Complex-valued Images Research Articles

Classification of PolSAR Images by Stacked Random Forests

This paper proposes the use of Stacked Random Forests (SRF) for the classification of Polarimetric Synthetic Aperture Radar images. SRF apply several Random Forest instances in a sequence where each individual uses the class estimate of its predecessor as an additional feature. To this aim, the internal node tests are designed to work not only directly on the complex-valued image data, but also on spatially varying probability distributions and thus allow a seamless integration of RFs within the stacking framework. Experimental results show that the classification performance is consistently improved by the proposed approach, i.e., the achieved accuracy is increased by 4 % and 7 % for one fully- and one dual-polarimetric dataset. This increase only comes at the cost of a linear increased training and prediction time, which is rather limited as the method converges quickly.

A method of solving tilt illumination for multiple distance phase retrieval

Multiple distance phase retrieval is a technique of using a series of intensity patterns to reconstruct a complex-valued image of object. However, tilt illumination originating from the off-axis displacement of incident light significantly impairs its imaging quality. To eliminate this affection, we use cross-correlation calibration to estimate oblique angle of incident light and a Fourier-based strategy to correct tilted illumination effect. Compared to other methods, binary and biological object are both stably reconstructed in simulation and experiment. This work provides a simple but beneficial method to solve the problem of tilt illumination for lens-free multi-distance system.

Constant-Time Calculation of Zernike Moments for Detection with Rotational Invariance

We construct a set of special complex-valued integral images and an algorithm that allows to calculate Zernike moments fast, namely in constant time. The technique is suitable for dense detection procedures, where the image is scanned by a sliding window at multiple scales, and where rotational invariance is required at the level of each window. We assume no preliminary image segmentation. Owing to the proposed integral images and binomial expansions, the extraction of each feature does not depend on the number of pixels in the window and thereby is an O(1) calculation. We analyze algorithmic properties of the proposition, such as: number of needed integral images, complex-conjugacy of integral images, number of operations involved in feature extraction, speed-up possibilities based on lookup tables. We also point out connections between Zernike and orthogonal Fourier-Mellin moments in the context of computations backed with integral images. Finally, we demonstrate three examples of detection tasks of varying difficulty. Detectors are trained on the proposed features by the RealBoost algorithm. When learning, the classifiers get acquainted only with examples of target objects in their upright position or rotated within a limited range. At the testing stage, generalization onto the full 360° angle takes place automatically.

Fast Spatial Resolution Analysis of Quadratic Penalized Least-Squares Image Reconstruction With Separate Real and Imaginary Roughness Penalty: Application to fMRI.

Penalized least-squares iterative image reconstruction algorithms used for spatial resolution-limited imaging, such as functional magnetic resonance imaging (fMRI), commonly use a quadratic roughness penalty to regularize the reconstructed images. When used for complex-valued images, the conventional roughness penalty regularizes the real and imaginary parts equally. However, these imaging methods sometimes benefit from separate penalties for each part. The spatial smoothness from the roughness penalty on the reconstructed image is dictated by the regularization parameter(s). One method to set the parameter to a desired smoothness level is to evaluate the full width at half maximum of the reconstruction method's local impulse response. Previous work has shown that when using the conventional quadratic roughness penalty, one can approximate the local impulse response using an FFT-based calculation. However, that acceleration method cannot be applied directly for separate real and imaginary regularization. This paper proposes a fast and stable calculation for this case that also uses FFT-based calculations to approximate the local impulse responses of the real and imaginary parts. This approach is demonstrated with a quadratic image reconstruction of fMRI data that uses separate roughness penalties for the real and imaginary parts.

