Entropy Imaging Research Articles

Transforming Retinal Photographs to Entropy Images in Deep Learning to Improve Automated Detection for Diabetic Retinopathy.

Entropy images, representing the complexity of original fundus photographs, may strengthen the contrast between diabetic retinopathy (DR) lesions and unaffected areas. The aim of this study is to compare the detection performance for severe DR between original fundus photographs and entropy images by deep learning. A sample of 21,123 interpretable fundus photographs obtained from a publicly available data set was expanded to 33,000 images by rotating and flipping. All photographs were transformed into entropy images using block size 9 and downsized to a standard resolution of 100 × 100 pixels. The stages of DR are classified into 5 grades based on the International Clinical Diabetic Retinopathy Disease Severity Scale: Grade 0 (no DR), Grade 1 (mild nonproliferative DR), Grade 2 (moderate nonproliferative DR), Grade 3 (severe nonproliferative DR), and Grade 4 (proliferative DR). Of these 33,000 photographs, 30,000 images were randomly selected as the training set, and the remaining 3,000 images were used as the testing set. Both the original fundus photographs and the entropy images were used as the inputs of convolutional neural network (CNN), and the results of detecting referable DR (Grades 2–4) as the outputs from the two data sets were compared. The detection accuracy, sensitivity, and specificity of using the original fundus photographs data set were 81.80%, 68.36%, 89.87%, respectively, for the entropy images data set, and the figures significantly increased to 86.10%, 73.24%, and 93.81%, respectively (all p values <0.001). The entropy image quantifies the amount of information in the fundus photograph and efficiently accelerates the generating of feature maps in the CNN. The research results draw the conclusion that transformed entropy imaging of fundus photographs can increase the machinery detection accuracy, sensitivity, and specificity of referable DR for the deep learning-based system.

Hepatic Steatosis Assessment with Ultrasound Small-Window Entropy Imaging

Nonalcoholic fatty liver disease is a type of hepatic steatosis that is not only associated with critical metabolic risk factors but can also result in advanced liver diseases. Ultrasound parametric imaging, which is based on statistical models, assesses fatty liver changes, using quantitative visualization of hepatic-steatosis–caused variations in the statistical properties of backscattered signals. One constraint with using statistical models in ultrasound imaging is that ultrasound data must conform to the distribution employed. Small-window entropy imaging was recently proposed as a non–model-based parametric imaging technique with physical meanings of backscattered statistics. In this study, we explored the feasibility of using small-window entropy imaging in the assessment of fatty liver disease and evaluated its performance through comparisons with parametric imaging based on the Nakagami distribution model (currently the most frequently used statistical model). Liver donors (n = 53) and patients (n = 142) were recruited to evaluate hepatic fat fractions (HFFs), using magnetic resonance spectroscopy and to evaluate the stages of fatty liver disease (normal, mild, moderate and severe), using liver biopsy with histopathology. Livers were scanned using a 3-MHz ultrasound to construct B-mode, small-window entropy and Nakagami images to correlate with HFF analyses and fatty liver stages. The diagnostic values of the imaging methods were evaluated using receiver operating characteristic curves. The results demonstrated that the entropy value obtained using small-window entropy imaging correlated well with log10(HFF), with a correlation coefficient r = 0.74, which was higher than those obtained for the B-scan and Nakagami images. Moreover, small-window entropy imaging also resulted in the highest area under the receiver operating characteristic curve (0.80 for stages equal to or more severe than mild; 0.90 for equal to or more severe than moderate; 0.89 for severe), which indicated that non–model-based entropy imaging—using the small-window technique—performs more favorably than other techniques in fatty liver assessment.

Performance Evaluations on Using Entropy of Ultrasound Log-Compressed Envelope Images for Hepatic Steatosis Assessment: An In Vivo Animal Study.

