QSM metrics across different patient cohorts and imaging settings in future clinical MRI studies.

Double-image encryption and authentication scheme based on compressed sensing and double random phase encoding

To enhance the security of image information, a double-image encryption and authentication scheme combining compressive sensing (CS) and double random phase encoding (DRPE) is proposed. First, two plaintext images are taken as real and imaginary parts to form a complex-valued image, which is then encoded using DRPE. Next, extract the phase of the encrypted complex-valued image and encode it into authentication information. Simultaneously, the complex-valued image is sampled using the measurement matrix, which is optimized by Schmidt orthogonalization, and then quantized to form a compressed image. Subsequently, the authentication information is embedded into the compressed image, and by applying the permutation and diffusion algorithm to it, the ciphertext image is obtained. At the receiving end, the ciphertext is decrypted using inverse permutation and inverse diffusion algorithms, and the authentication information is decoded to acquire the authentication image. Finally, synchronous authentication of the two reconstructed images is achieved using a nonlinear cross-correlation method. Additionally, the keys in the proposed scheme are generated using high-dimensional chaotic systems, effectively reducing the required storage space and transmission bandwidth. Simulation results demonstrate that the proposed scheme has high image reconstruction performance at different compression ratios and possesses outstanding security and authentication capabilities.

Low-Sidelobe Imaging Method Utilizing Improved Spatially Variant Apodization for Forward-Looking Sonar

For two-dimensional forward-looking sonar imaging, high sidelobes significantly degrade the quality of sonar images. The cosine window function weighting method is often applied to suppress the sidelobe levels in the angular and range dimensions, at the expense of the main lobe resolutions. Therefore, an improved spatially variant apodization imaging method for forward-looking sonar is proposed, to reduce sidelobes without degrading the main lobe resolution in angular-range dimensions. The proposed method is a nonlinear postprocessing operation in which the raw complex-valued sonar image produced by a conventional beamformer and matched filter is weighted by a spatially variant coefficient. To enhance the robustness of the spatially variant apodization approach, the array magnitude and phase errors are calibrated to prevent the occurrence of beam sidelobe increase prior to beamforming operations. The analyzed results of numerical simulations and a lake experiment demonstrate that the proposed method can greatly reduce the sidelobes to approximately −40 dB, while the main lobe width remains unchanged. Moreover, this method has an extremely simple computational process.

Radial Undersampled MRI Reconstruction Using Deep Learning With Mutual Constraints Between Real and Imaginary Components of K-Space.

The deep learning method is an efficient solution for improving the quality of undersampled magnetic resonance (MR) image reconstruction while reducing lengthy data acquisition. Most deep learning methods neglect the mutual constraints between the real and imaginary components of complex-valued k-space data. In this paper, a new complex-valued convolutional neural network, namely, Dense-U-Dense Net (DUD-Net), is proposed to interpolate the undersampled k-space data and reconstruct MR images. The proposed network comprises dense layers, U-Net, and other dense layers in sequence. The dense layers are used to simulate the mutual constraints between real and imaginary components, and U-Net performs feature sparsity and interpolation estimation for k-space data. Two MRI datasets were used to evaluate the proposed method: brain magnitude-only MR images and knee complex-valued k-space data. Several operations were conducted for data preprocessing. First, the complex-valued MR images were synthesized by phase modulation on magnitude-only images. Second, a radial trajectory based on the golden angle was used for k-space undersampling, whereby a reversible normalization method was proposed to balance the distribution of positive and negative values in k-space data. The optimal performance of DUD-Net was demonstrated based on a quantitative evaluation of inter-method and intra-method comparisons. When compared with other methods, significant improvements were achieved, PSNRs were increased by 10.78 and 5.74dB, whereas RMSEs were decreased by 71.53% and 30.31% for magnitude and phase image, respectively. It is concluded that DUD-Net significantly improves the performance of MR image reconstruction.

