CohereNet: A Deep Learning Architecture for Ultrasound Spatial Correlation Estimation and Coherence-Based Beamforming

Comparative Assessment of Real-Time and Offline Short-Lag Spatial Coherence Imaging of Ultrasound Breast Masses

OBJECTIVE

To perform the first known investigation of differences between real-time and offline B-mode and short-lag spatial coherence (SLSC) images when evaluating fluid or solid content in 60 hypoechoic breast masses.

METHODS

Real-time and retrospective (i.e., offline) reader studies were conducted with three board-certified breast radiologists, followed by objective, reader-independent discrimination using generalized contrast-to-noise ratio (gCNR).

RESULTS

The content of 12 fluid, solid and mixed (i.e., containing fluid and solid components) masses were uncertain when reading real-time B-mode images. With real-time and offline SLSC images, 15 and 5, respectively, aggregated solid and mixed masses (and no fluid masses) were uncertain. Therefore, with real-time SLSC imaging, uncertainty about solid masses increased relative to offline SLSC imaging, while uncertainty about fluid masses decreased relative to real-time B-mode imaging. When assessing real-time SLSC reader results, 100% (11/11) of solid masses with uncertain content were correctly classified with a gCNR<0.73 threshold applied to real-time SLSC images. The areas under receiver operator characteristic curves characterizing gCNR as an objective metric to discriminate complicated cysts from solid masses were 0.963 and 0.998 with real-time and offline SLSC images, respectively, which are both considered excellent for diagnostic testing.

CONCLUSION

Results are promising to support real-time SLSC imaging and gCNR application to real-time SLSC images to enhance sensitivity and specificity, reduce reader variability, and mitigate uncertainty about fluid or solid content, particularly when distinguishing complicated cysts (which are benign) from hypoechoic solid masses (which could be cancerous).

Overfit detection method for deep neural networks trained to beamform ultrasound images

Deep neural networks (DNNs) have remarkable potential to reconstruct ultrasound images. However, this promise can suffer from overfitting to training data, which is typically detected via loss function monitoring during an otherwise time-consuming training process or via access to new sources of test data. We present a method to detect overfitting with associated evaluation approaches that only require knowledge of a network architecture and associated trained weights. Three types of artificial DNN inputs (i.e., zeros, ones, and Gaussian noise), unseen during DNN training, were input to three DNNs designed for ultrasound image formation, trained on multi-site data, and submitted to the Challenge on Ultrasound Beamforming with Deep Learning (CUBDL). Overfitting was detected using these artificial DNN inputs. Qualitative and quantitative comparisons of DNN-created images to ground truth images immediately revealed signs of overfitting (e.g., zeros input produced mean output values ≥0.08, ones input produced mean output values ≤0.07, with corresponding image-to-image normalized correlations ≤0.8). The proposed approach is promising to detect overfitting without requiring lengthy network retraining or the curation of additional test data. Potential applications include sanity checks during federated learning, as well as optimization, security, public policy, regulation creation, and benchmarking.

Hardware-Independent Deep Signal Processing: A Feasibility Study in Echocardiography

Deep learning (DL) models have emerged as alternative methods to conventional ultrasound (US) signal processing, offering the potential to mimic signal processing chains, reduce inference time, and enable the portability of processing chains across hardware. This article proposes a DL model that replicates the fine-tuned BMode signal processing chain of a high-end US system and explores the potential of using it with a different probe and a lower end system. A deep neural network (DNN) was trained in a supervised manner to map raw beamformed in-phase and quadrature component data into processed images. The dataset consisted of 30 000 cardiac image frames acquired using the GE HealthCare Vivid E95 system with the 4Vc-D matrix array probe. The signal processing chain includes depth-dependent bandpass filtering, elevation compounding, frequency compounding, and image compression and filtering. The results indicate that a lightweight DL model can accurately replicate the signal processing chain of a commercial scanner for a given application. Evaluation on a 15-patient test dataset of about 3000 image frames gave a structural similarity index measure (SSIM) of 98.56 ± 0.49. Applying the DL model to data from another probe showed equivalent or improved image quality. This indicates that a single DL model may be used for a set of probes on a given system that targets the same application, which could be a cost-effective tuning and implementation strategy for vendors. Furthermore, the DL model enhanced image quality on a Verasonics dataset, suggesting the potential to port features from high-end US systems to lower end counterparts.