Ultrasound B-mode imaging based on log-compressed envelope data has been widely applied to examine hepatic steatosis. Modeling raw backscattered signals returned from the liver parenchyma by using statistical distributions can provide additional information to assist in hepatic steatosis diagnosis. Since raw data are not always available in modern ultrasound systems, information entropy, which is a widely known nonmodel-based approach, may allow ultrasound backscattering analysis using B-scan for assessing hepatic steatosis. In this study, we explored the feasibility of using ultrasound entropy imaging constructed using log-compressed backscattered envelopes for assessing hepatic steatosis. Different stages of hepatic steatosis were induced in male Wistar rats fed with a methionine- and choline-deficient diet for 0 (i.e., normal control) and 1, 1.5, and 2 weeks (n = 48; 12 rats in each group). In vivo scanning of rat livers was performed using a commercial ultrasound machine (Model 3000, Terason, Burlington, MA, USA) equipped with a 7-MHz linear array transducer (Model 10L5, Terason) for ultrasound B-mode and entropy imaging based on uncompressed (HE image) and log-compressed envelopes (HB image), which were subsequently compared with histopathological examinations. Receiver operating characteristic (ROC) curve analysis and areas under the ROC curves (AUC) were used to assess diagnostic performance levels. The results showed that ultrasound entropy imaging can be used to assess hepatic steatosis. The AUCs obtained from HE imaging for diagnosing different steatosis stages were 0.93 (≥mild), 0.89 (≥moderate), and 0.89 (≥severe), respectively. HB imaging produced AUCs ranging from 0.74 (≥mild) to 0.84 (≥severe) as long as a higher number of bins was used to reconstruct the signal histogram for estimating entropy. The results indicated that entropy use enables ultrasound parametric imaging based on log-compressed envelope signals with great potential for diagnosing hepatic steatosis.

High-Intensity Focused Ultrasound Thermal Lesion Detection Using Entropy Imaging of Ultrasound Radio Frequency Signal Time Series.

Background:During the past few decades, high-intensity focused ultrasound (HIFU) modality has been gaining surging interest in various therapeutic applications such as non- or minimally-invasive cancer treatment. Among other attributes, robust and real-time HIFU treatment monitoring and lesion detection have become essential issues for successful clinical acceptance of the modality. More recently, ultrasound radio frequency (RF) time series imaging has been studied by a number of researchers.Materials and Methods:The objective of this study is to investigate the applicability of entropy parameter of RF time series of ultrasound backscattered signals, a. k. a. Entropy imaging, toward HIFU thermal lesion detection. To this end, five fresh ex vivo porcine muscle tissue samples were exposed to HIFU exposures with total acoustic powers ranging from 30 to 110 Watts. The contrast-to-speckle ratio (CSR) values of the entropy images and their corresponding B-mode images of pre-, during- and post-HIFU exposure for each acoustic power were calculated.Results:The novelty of this study is the use of Entropy parameter on ultrasound RF time series for the first time. Statistically significant differences were obtained between the CSR values for the B mode and entropy images at various acoustic powers. In case of 110 Watt, a CSR value 3.4 times higher than B-mode images was accomplished using the proposed method. Furthermore, the proposed method is compared with the scaling parameter of Nakagami imaging and same data which are used in this study.Conclusion:Entropy has the potential for using as an imaging parameter for differentiating lesions in HIFU surgery.

Small-window parametric imaging based on information entropy for ultrasound tissue characterization

Constructing ultrasound statistical parametric images by using a sliding window is a widely adopted strategy for characterizing tissues. Deficiency in spatial resolution, the appearance of boundary artifacts, and the prerequisite data distribution limit the practicability of statistical parametric imaging. In this study, small-window entropy parametric imaging was proposed to overcome the above problems. Simulations and measurements of phantoms were executed to acquire backscattered radiofrequency (RF) signals, which were processed to explore the feasibility of small-window entropy imaging in detecting scatterer properties. To validate the ability of entropy imaging in tissue characterization, measurements of benign and malignant breast tumors were conducted (n = 63) to compare performances of conventional statistical parametric (based on Nakagami distribution) and entropy imaging by the receiver operating characteristic (ROC) curve analysis. The simulation and phantom results revealed that entropy images constructed using a small sliding window (side length = 1 pulse length) adequately describe changes in scatterer properties. The area under the ROC for using small-window entropy imaging to classify tumors was 0.89, which was higher than 0.79 obtained using statistical parametric imaging. In particular, boundary artifacts were largely suppressed in the proposed imaging technique. Entropy enables using a small window for implementing ultrasound parametric imaging.