A stochastic ADMM algorithm for large-scale ptychography with weighted difference of anisotropic and isotropic total variation

Ptychography, a prevalent imaging technique in fields such as biology and optics, poses substantial challenges in its reconstruction process, characterized by nonconvexity and large-scale requirements. This paper presents a novel approach by introducing a class of variational models that incorporate the weighted difference of anisotropic–isotropic total variation. This formulation enables the handling of measurements corrupted by Gaussian or Poisson noise, effectively addressing the nonconvex challenge. To tackle the large-scale nature of the problem, we propose an efficient stochastic alternating direction method of multipliers, which guarantees convergence under mild conditions. Numerical experiments validate the superiority of our approach by demonstrating its capability to successfully reconstruct complex-valued images, especially in recovering the phase components even in the presence of highly corrupted measurements.

Spatially-coded Fourier ptychography: flexible and detachable coded thin films for quantitative phase imaging with uniform phase transfer characteristics.

Fourier ptychography (FP) is an enabling imaging technique that produces high-resolution complex-valued images with extended field coverages. However, when FP images a phase object with any specific spatial frequency, the captured images contain only constant values, rendering the recovery of the corresponding linear phase ramp impossible. This challenge is not unique to FP but also affects other common microscopy techniques -- a rather counterintuitive outcome given their widespread use in phase imaging. The underlying issue originates from the non-uniform phase transfer characteristic inherent in microscope systems, which impedes the conversion of object wavefields into discernible intensity variations. To address this challenge, we present spatially-coded Fourier ptychography (scFP), a new method that synergizes FP with spatial-domain coded detection for true quantitative phase imaging. In scFP, a flexible and detachable coded thin film is attached atop the image sensor in a regular FP setup. The spatial modulation of this thin film ensures a uniform phase response across the entire synthetic bandwidth. It improves reconstruction quality and corrects refractive index underestimation issues prevalent in conventional FP and related tomographic implementations. The inclusion of the coded thin film further adds a new dimension of measurement diversity in the spatial domain. The development of scFP is expected to catalyse new research directions and applications for phase imaging, emphasizing the need for true quantitative accuracy with uniform frequency response.

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

Complex-valued universal linear transformations and image encryption using spatially incoherent diffractive networks

SemiPSCN: Polarization Semantic Constraint Network for Semi-Supervised Segmentation in Large-Scale and Complex-Valued PolSAR Images

SemiPSCN: Polarization Semantic Constraint Network for Semi-Supervised Segmentation in Large-Scale and Complex-Valued PolSAR Images

Accelerated chemical shift encoded cardiovascular magnetic resonance imaging with use of a resolution enhancement network

BackgroundCardiovascular magnetic resonance (CMR) chemical shift encoding (CSE) enables myocardial fat imaging. We sought to develop a deep learning network (FastCSE) to accelerate CSE. MethodsFastCSE was built on a super-resolution generative adversarial network extended to enhance complex-valued image sharpness. FastCSE enhances each echo image independently before water-fat separation. FastCSE was trained with retrospectively identified cines from 1519 patients (56 ± 16 years; 866 men) referred for clinical 3T CMR. In a prospective study of 16 participants (58 ± 19 years; 7 females) and 5 healthy individuals (32 ± 17 years; 5 females), dual-echo CSE images were collected with 1.5 × 1.5mm2, 2.5 × 1.5 mm2, and 3.8 × 1.9mm2 resolution using generalized autocalibrating partially parallel acquisition (GRAPPA). FastCSE was applied to images collected with resolution of 2.5 × 1.5mm2 and 3.8 × 1.9 mm2 to restore sharpness. Fat images obtained from two-point Dixon reconstruction were evaluated using a quantitative blur metric and analyzed with 5-way analysis of variance. ResultsFastCSE successfully reconstructed CSE images inline. FastCSE acquisition, with a resolution of 2.5 × 1.5mm² and 3.8 × 1.9 mm², reduced the number of breath-holds without impacting visualization of fat by approximately 1.5-fold and 3-fold compared to GRAPPA acquisition with a resolution of 1.5 × 1.5 mm², from 3.0 ± 0.8 breath-holds to 2.0 ± 0.2 and 1.1 ± 0.4 breath-holds, respectively. FastCSE improved image sharpness and removed ringing artifacts in GRAPPA fat images acquired with a resolution of 2.5 × 1.5 mm2 (0.31 ± 0.03 vs. 0.35 ± 0.04, P < 0.001) and 3.8 × 1.9 mm2 (0.31 ± 0.03 vs. 0.42 ± 0.06, P < 0.001). Blurring in FastCSE images was similar to blurring in images with 1.5 × 1.5 mm² resolution (0.32 ±0.03 vs. 0.31 ± 0.03, P = 0.78; 0.32 ± 0.03 vs. 0.31 ± 0.03, P = 0.90). ConclusionWe showed that a deep learning-accelerated CSE technique based on complex-valued resolution enhancement can reduce the number of breath-holds in CSE imaging without impacting the visualization of fat. FastCSE showed similar image sharpness compared to a standardized parallel imaging method.