Deep coherence learning: An unsupervised deep beamformer for high quality single plane wave imaging in medical ultrasound

Plane wave imaging (PWI) in medical ultrasound is becoming an important reconstruction method with high frame rates and new clinical applications. Recently, single PWI based on deep learning (DL) has been studied to overcome lowered frame rates of traditional PWI with multiple PW transmissions. However, due to the lack of appropriate ground truth images, DL-based PWI still remains challenging for performance improvements. To address this issue, in this paper, we propose a new unsupervised learning approach, i.e., deep coherence learning (DCL)-based DL beamformer (DL-DCL), for high-quality single PWI. In DL-DCL, the DL network is trained to predict highly correlated signals with a unique loss function from a set of PW data, and the trained DL model encourages high-quality PWI from low-quality single PW data. In addition, the DL-DCL framework based on complex baseband signals enables a universal beamformer. To assess the performance of DL-DCL, simulation, phantom and in vivo studies were conducted with public datasets, and it was compared with traditional beamformers (i.e., DAS with 75-PWs and DMAS with 1-PW) and other DL-based methods (i.e., supervised learning approach with 1-PW and generative adversarial network (GAN) with 1-PW). From the experiments, the proposed DL-DCL showed comparable results with DMAS with 1-PW and DAS with 75-PWs in spatial resolution, and it outperformed all comparison methods in contrast resolution. These results demonstrated that the proposed unsupervised learning approach can address the inherent limitations of traditional PWIs based on DL, and it also showed great potential in clinical settings with minimal artifacts.

Spatial Coherence Approaches to Distinguish Suspicious Mass Contents in Fundamental and Harmonic Breast Ultrasound Images

When compared to fundamental B-mode imaging, coherence-based beamforming, and harmonic imaging are independently known to reduce acoustic clutter, distinguish solid from fluid content in indeterminate breast masses, and thereby reduce unnecessary biopsies during a breast cancer diagnosis. However, a systematic investigation of independent and combined coherence beamforming and harmonic imaging approaches is necessary for the clinical deployment of the most optimal approach. Therefore, we compare the performance of fundamental and harmonic images created with short-lag spatial coherence (SLSC), M-weighted SLSC (M-SLSC), SLSC combined with robust principal component analysis with no M-weighting (r-SLSC), and r-SLSC with M-weighting (R-SLSC), relative to traditional fundamental and harmonic B-mode images, when distinguishing solid from fluid breast masses. Raw channel data acquired from 40 total breast masses (28 solid, 7 fluid, 5 mixed) were beamformed and analyzed. The contrast of fluid masses was better with fundamental rather than harmonic coherence imaging, due to the lower spatial coherence within the fluid masses in the fundamental coherence images. Relative to SLSC imaging, M-SLSC, r-SLSC, and R-SLSC imaging provided similar contrast across multiple masses (with the exception of clinically challenging complicated cysts) and minimized the range of generalized contrast-to-noise ratios (gCNRs) of fluid masses, yet required additional computational resources. Among the eight coherence imaging modes compared, fundamental SLSC imaging best identified fluid versus solid breast mass contents, outperforming fundamental and harmonic B-mode imaging. With fundamental SLSC images, the specificity and sensitivity to identify fluid masses using the reader-independent metrics of contrast difference, mean lag one coherence (LOC), and gCNR were 0.86 and 1, 1 and 0.89, and 1 and 1, respectively. Results demonstrate that fundamental SLSC imaging and gCNR (or LOC if no coherence image or background region of interest is introduced) have the greatest potential to impact clinical decisions and improve the diagnostic certainty of breast mass contents. These observations are additionally anticipated to extend to masses in other organs.