Methods and tools for denoising of complex-valued images based on block-matching and high order singular value decomposition

Noise suppression in complex-valued data is an important task for a wide class of applications, in particular concerning the phase retrieval in coherent imaging. The approaches based on BM3D techniques are ones of the most successful in the field. In this paper, we propose and develop a new class of BM3D-style algorithms, which use high order (3D and 4D) singular value decomposition (HOSVD) for transform design in complex domain. This set of the novel algorithms is implemented as a toolbox In Matlab. This development is produced for various types of the complex-domain sparsity: directly in complex domain, real/imaginary and phase/ amplitude parts of complexvalued variables. The group-wise transform design is combined with the different kinds of thresholding including multivariable Wiener filtering. The toolbox includes iterative and non-iterative novel complex-domain algorithms (filters). The efficiency of the developed algorithms is demonstrated on denoising problems with an additive Gaussian complex-valued noise. A special set of the complex-valued test-images was developed with spatially varying correlated phase and amplitudes imitating data typical for optical interferometry and holography. It is shown that for this class of the test-images the developed algorithms demonstrate the state-of-the-art performance.

Single-shot full resolution region-of-interest (ROI) reconstruction in image plane digital holographic microscopy

We describe a numerical processing technique that allows single-shot region-of-interest (ROI) reconstruction in image plane digital holographic microscopy with full pixel resolution. The ROI reconstruction is modelled as an optimization problem where the cost function to be minimized consists of an L2-norm squared data fitting term and a modified Huber penalty term that are minimized alternately in an adaptive fashion. The technique can provide full pixel resolution complex-valued images of the selected ROI which is not possible to achieve with the commonly used Fourier transform method. The technique can facilitate holographic reconstruction of individual cells of interest from a large field-of-view digital holographic microscopy data. The complementary phase information in addition to the usual absorption information already available in the form of bright field microscopy can make the methodology attractive to the biomedical user community.

Brain functional BOLD perturbation modelling for forward fMRI and inverse mapping.

PurposeTo computationally separate dynamic brain functional BOLD responses from static background in a brain functional activity for forward fMRI signal analysis and inverse mapping.MethodsA brain functional activity is represented in terms of magnetic source by a perturbation model: χ = χ0 +δχ, with δχ for BOLD magnetic perturbations and χ0 for background. A brain fMRI experiment produces a timeseries of complex-valued images (T2* images), whereby we extract the BOLD phase signals (denoted by δP) by a complex division. By solving an inverse problem, we reconstruct the BOLD δχ dataset from the δP dataset, and the brain χ distribution from a (unwrapped) T2* phase image. Given a 4D dataset of task BOLD fMRI, we implement brain functional mapping by temporal correlation analysis.ResultsThrough a high-field (7T) and high-resolution (0.5mm in plane) task fMRI experiment, we demonstrated in detail the BOLD perturbation model for fMRI phase signal separation (P + δP) and reconstructing intrinsic brain magnetic source (χ and δχ). We also provided to a low-field (3T) and low-resolution (2mm) task fMRI experiment in support of single-subject fMRI study. Our experiments show that the δχ-depicted functional map reveals bidirectional BOLD χ perturbations during the task performance.ConclusionsThe BOLD perturbation model allows us to separate fMRI phase signal (by complex division) and to perform inverse mapping for pure BOLD δχ reconstruction for intrinsic functional χ mapping. The full brain χ reconstruction (from unwrapped fMRI phase) provides a new brain tissue image that allows to scrutinize the brain tissue idiosyncrasy for the pure BOLD δχ response through an automatic function/structure co-localization.

Comparative study of description algorithms for complex-valued gradient fields of digital images using linear dimensionality reduction methods

The paper presents an analysis of various approaches to constructing descriptions for the gradient fields of digital images. The analyzed approaches are based on the well-known methods for data dimensionality reduction, such as Principal (PCA) and Independent (ICA) Component Analysis, Linear Discriminant Analysis (LDA). We apply these methods not to the original image, represented as a two-dimensional field of brightness (a halftone image), but to its secondary representation in the form of a two-dimensional gradient field, that is, a complex-valued image. In this case, approaches based on using both the entire gradient field and only its phase component are considered. In addition, two independent ways of forming the final description of the original object are considered: using expansion coefficients of the gradient field in a derived basis and using an original authors' design that is called model-oriented descriptors. With the latter, the number of real coefficients used in the description of the original object can be halved. The studies are conducted via solving a face recognition problem. The effectiveness of the analyzed methods is demonstrated by applying them to images from Extended Yale Face Database B. The comparison is made using a nearest neighbor's classifier.