Dimensionality reduction technique based phase aberration compensation and spurious fringe removal in off-axis digital holographic microscopy

A dimensionality reduction technique based on singular value decomposition (SVD) is proposed for the aberration and spurious fringe removal from the phase measurement in off-axis digital holographic microscopy. The SVD of complex-valued virtual image obtained from numerically reconstructed hologram is computed. The phase aberration and spurious fringe compensated phase estimate is obtained by appropriate selection of singular values to reconstruct the denoised phase image. In order to remove the artifacts created along the x and y axis due to the SVD, the filtering procedure is implemented by rotating the phase image a fixed number of times. The effective denoised image is obtained by the weighted combination of denoised image evaluated for each rotation. Simulation and experimental studies are conducted to demonstrate the practical applicability of the proposed method.

Target Recognition in SAR Images Using Complex-Valued Network Guided with Sub-Aperture Decomposition

Synthetic aperture radar (SAR) images have special physical scattering characteristics owing to their unique imaging mechanism. Traditional deep learning algorithms usually extract features from real-valued SAR images in a purely data-driven manner, which may ignore some important physical scattering characteristics and sacrifice some useful target information in SAR images. This undoubtedly limits the improvement in performance for SAR target recognition. To take full advantage of the physical information contained in SAR images, a complex-valued network guided with sub-aperture decomposition (CGS-Net) for SAR target recognition is proposed. According to the fact that different targets have different physical scattering characteristics at different angles, the sub-aperture decomposition is used to improve accuracy with a multi-task learning strategy. Specifically, the proposed method includes main and auxiliary tasks, which can improve the performance of the main task by learning and sharing useful information from the auxiliary task. Here, the main task is the target recognition task, and the auxiliary task is the target reconstruction task. In addition, a complex-valued network is used to extract the features from the original complex-valued SAR images, which effectively utilizes the amplitude and phase information in SAR images. The experimental results obtained using the MSTAR dataset illustrate that the proposed CGS-Net achieved an accuracy of 99.59% (without transfer learning or data augmentation) for the ten-classes targets, which is superior to the other popular deep learning methods. Moreover, the proposed method has a lightweight network structure, which is suitable for SAR target recognition tasks because SAR images usually lack a large number of labeled data. Here, the experimental results obtained using the small dataset further demonstrate the excellent performance of the proposed CGS-Net.