A Single-Shot Harmonic Imaging Approach Utilizing Deep Learning for Medical Ultrasound

Tissue harmonic imaging (THI) is an invaluable tool in clinical ultrasound due to its enhanced contrast resolution and reduced reverberation clutter in comparison with fundamental mode imaging. However, harmonic content separation based on high-pass filtering suffers from potential contrast degradation or lower axial resolution due to spectral leakage, whereas nonlinear multipulse harmonic imaging schemes, such as amplitude modulation and pulse inversion, suffer from a reduced frame rate and comparatively higher motion artifacts due to the necessity of at least two pulse echo acquisitions. To address this problem, we propose a deep-learning-based single-shot harmonic imaging technique capable of generating comparable image quality to pulse amplitude modulation methods, yet at a higher frame rate and with fewer motion artifacts. Specifically, an asymmetric convolutional encoder-decoder structure is designed to estimate the combination of the echoes resulting from the half-amplitude transmissions using the echo produced from the full amplitude transmission as input. The echoes were acquired with the checkerboard amplitude modulation technique for training. The model was evaluated across various targets and samples to illustrate generalizability as well as the possibility and impact of transfer learning. Furthermore, for possible interpretability of the network, we investigate if the latent space of the encoder holds information on the nonlinearity parameter of the medium. We demonstrate the ability of the proposed approach to generate harmonic images with a single firing that are comparable to those from a multipulse acquisition.

Ultrasound Signal Processing: From Models to Deep Learning

Medical ultrasound imaging relies heavily on high-quality signal processing to provide reliable and interpretable image reconstructions. Conventionally, reconstruction algorithms have been derived from physical principles. These algorithms rely on assumptions and approximations of the underlying measurement model, limiting image quality in settings where these assumptions break down. Conversely, more sophisticated solutions based on statistical modeling or careful parameter tuning or derived from increased model complexity can be sensitive to different environments. Recently, deep learning-based methods, which are optimized in a data-driven fashion, have gained popularity. These model-agnostic techniques often rely on generic model structures and require vast training data to converge to a robust solution. A relatively new paradigm combines the power of the two: leveraging data-driven deep learning and exploiting domain knowledge. These model-based solutions yield high robustness and require fewer parameters and training data than conventional neural networks. In this work we provide an overview of these techniques from the recent literature and discuss a wide variety of ultrasound applications. We aim to inspire the reader to perform further research in this area and to address the opportunities within the field of ultrasound signal processing. We conclude with a future perspective on model-based deep learning techniques for medical ultrasound.

Coherence Metrics for Reader-Independent Differentiation of Cystic From Solid Breast Masses in Ultrasound Images

Traditional breast ultrasound imaging is a low-cost, real-time and portable method to assist with breast cancer screening and diagnosis, with particular benefits for patients with dense breast tissue. We previously demonstrated that incorporating coherence-based beamforming additionally improves the distinction of fluid-filled from solid breast masses, based on qualitative image interpretation by board-certified radiologists. However, variable sensitivity (range: 0.71-1.00 when detecting fluid-filled masses) was achieved by the individual radiologist readers. Therefore, we propose two objective coherence metrics, lag-one coherence (LOC) and coherence length (CL), to quantitatively determine the content of breast masses without requiring reader assessment. Data acquired from 31 breast masses were analyzed. Ideal separation (i.e., 1.00 sensitivity and specificity) was achieved between fluid-filled and solid breast masses based on the mean or median LOC value within each mass. When separated based on mean and median CL values, the sensitivity/specificity decreased to 1.00/0.95 and 0.92/0.89, respectively. The greatest sensitivity and specificity were achieved in dense, rather than non-dense, breast tissue. These results support the introduction of an objective, reader-independent method for automated diagnoses of cystic breast masses.

Deep-fUS: A Deep Learning Platform for Functional Ultrasound Imaging of the Brain Using Sparse Data

Functional ultrasound (fUS) is a rapidly emerging modality that enables whole-brain imaging of neural activity in awake and mobile rodents. To achieve sufficient blood flow sensitivity in the brain microvasculature, fUS relies on long ultrasound data acquisitions at high frame rates, posing high demands on the sampling and processing hardware. Here we develop an image reconstruction method based on deep learning that significantly reduces the amount of data necessary while retaining imaging performance. We trained convolutional neural networks to learn the power Doppler reconstruction function from sparse sequences of ultrasound data with compression factors of up to 95%. High-quality images from in vivo acquisitions in rats were used for training and performance evaluation. We demonstrate that time series of power Doppler images can be reconstructed with sufficient accuracy to detect the small changes in cerebral blood volume (~10%) characteristic of task-evoked cortical activation, even though the network was not formally trained to reconstruct such image series. The proposed platform may facilitate the development of this neuroimaging modality in any setting where dedicated hardware is not available or in clinical scanners.