Total Variation--Based Phase Retrieval for Poisson Noise Removal

Phase retrieval plays an important role in vast industrial and scientific applications. We consider a noisy phase retrieval problem in which the magnitudes of the Fourier transform (or a general linear transform) of an underling object are corrupted by Poisson noise, since any optical sensors detect photons, and the number of detected photons follows the Poisson distribution. We propose a variational model for phase retrieval based on a total variation regularization as an image prior and maximum a posteriori estimation of a Poisson noise model, which is referred to as “TV-PoiPR”. We also propose an efficient numerical algorithm based on an alternating direction method of multipliers and establish its convergence. Extensive experiments for coded diffraction, holographic, and ptychographic patterns are conducted using both real- and complex-valued images to demonstrate the effectiveness of our proposed methods.

Performance evaluation of Bragg coherent diffraction imaging

In this study, we present a numerical framework for modeling three-dimensional (3D) diffraction data in Bragg coherent diffraction imaging (Bragg CDI) experiments and evaluating the quality of obtained 3D complex-valued real-space images recovered by reconstruction algorithms under controlled conditions. The approach is used to systematically explore the performance and the detection limit of this phase-retrieval-based microscopy tool. The numerical investigation suggests that the superb performance of Bragg CDI is achieved with an oversampling ratio above 30 and a detection dynamic range above 6 orders. The observed performance degradation subject to the data binning processes is also studied. This numerical tool can be used to optimize experimental parameters and has the potential to significantly improve the throughput of Bragg CDI method.

Challenges in MR-only seed localization for postimplant dosimetry in permanent prostate brachytherapy.

An MR-only postimplant dosimetry workflow for low dose rate (LDR) brachytherapy could reduce patient burden, improve accuracy, and improve cost efficiency. However, localization of brachytherapy seeds on MRI scans remains a major challenge for this type of workflow. In this study, we propose and validate an MR-only seed localization method and identify remaining challenges. The localization method was based on template matching of simulations of complex-valued imaging artifacts around metal brachytherapy seeds. The method was applied to MRI scans of 25 prostate cancer patients who underwent LDR brachytherapy and for whom postimplant dosimetry was performed after 4 weeks. The seed locations found with the MR-only method were validated against the seed locations found on CT. The circumstances in which detection errors were made were classified to gain an insight in the nature of the errors. A total of 1490 of 1557 (96%) seeds were correctly detected, while 67 false-positive errors were made. The correctly detected seed locations had a high spatial accuracy with an average error of 0.8 mm compared with CT. A majority of the false positives occurred near other seeds. Most false negatives were found in either stranded configurations without spacers or near other seeds. The low detection error rate and high localization accuracy obtained by the complex-valued template matching approach are promising for future clinical application of MR-only dosimetry. The most important remaining challenge is robustness with regard to configurations of multiple seeds in close vicinity, such as in strands of seeds without spacers. This issue could potentially be resolved by simulating specific configurations of multiple seeds or by constraining the treatment planning to avoid these configurations, which could make the proposed method competitive with CT-based seed localization.

High-TV Based CS Framework Using MAP Estimator for SAR Image Enhancement

Synthetic aperture radar (SAR) images have two main problems: Degradation by speckle that causes low-contrast images and misinterpretation, and the large amount of data that makes the computation time an important issue. In addition to denoising, it is necessary to recover the missing data due to errors in the onboard SAR equipment, downlink equipment, and ground data registration. In this paper, we propose a method using high-order total variation (High-TV) denoising in compressive sensing (CS) framework, based on maximum a posteriori (MAP) estimation to simultaneously denoise and recover the large-size, complex-valued SAR images. Experiments on RADARSAT-1 raw data showed that the proposed method, called MAP High-TV, can suppress the speckle effectively without exhibiting a staircase effect on the images, and perfectly recovers the missed data. The performance comparison among the proposed method, MAP-MIDAL (the pioneer CS-based method), and three state of the art filters (NSM, POTDF and FANS), explores the capability of MAP High-TV for both denoising and recovering the complex-valued SAR images.