Self-supervised learning of hologram reconstruction using physics consistency

Existing applications of deep learning in computational imaging and microscopy mostly depend on supervised learning, requiring large-scale, diverse and labelled training data. The acquisition and preparation of such training image datasets is often laborious and costly, leading to limited generalization to new sample types. Here we report a self-supervised learning model, termed GedankenNet, that eliminates the need for labelled or experimental training data, and demonstrate its effectiveness and superior generalization on hologram reconstruction tasks. Without prior knowledge about the sample types, the self-supervised learning model was trained using a physics-consistency loss and artificial random images synthetically generated without any experiments or resemblance to real-world samples. After its self-supervised training, GedankenNet successfully generalized to experimental holograms of unseen biological samples, reconstructing the phase and amplitude images of different types of object using experimentally acquired holograms. Without access to experimental data, knowledge of real samples or their spatial features, GedankenNet achieved complex-valued image reconstructions consistent with the wave equation in free space. The GedankenNet framework also shows resilience to random, unknown perturbations in the physical forward model, including changes in the hologram distances, pixel size and illumination wavelength. This self-supervised learning of image reconstruction creates new opportunities for solving inverse problems in holography, microscopy and computational imaging.

Dynamic Fourier ptychography with deep spatiotemporal priors

Fourier ptychography (FP) involves the acquisition of several low-resolution intensity images of a sample under varying illumination angles. They are then combined into a high-resolution complex-valued image by solving a phase-retrieval problem. The objective in dynamic FP is to obtain a sequence of high-resolution images of a moving sample. There, the application of standard frame-by-frame reconstruction methods limits the temporal resolution due to the large number of measurements that must be acquired for each frame. In this work instead, we propose a neural-network-based reconstruction framework for dynamic FP. Specifically, each reconstructed image in the sequence is the output of a shared deep convolutional network fed with an input vector that lies on a one-dimensional manifold that encodes time. We then optimize the parameters of the network to fit the acquired measurements. The architecture of the network and the constraints on the input vectors impose a spatiotemporal regularization on the sequence of images. This enables our method to achieve high temporal resolution without compromising the spatial resolution. The proposed framework does not require training data. It also recovers the pupil function of the microscope. Through numerical experiments, we show that our framework paves the way for high-quality ultrafast FP.

Liver PDFF estimation using a multi-decoder water-fat separation neural network with a reduced number of echoes

ObjectiveTo accurately estimate liver PDFF from chemical shift-encoded (CSE) MRI using a deep learning (DL)-based Multi-Decoder Water-Fat separation Network (MDWF-Net), that operates over complex-valued CSE-MR images with only 3 echoes.MethodsThe proposed MDWF-Net and a U-Net model were independently trained using the first 3 echoes of MRI data from 134 subjects, acquired with conventional 6-echoes abdomen protocol at 1.5 T. Resulting models were then evaluated using unseen CSE-MR images obtained from 14 subjects that were acquired with a 3-echoes CSE-MR pulse sequence with a shorter duration compared to the standard protocol. Resulting PDFF maps were qualitatively assessed by two radiologists, and quantitatively assessed at two corresponding liver ROIs, using Bland Altman and regression analysis for mean values, and ANOVA testing for standard deviation (STD) (significance level: .05). A 6-echo graph cut was considered ground truth.ResultsAssessment of radiologists demonstrated that, unlike U-Net, MDWF-Net had a similar quality to the ground truth, despite it considered half of the information. Regarding PDFF mean values at ROIs, MDWF-Net showed a better agreement with ground truth (regression slope = 0.94, R2 = 0.97) than U-Net (regression slope = 0.86, R2 = 0.93). Moreover, ANOVA post hoc analysis of STDs showed a statistical difference between graph cuts and U-Net (p < .05), unlike MDWF-Net (p = .53).ConclusionMDWF-Net showed a liver PDFF accuracy comparable to the reference graph cut method, using only 3 echoes and thus allowing a reduction in the acquisition times.Clinical relevance statementWe have prospectively validated that the use of a multi-decoder convolutional neural network to estimate liver proton density fat fraction allows a significant reduction in MR scan time by reducing the number of echoes required by 50%.Key Points• Novel water-fat separation neural network allows for liver PDFF estimation by using multi-echo MR images with a reduced number of echoes.• Prospective single-center validation demonstrated that echo reduction leads to a significant shortening of the scan time, compared to standard 6-echo acquisition.• Qualitative and quantitative performance of the proposed method showed no significant differences in PDFF estimation with respect to the reference technique.