Ultrasound Statistical Parametric Imaging in the Assessment of Fatty Liver

Hepatitis steatosis may progress to nonalcoholic steatohepatitis, fibrosis, cirrhosis, and hepatocellular carcinoma. Nonalcoholic fatty liver disease (NAFLD) is the type of hepatic steatosis that most commonly leads to chronic liver disease. NAFLD is also related to metabolic risk factors. How to characterize fatty liver is attracting growing medical and health research interest. Notably, the speckle pattern is formed by ultrasound backscattered echoes, which are typically treated as random signals. Thus, analyzing the statistical distribution of the echo amplitude (i.e., the envelope signal) may provide useful clues associated with fatty liver diseases. Many investigators have began to study the relationship between the probability property of inverse scattering and the characteristics of tissue. Commonly used statistical models include the Rayleigh distribution, Rician distribution, K distribution, homodyned K distribution, Nakagami distribution, and compounding Nakagami distribution. One requisite of using statistical models to fit echo amplitude distributions is that the ultrasound envelope data must conform to the used distribution. To overcome the limitations mentioned above, we need to set a new direction for constructing the images of ultrasound parameters outside the statistical model ultrasonic method. Recall that Shannon established information theory and defined entropy as a measure of information uncertainty. Hughes pioneered using Shannon entropy for analyzing ultrasound signals, indicating that entropy is able to quantitatively describe changes in the microstructures of scattering media. Recently, we also developed the small-window entropy image of ultrasound by using a simple model of histograms and defined the weighted entropy to provide greater sensitivity in diagnosing the changes of the scattering microstructures of tissues. The results showed that fatty infiltration increases the uncertainty of backscattered signals from livers. Ultrasound entropy imaging has potential for the routine examination of fatty liver disease.

Effects of Fatty Infiltration of the Liver on the Shannon Entropy of Ultrasound Backscattered Signals

This study explored the effects of fatty infiltration on the signal uncertainty of ultrasound backscattered echoes from the liver. Standard ultrasound examinations were performed on 107 volunteers. For each participant, raw ultrasound image data of the right lobe of liver were acquired using a clinical scanner equipped with a 3.5-MHz convex transducer. An algorithmic scheme was proposed for ultrasound B-mode and entropy imaging. Fatty liver stage was evaluated using a sonographic scoring system. Entropy values constructed using the ultrasound radiofrequency (RF) and uncompressed envelope signals (denoted by HR and HE, respectively) as a function of fatty liver stage were analyzed using the Pearson correlation coefficient. Data were expressed as the median and interquartile range (IQR). Receiver operating characteristic (ROC) curve analysis with 95% confidence intervals (CIs) was performed to obtain the area under the ROC curve (AUC). The brightness of the entropy image typically increased as the fatty stage varied from mild to severe. The median value of HR monotonically increased from 4.69 (IQR: 4.60–4.79) to 4.90 (IQR: 4.87–4.92) as the severity of fatty liver increased (r = 0.63, p &lt; 0.0001). Concurrently, the median value of HE increased from 4.80 (IQR: 4.69–4.89) to 5.05 (IQR: 5.02–5.07) (r = 0.69, p &lt; 0.0001). In particular, the AUCs obtained using HE (95% CI) were 0.93 (0.87–0.99), 0.88 (0.82–0.94), and 0.76 (0.65–0.87) for fatty stages ≥mild, ≥moderate, and ≥severe, respectively. The sensitivity, specificity, and accuracy were 93.33%, 83.11%, and 86.00%, respectively (≥mild). Fatty infiltration increases the uncertainty of backscattered signals from livers. Ultrasound entropy imaging has potential for the routine examination of fatty liver disease.

Additional results for "joint entropy of continuously differentiable ultrasonic waveforms" [J. Acoust. Soc. Am. 133(1), 283-300 (2013)

Previous results on the use of joint entropy for detection of targeted nanoparticles accumulating in the neovasculature of MDA435 tumors [Fig. 7 of M. S. Hughes et al., J. Acoust. Soc. Am. 133, 283-300 (2013)] are extended, with sensitivity improving by nearly another factor of 2. This result is obtained using a "quasi-optimal" reference waveform in the computation of the joint entropy imaging technique used to image the accumulating nanoparticles.

Optimal smoothing splines improve efficiency of entropy imaging for detection of therapeutic benefit in muscular dystrophy

We have reported previously on sensitivity comparisons of signal energy and several entropies to changes in skeletal muscle architecture in experimental muscular dystrophy before and after pharmacological therapeutic intervention [M. S. Hughes, IEEE Trans. UFFC. 54, 2291–2299 (2007)]. The study was based on a moving window analysis of simple cubic splines that were fit to the backscattered ultrasound and required that the radio frequency ultrasound (RF) be highly oversampled. The current study employs optimal smoothing splines instead to determine the effect of analyzing the same data with increasing levels of decimation. The RF data were obtained from selected skeletal muscles of muscular dystrophy mice (mdx: dystrophin -/-) that were randomly blocked into two groups: 4 receiving steroid treatment over 2 weeks, and 4 untreated positive controls. Ultrasonic imaging was performed on day 15. All mice were anesthetized then each forelimb was imaged in transverse cross sections using a Vevo-660 with a single-element 40 MHz wobbler-transducer (model RMV-704, Visualsonics). The result of each scan was a three dimensional data set 384 × 8192 × # frames in size. We find the equivalent sensitivity of this new approach for detecting treatment benefits as before (p&amp;lt;0.03), but now at a decimated sampling rate slightly below the Nyquist frequency. This implies that optimal smoothing splines are useful for analysis of data acquired from point of care imaging devices where hardware cost and power consumption must be minimized.