3D imaging of optically cleared tissue using a simplified CLARITY method and on-chip microscopy.

High-throughput sectioning and optical imaging of tissue samples using traditional immunohistochemical techniques can be costly and inaccessible in resource-limited areas. We demonstrate three-dimensional (3D) imaging and phenotyping in optically transparent tissue using lens-free holographic on-chip microscopy as a low-cost, simple, and high-throughput alternative to conventional approaches. The tissue sample is passively cleared using a simplified CLARITY method and stained using 3,3'-diaminobenzidine to target cells of interest, enabling bright-field optical imaging and 3D sectioning of thick samples. The lens-free computational microscope uses pixel super-resolution and multi-height phase recovery algorithms to digitally refocus throughout the cleared tissue and obtain a 3D stack of complex-valued images of the sample, containing both phase and amplitude information. We optimized the tissue-clearing and imaging system by finding the optimal illumination wavelength, tissue thickness, sample preparation parameters, and the number of heights of the lens-free image acquisition and implemented a sparsity-based denoising algorithm to maximize the imaging volume and minimize the amount of the acquired data while also preserving the contrast-to-noise ratio of the reconstructed images. As a proof of concept, we achieved 3D imaging of neurons in a 200-μm-thick cleared mouse brain tissue over a wide field of view of 20.5 mm2. The lens-free microscope also achieved more than an order-of-magnitude reduction in raw data compared to a conventional scanning optical microscope imaging the same sample volume. Being low cost, simple, high-throughput, and data-efficient, we believe that this CLARITY-enabled computational tissue imaging technique could find numerous applications in biomedical diagnosis and research in low-resource settings.

Regularized non-convex image reconstruction in digital holographic microscopy.

Inverse problem approaches for image reconstruction can improve resolution recovery over spatial filtering methods while reducing interference artifacts in digital off-axis holography. Prior works implemented explicit regularization operators in the image space and were only able to match intensity measurements approximatively. As a consequence, convergence to a strictly compatible solution was not possible. In this paper, we replace the non-convex image reconstruction problem for a sequence of surrogate convex problems. An iterative numerical solver is designed using a simple projection operator in the data domain and a Nesterov acceleration of the simultaneous Kaczmarz method. For regularization, the complex-valued object wavefield image is represented in the multiresolution CDF 9/7 wavelet domain and an energy-weighted preconditioning promotes minimum-norm solutions. Experiments demonstrate improved resolution recovery and reduced spurious artifacts in reconstructed images. Furthermore, the method is resilient to additive Gaussian noise and subsampling of intensity measurements.

Compressed sensing application in interferometric synthetic aperture radar

A novel interferometric synthetic aperture radar (InSAR) signal processing method based on compressed sensing (CS) theory is investigated in this paper. InSAR image formation provides the scene reflectivity estimation along azimuth and range coordinates with the height information. While surveying the height information of the illuminated scene, the data volume enlarges. CS theory allows sparse sampling during the data acquisition, which can reduce the data volume and release the pressure on the record devices. InSAR system which configures two antennas to cancel the common backscatter random phase in each resolution element implies the sparse nature of the complex-valued InSAR image. The complex-valued image after conjugate multiplication that only a phase term proportional to the differential path delay is left becomes sparse in the transform domain. Sparse sampling such as M-sequence can be implemented during the data acquisition. CS theory can be introduced to the processing due to the sparsity and a link between raw data and interferometric complex-valued image can be built. By solving the CS inverse problem, the magnitude image and interferometric phase are generated at the same time. Results on both the simulated data and real data are presented. In comparison with the conventional SAR interferometry processing results, CS-based method shows the ability to keep the imaging quality with less data acquisition.

Use of Kramers-Kronig relation in phase retrieval calculation in X-ray spectro-ptychography.