Requirements and Hardware Limitations of High-Frame-Rate 3-D Ultrasound Imaging Systems

The spread of high frame rate and 3-D imaging techniques has raised pressing requirements for ultrasound systems. In particular, the processing power and data transfer rate requirements may be so demanding to hinder the real-time (RT) implementation of such techniques. This paper first analyzes the general requirements involved in RT ultrasound systems. Then, it identifies the main bottlenecks in the receiving section of a specific RT scanner, the ULA-OP 256, which is one of the most powerful available open scanners and may therefore be assumed as a reference. This case study has evidenced that the “star” topology, used to digitally interconnect the system’s boards, may easily saturate the data transfer bandwidth, thus impacting the achievable frame/volume rates in RT. The architecture of the digital scanner was exploited to tackle the bottlenecks by enabling a new “ring“ communication topology. Experimental 2-D and 3-D high-frame-rate imaging tests were conducted to evaluate the frame rates achievable with both interconnection modalities. It is shown that the ring topology enables up to 4400 frames/s and 510 volumes/s, with mean increments of +230% (up to +620%) compared to the star topology.

Spatial Coherence in Medical Ultrasound: A Review

Traditional pulse-echo ultrasound imaging heavily relies on the discernment of signals based on their relative magnitudes but is limited in its ability to mitigate sources of image degradation, the most prevalent of which is acoustic clutter. Advances in computing power and data storage have made it possible for echo data to be alternatively analyzed through the lens of spatial coherence, a measure of the similarity of these signals received across an array. Spatial coherence is not currently explicitly calculated on diagnostic ultrasound scanners but a large number of studies indicate that it can be employed to describe image quality, to adaptively select system parameters and to improve imaging and target detection. With the additional insights provided by spatial coherence, it is poised to play a significant role in the future of medical ultrasound. This review details the theory of spatial coherence in pulse-echo ultrasound and key advances made over the last few decades since its introduction in the 1980s.

Gaussian process regression for ultrasound scanline interpolation

Purpose: In ultrasound imaging, interpolation is a key step in converting scanline data to brightness-mode (B-mode) images. Conventional methods, such as bilinear interpolation, do not fully capture the spatial dependence between data points, which leads to deviations from the underlying probability distribution at the interpolation points. Approach: We propose Gaussian process ( GP ) regression as an improved method for ultrasound scanline interpolation. Using ultrasound scanlines acquired from two different ultrasound scanners during in vivo trials, we compare the scanline conversion accuracy of three standard interpolation methods with that of GP regression, measuring the peak signal-to-noise ratio (PSNR) and mean absolute error (MAE) for each method. Results: The PSNR and MAE scores show that GP regression leads to more accurate scanline conversion compared to the nearest neighbor, bilinear, and cubic spline interpolation methods, for both datasets. Furthermore, limiting the interpolation window size of GP regression to 15 reduces computation time with minimal to no reduction in PSNR. Conclusions: GP regression quantitatively leads to more accurate scanline conversion and provides uncertainty estimates at each of the interpolation points. Our windowing method reduces the computational cost of using GP regression for scanline conversion.

A Review of Deep Learning Applications in Lung Ultrasound Imaging of COVID-19 Patients

The massive and continuous spread of COVID-19 has motivated researchers around the world to intensely explore, understand, and develop new techniques for diagnosis and treatment. Although lung ultrasound imaging is a less established approach when compared to other medical imaging modalities such as X-ray and CT, multiple studies have demonstrated its promise to diagnose COVID-19 patients. At the same time, many deep learning models have been built to improve the diagnostic efficiency of medical imaging. The integration of these initially parallel efforts has led multiple researchers to report deep learning applications in medical imaging of COVID-19 patients, most of which demonstrate the outstanding potential of deep learning to aid in the diagnosis of COVID-19. This invited review is focused on deep learning applications in lung ultrasound imaging of COVID-19 and provides a comprehensive overview of ultrasound systems utilized for data acquisition, associated datasets, deep learning models, and comparative performance.