Entropic imaging of cataract lens: an in vitro study.

Phacoemulsification is a common surgical method for treating advanced cataracts. Determining the optimal phacoemulsification energy depends on the hardness of the lens involved. Previous studies have shown that it is possible to evaluate lens hardness via ultrasound parametric imaging based on statistical models that require data to follow a specific distribution. To make the method more system-adaptive, nonmodel-based imaging approach may be necessary in the visualization of lens hardness. This study investigated the feasibility of applying an information theory derived parameter – Shannon entropy from ultrasound backscatter to quantify lens hardness. To determine the physical significance of entropy, we performed computer simulations to investigate the relationship between the signal-to-noise ratio (SNR) based on the Rayleigh distribution and Shannon entropy. Young's modulus was measured in porcine lenses, in which cataracts had been artificially induced by the immersion in formalin solution in vitro. A 35-MHz ultrasound transducer was used to scan the cataract lenses for entropy imaging. The results showed that the entropy is 4.8 when the backscatter data form a Rayleigh distribution corresponding to an SNR of 1.91. The Young's modulus of the lens increased from approximately 8 to 100 kPa when we increased the immersion time from 40 to 160 min (correlation coefficient r = 0.99). Furthermore, the results indicated that entropy imaging seemed to facilitate visualizing different degrees of lens hardening. The mean entropy value increased from 2.7 to 4.0 as the Young's modulus increased from 8 to 100 kPa (r = 0.85), suggesting that entropy imaging may have greater potential than that of conventional statistical parametric imaging in determining the optimal energy to apply during phacoemulsification.

A biomechanics comparison of grasping in locomotion and feeding with the mouse lemur (Microcebus murinus, Primate): a study case

Functional magnetic resonance imaging (fMRI) data-processing methods in the time domain include correlation analysis and the general linear model, among others. Virtually, many fMRI processing strategies utilise temporal information and ignore or pay little attention to phase information, resulting in an unnecessary loss of efficiency. We proposed a novel method named Hilbert phase entropy imaging (HPEI) that used the discrete Hilbert transform of the magnitude time series to detect brain functional activation. The data from two simulation studies and two in vivo fMRI studies that both contained block-design and event-related experiments revealed that the HPEI method enabled the effective detection of brain functional activation and the distinction of different response patterns. Our results demonstrate that this method is useful as a complementary analysis, but hypothesis-constrained, in revealing additional information regarding the complex nature of fMRI time series.

Hilbert phase entropy imaging of fMRI time series

Functional magnetic resonance imaging (fMRI) data-processing methods in the time domain include correlation analysis and the general linear model, among others. Virtually, many fMRI processing strategies utilise temporal information and ignore or pay little attention to phase information, resulting in an unnecessary loss of efficiency. We proposed a novel method named Hilbert phase entropy imaging (HPEI) that used the discrete Hilbert transform of the magnitude time series to detect brain functional activation. The data from two simulation studies and two in vivo fMRI studies that both contained block-design and event-related experiments revealed that the HPEI method enabled the effective detection of brain functional activation and the distinction of different response patterns. Our results demonstrate that this method is useful as a complementary analysis, but hypothesis-constrained, in revealing additional information regarding the complex nature of fMRI time series.

Shannon entropy can detect myocardial anisotropy without specular echo gating in vitro.

Ultrasonic images are often corrupted by specular echoes that obscure features near interfacial boundaries. This problem can be especially severe for in vitro examination of excised tissues (e.g., myocardium) which must often be sliced into thin sections to permit examination by other techniques in addition to ultrasound (e.g., optical, MRI, and histology), in order to characterize infarct region size and myofiber orientation. In many of these studies, myocardial anisotropy is obscured without removal of specular echoes by gating. Here, it is demonstrated that entropy imaging enables visualization of myocardial anisotropy without gating. Short axis slice of mouse heart (n=4) was C-scanned on a 55×55 grid, with 0.1 mm stepsize. At each point one 8-bit, 2048 point, time-averaged A-line was acquired. These were analyzed using three signal receivers, log variance, log energy (sum of squared), and Shannon entropy, to produce one pixel value at each location in the C-scan. Diffusion-tensor-weighted magnetic resonance at 12 T was used to validate the ultrasonic result. Among the three signal receivers, only entropy clearly resolves myocardial anisotropy without specular echo removal. [This work supported by NIH CA119342, and NSC-095-SAF-I-564-051-TMS.]