Coherent diffraction imaging (CDI) is a method for reconstructing the complex-valued image of an object from diffraction intensities by using iterative phasing methods. X-ray ptychography is a scanning type of CDI using X-rays, allowing us to visualize the complex transmission function of an extended specimen. We here propose the use of the Kramers-Kronig relation (KKR) as an additional constraint in phase retrieval algorithms for multiple-energy X-ray ptychography using the absorption edge of a specific element. A numerical simulation showed that the speed of convergence was increased by using the improved algorithm with the KKR. We successfully demonstrated its usefulness in a proof-of-principle experiment at SPring-8. The present algorithm is particularly useful for imaging X-ray absorption fine structures of a specific element buried within thick samples by hard X-ray spectro-ptychography.

Nonlinear image encryption system using the Gyrator transform and truncation operations

A new nonlinear system for image encryption using the Gyrator transform (GT) and the truncation operations is proposed in this work. The original image is encoded in phase at the beginning of the encryption process. The encryption-decryption system is based on the double random phase encoding (DRPE) in the Gyrator domain (GD). The rotation angle of the Gyrator transform is a new key that increases the security of the encryption system. The amplitude and phase truncation operations are nonlinear and no unitary, these truncation operations allow to select the information of amplitude or phase from a complex-valued image. We apply the truncation operations in the image encryption-decryption system in order to generate two new keys, convert the system in nonlinear and increase the security of the system. To retrieve the original image without error (noise-free) in the decryption system, it is needed all the correct security keys: the two RPMs, the rotation angle of the GT and the two key generated by the amplitude and phase truncation operations. The feasibility of this nonlinear encryption-decryption system is verified and analyzed by numerical simulations.

Video stabilization in atmosphere turbulent conditions based on the Laplacian-Riesz pyramid.

Video stabilization in atmosphere turbulent conditions is aimed at removing spatiotemporally varying distortions from video recordings. Conventional shaky video stabilization approaches do not perform effectively under turbulent circumstances due to the erratic motion common to those conditions. Using complex-valued image pyramids, we propose a method to mitigate this erratic motion in videos. First, each frame of a video is decomposed into different spatial frequencies using the Laplacian pyramid. Second, a Riesz transform is adopted to extract the local amplitude and the local phase of each sub-band. Next, low-pass filters are designed to attenuate the local amplitude and phase variations to remove turbulence-induced distortions. Experimental results show that the proposed approach is efficient and provides stabilizing video in atmosphere turbulent conditions.

An Augmented Lagrangian Method for Complex-Valued Compressed SAR Imaging

In this paper, we present a solution to the complex synthetic aperture radar (SAR) imaging problem within a constrained optimization formulation where the objective function includes a combination of the $\ell _1$ -norm and the total variation of the magnitude of the complex valued reflectivity field. The technique we present relies on recent advances in the solution of optimization problems, based on Augmented Lagrangian Methods, and in particular on the Alternating Direction Method of Multipliers (ADMM). We rigorously derive the proximal mapping operators, associated with a linear transform of the magnitude of the reflectivity vector and magnitude-total-variation cost functions, for complex-valued SAR images, and thus enable the use of ADMM techniques to obtain computationally efficient solutions for radar imaging. We study the proposed techniques with multiple features (sparse and piecewise-constant in magnitude) based on a weighted sum of the 1-norm and magnitude-total-variation. We derive a fast implementation of the algorithm using only two transforms per iteration for problems admitting unitary transforms as forward models. Experimental results on real data from TerraSAR-X and SARPER —airborne SAR system developed by ASELSAN—demonstrate the effectiveness of the proposed approach.

A New Maximum-Likelihood Change Estimator for Two-Pass SAR Coherent Change Detection

In past research, two-pass repeat-geometry synthetic aperture radar (SAR) coherent change detection (CCD) predominantly utilized the sample degree of coherence as a measure of the temporal change occurring between two complex-valued image collects. Previous coherence-based CCD approaches tend to show temporal change when there is none in areas of the image that have a low clutter-to-noise power ratio. Instead of employing the sample coherence magnitude as a change metric, in this paper, we derive a new maximum-likelihood (ML) temporal change estimate—the complex reflectance change detection (CRCD) metric to be used for SAR coherent temporal change detection. The new CRCD estimator is a surprisingly simple expression, easy to implement, and optimal in the ML sense. This new estimate produces improved results in the coherent pair collects that we have tested.