An Upgraded Siamese Neural Network for Motion Tracking in Ultrasound Image Sequences

Deep learning is heavily being borrowed to solve problems in medical imaging applications, and Siamese neural networks are the front runners of motion tracking. In this article, we propose to upgrade one such Siamese architecture-based neural network for robust and accurate landmark tracking in ultrasound images to improve the quality of image-guided radiation therapy. Although several researchers have improved the Siamese architecture-based networks with sophisticated detection modules and by incorporating transfer learning, the inherent assumptions of the constant position model and the missing motion model remain unaddressed limitations. In our proposed model, we overcome these limitations by introducing two modules into the original architecture. We employ a reference template update to resolve the constant position model and a linear Kalman filter (LKF) to address the missing motion model. Moreover, we demonstrate that the proposed architecture provides promising results without transfer learning. The proposed model was submitted to an open challenge organized by MICCAI and was evaluated exhaustively on the Liver US Tracking (CLUST) 2D dataset. Experimental results proved that the proposed model tracked the landmarks with promising accuracy. Furthermore, we also induced synthetic occlusions to perform a qualitative analysis of the proposed approach. The evaluations were performed on the training set of the CLUST 2D dataset. The proposed method outperformed the original Siamese architecture by a significant margin.

Deep Learning for Ultrasound Image Formation: CUBDL Evaluation Framework and Open Datasets

Deep learning for ultrasound image formation is rapidly garnering research support and attention, quickly rising as the latest frontier in ultrasound image formation, with much promise to balance both image quality and display speed. Despite this promise, one challenge with identifying optimal solutions is the absence of unified evaluation methods and datasets that are not specific to a single research group. This article introduces the largest known international database of ultrasound channel data and describes the associated evaluation methods that were initially developed for the challenge on ultrasound beamforming with deep learning (CUBDL), which was offered as a component of the 2020 IEEE International Ultrasonics Symposium. We summarize the challenge results and present qualitative and quantitative assessments using both the initially closed CUBDL evaluation test dataset (which was crowd-sourced from multiple groups around the world) and additional in vivo breast ultrasound data contributed after the challenge was completed. As an example quantitative assessment, single plane wave images from the CUBDL Task 1 dataset produced a mean generalized contrast-to-noise ratio (gCNR) of 0.67 and a mean lateral resolution of 0.42 mm when formed with delay-and-sum beamforming, compared with a mean gCNR as high as 0.81 and a mean lateral resolution as low as 0.32 mm when formed with networks submitted by the challenge winners. We also describe contributed CUBDL data that may be used for training of future networks. The compiled database includes a total of 576 image acquisition sequences. We additionally introduce a neural-network-based global sound speed estimator implementation that was necessary to fairly evaluate the results obtained with this international database. The integration of CUBDL evaluation methods, evaluation code, network weights from the challenge winners, and all datasets described herein are publicly available (visit https://cubdl.jhu.edu for details).

ApodNet: Learning for High Frame Rate Synthetic Transmit Aperture Ultrasound Imaging

Two-way dynamic focusing in synthetic transmit aperture (STA) beamforming can benefit high-quality ultrasound imaging with higher lateral spatial resolution and contrast resolution. However, STA requires the complete dataset for beamforming in a relatively low frame rate and transmit power. This paper proposes a deep-learning architecture to achieve high frame rate STA imaging with two-way dynamic focusing. The network consists of an encoder and a joint decoder. The encoder trains a set of binary weights as the apodizations of the high-frame-rate plane wave transmissions. In this respect, we term our network ApodNet. The decoder can recover the complete dataset from the acquired channel data to achieve dynamic transmit focusing. We evaluate the proposed method by simulations at different levels of noise and in-vivo experiments on the human biceps brachii and common carotid artery. The experimental results demonstrate that ApodNet provides a promising strategy for high frame rate STA imaging, obtaining comparable lateral resolution and contrast resolution with four-times higher frame rate than conventional STA imaging in the in-vivo experiments. Particularly, ApodNet improves contrast resolution of the hypoechoic targets with much shorter computational time when compared with other high-frame-rate methods in both simulations and in-vivo experiments.

Combined Ultrasound and Photoacoustic Image Guidance of Spinal Pedicle Cannulation Demonstrated With Intact ex vivo Specimens

OBJECTIVE

Spinal fusion surgeries require accurate placement of pedicle screws in anatomic corridors without breaching bone boundaries. We are developing a combined ultrasound and photoacoustic image guidance system to avoid pedicle screw misplacement and accidental bone breaches, which can lead to nerve damage.