Efficient complex-valued image reconstruction for compressed sensing MRI using single real-valued convolutional neural network

Efficient complex-valued image reconstruction for compressed sensing MRI using single real-valued convolutional neural network

CryoEM single particle reconstruction with a complex-valued particle stack

Single particle reconstruction (SPR) in cryoEM is an image processing task with an elaborate hierarchy that starts with many very noisy multi-frame images. Efficient representation of the intermediary image structures is critical for keeping the calculations manageable. One such intermediary structure is called a particle stack and contains cut-out images of particles in square boxes of predefined size. The micrograph that is the source of the boxed images is usually corrected for motion between frames prior to particle stack creation. However, the contrast transfer function (CTF) or its Fourier Transform point spread function (PSF) are not considered at this step. Historically, the particle stack was intended for large particles and for a tighter PSF, which is characteristic of lower resolution data. The field now performs analyses of smaller particles and to higher resolution, and these conditions result in a broader PSF that requires larger padding and slower calculations to integrate information for each particle. Consequently, the approach to handling structures such as the particle stack should be reexamined to optimize data processing.Here we propose to use as a source image for the particle stack a complex-valued image, in which CTF correction is implicitly applied as a real component of the image. We can achieve it by applying an initial CTF correction to the entire micrograph first and perform box cutouts as a subsequent step. The final CTF correction that we refine and apply later has a very narrow PSF, and so cutting out particles from micrographs that were approximately corrected for CTF does not require extended buffering, i.e. the boxes during the analysis only have to be large enough to encompass the particle. The Fourier Transform of an exit-wave reconstruction creates an image that has complex values. This is a complex value image considered in real space, opposed to standard SPR data processing where complex numbers appear only in Fourier space. This extension of the micrograph concept provides multiple advantages because the particle box size can be small and calculations crucial for high resolution reconstruction such as Ewald sphere correction, aberration refinement, and particle-specific defocus refinement can be performed on the small box data.

Moving Targets Artifacts Removal in Multiaspect SAR Imagery Based on Logarithm Background Subtraction

Multiaspect SAR has the capability of providing a high-resolution image due to its long synthetic aperture feature. However, a moving target can generate long and complex signatures in a multiaspect SAR image, which may hamper the applications like image interpretation and target detection. In this article, two methods are proposed to remove the moving target signature in a single-channel multiaspect SAR image. The two methods are all based on logarithm background subtraction. The first one is a fast scheme with a cost of reduced resolution. While the second one focuses on preserving the high resolution, it takes more time than the previous one. The first method utilizes the fact of target signal position changes in subaperture image sequence to obtain the static background. The second method combines the detection results to exclude the moving target signal in each complex-valued subaperture image, then obtaining the high resolution of static background by coherent summation. The methods are validated by synthetic and real airborne SAR data.

An application of deep dual convolutional neural network for enhanced medical image denoising.

This work investigates the medical image denoising (MID) application of the dual denoising network (DudeNet) model for chest X-ray (CXR). The DudeNet model comprises four components: a feature extraction block with a sparse mechanism, an enhancement block, a compression block, and a reconstruction block. The developed model uses residual learning to boost denoising performance and batch normalization to accelerate the training process. The name proposed for this model is dual convolutional medical image-enhanced denoising network (DCMIEDNet). The peak signal-to-noise ratio (PSNR) and structure similarity index measurement (SSIM) are used to assess the MID performance for five different additive white Gaussian noise (AWGN) levels of σ = 15, 25, 40, 50, and 60 in CXR images. Presented investigations revealed that the PSNR and SSIM offered by DCMIEDNet are better than several popular state-of-the-art models such as block matching and 3D filtering, denoising convolutional neural network, and feature-guided denoising convolutional neural network. In addition, it is also superior to the recently reported MID models like deep convolutional neural network with residual learning, real-valued medical image denoising network, and complex-valued medical image denoising network. Therefore, based on the presented experiments, it is concluded that applying the DudeNet methodology for DCMIEDNet promises to be quite helpful for physicians.