METHODS

Pedicle cannulation was performed on a human cadaver, with co-registered photoacoustic and ultrasound images acquired at various time points during the procedure. Bony landmarks obtained from coherence-based ultrasound images of lumbar vertebrae were registered to post-operative CT images. Registration methods were additionally tested on an ex vivo caprine vertebra.

RESULTS

Locally weighted short-lag spatial coherence (LW-SLSC) ultrasound imaging enhanced the visualization of bony structures with generalized contrast-to-noise ratios (gCNRs) of 0.99 and 0.98-1.00 in the caprine and human vertebrae, respectively. Short-lag spatial coherence (SLSC) and amplitude-based delay-and-sum (DAS) ultrasound imaging generally produced lower gCNRs of 0.98 and 0.84, respectively, in the caprine vertebra and 0.84-0.93 and 0.34-0.99, respectively, in the human vertebrae. The mean ± standard deviation of the area of -6 dB contours created from DAS photoacoustic images acquired with an optical fiber inserted in prepared pedicle holes (i.e., fiber surrounded by cancellous bone) and holes created after intentional breaches (i.e., fiber exposed to cortical bone) was 10.06 ±5.22 mm ² and 2.47 ±0.96 mm ², respectively (p 0.01).

CONCLUSIONS

Coherence-based LW-SLSC and SLSC beamforming improved visualization of bony anatomical landmarks for ultrasound-to-CT registration, while amplitude-based DAS beamforming successfully distinguished photoacoustic signals within the pedicle from less desirable signals characteristic of impending bone breaches.

SIGNIFICANCE

These results are promising to improve visual registration of ultrasound and photoacoustic images with CT images, as well as to assist surgeons with identifying and avoiding impending bone breaches during pedicle cannulation in spinal fusion surgeries.

Evaluating Input Domain and Model Selection for Deep Network Ultrasound Beamforming

Improving ultrasound B-mode image quality remains an important area of research. Recently, there has been increased interest in using deep neural networks (DNNs) to perform beamforming to improve image quality more efficiently. Several approaches have been proposed that use different representations of channel data for network processing, including a frequency-domain approach that we previously developed. We previously assumed that the frequency domain would be more robust to varying pulse shapes. However, frequency- and time-domain implementations have not been directly compared. In addition, because our approach operates on aperture domain data as an intermediate beamforming step, a discrepancy often exists between network performance and image quality on fully reconstructed images, making model selection challenging. Here, we perform a systematic comparison of frequency- and time-domain implementations. In addition, we propose a contrast-to-noise ratio (CNR)-based regularization to address previous challenges with model selection. Training channel data were generated from simulated anechoic cysts. Test channel data were generated from simulated anechoic cysts with and without varied pulse shapes, in addition to physical phantom and in vivo data. We demonstrate that simplified time-domain implementations are more robust than we previously assumed, especially when using phase preserving data representations. Specifically, 0.39- and 0.36-dB median improvements in in vivo CNR compared to DAS were achieved with frequency- and time-domain implementations, respectively. We also demonstrate that CNR regularization improves the correlation between training validation loss and simulated CNR by 0.83 and between simulated and in vivo CNR by 0.35 compared to DNNs trained without CNR regularization.

Instantaneous Frequency Image

The instantaneous frequency (IF) image is proposed in this work. It is obtained by the differentiation of the instantaneous phase (IP) image, which in turn is calculated by replacing the amplitude information with the IP in the delay-and-sum beamforming. The IP image is a coherence factor that reduces artifacts and sidelobes influence, and it will be shown that the IF image will keep these same positive characteristics. In amplitude images the reflector representation level varies according to the experimental conditions, even using time-gain compensation. In IP images, the reflector is represented by a - π to π rad variation. An important feature of the IF image is that a reflector is represented by a constant level that is determined by the central frequency of the signal. Farther reflectors are represented with similar magnitudes as closer ones, being less influenced by distance than IP images and resulting in better contrast. Amplitude, IP, and IF images are obtained from point spread function simulations and a medical phantom in different experimental cases: vertical distances, contrast reflectors, axial and lateral separation, and a sparse array. The improper choice of dynamic range can result in low contrast or nondetection of a reflector. For the IF image, the dynamic range is determined by the central frequency of the signal and the zero-mean Gaussian distribution of the IF of noise. The IF image can be used to improve reflector detection, as additional information to assist the interpretation of pixels intensities in conventional amplitude images, or as a new coherence factor.