Maximum Entropy imaging with INTEGRAL/SPI data

The application of the Maximum Entropy method for sky imaging with the SPI instrument on INTEGRAL is de- scribed. While intended primarily for extended emission, point sources are also mapped by this method. The technique is implemented as the program spiskymax in the data analysis distribution provided by the INTEGRAL Science Data Centre. We briefly introduce the method, describe the particular requirements for the application to SPI, and show some example images using flight data from the early mission.

Vector entropy imaging theory with application to computerized tomography

Medical imaging theory for x-ray CT and PET is based on image reconstruction from projections. In this paper a novel vector entropy imaging theory under the framework of multiple criteria decision making is presented. We also study the most frequently used image reconstruction methods, namely, least square, maximum entropy, and filtered back-projection methods under the framework of the single performance criterion optimization. Finally, we introduce some of the results obtained by various reconstruction algorithms using computer-generated noisy projection data from the Hoffman phantom and real CT scanner data. Comparison of the reconstructed images indicates that the vector entropy method gives the best in error (difference between the original phantom data and reconstruction), smoothness (suppression of noise), grey value resolution and is free of ghost images.

Dynamics in the spin-boson model by maximum entropy moment imaging

The spin–spin time correlation function of the spin-boson model is studied using a maximum entropy imaging procedure founded on knowledge of early time derivatives or moments of the corresponding spectral density. The coherent–incoherent boundary is reproduced in agreement with the results of dynamical path-integral Monte Carlo and the procedure is shown to be stable numerically at both long time and low temperature.

Molecular time scale generalized Langevin equation theory and polynomial maximum entropy imaging of spectral densities

Molecular time scale generalized Langevin equation (MTGLE) theory is discussed as an approach to condensed phase dynamics. A polynomial maximum entropy (MaxEnt) process for imaging required MTGLE spectral densities based on knowledge of the moments of the spectral density is introduced. The process is based on the use of interpolation polynomials which serve both to image the spectral density as well as provide a numerical procedure to compute the inverse Hessian matrix in a Newton-type minimization. A default model is added to allow for the inclusion of additional information in forming the image. The polynomial MaxEnt imaging process is found to be a fast, numerically stable, computational procedure which produces images comparable in quality to images obtained by other imaging processes. The polynomial MaxEnt imaging process is examined in the context of imaging MTGLE bath spectral densities with special emphasis on a coupled linear chain model. Standard harmonic oscillator, Hamiltonian bath models such as Ohmic-exponential and Ohmic-Gaussian are shown to possess regions of parameter space for which the MTGLE adiabatic frequency is imaginary. When the adiabatic frequency is zero, it is shown that imaging of the friction kernel is the best approach.

Maximum entropy imaging and quantum molecular timescale generalized langevin equation theory

Abstract A new maximum entropy (MaxEnt) imaging procedure is introduced to treat the inverse problem in quantum molecular timescale generalized Langevin equation (MTGLE) theory. In particular MaxEnt imaging is used to construct the MTGLE bath spectral density from knowledge of its moments.

The GDDSYN light curve synthesis method

We present a close binary system light curve synthesis algorighm called geodesic distribution binary synthesis (GDDSYN), which uses a novel surface element distribution and partial visibility computational scheme for the Roche model. The surface element distribution, based on the geodesic sphere, is well suited to maximum entropy imaging of surface features on eclipsing binaries. It allows the fitting of spot distributions which are less sensitive to observational errors than schemes which have too many low weight surface elements.

Two‐dimensional maximum entropy reconstruction of radio brightness

This paper describes a procedure for maximum entropy reconstruction of two‐dimensional radio brightness maps from noisy interferometer measurements. The method defines a map that obeys the nonnegativity constraint and is, in a sense, the smoothest of all brightness distributions that agree with the visibility measurements within the errors of observation. This approach acknowledges the fact that signal‐to‐noise considerations have a strong influence on useful resolution; fine structure appears only to the extent justified by measurement accuracy. Iterative computing is needed to find the maximum entropy image. It is shown that the primary computational burden of maximum entropy reconstruction involves calculations that are efficiently performed by fast Fourier transform techniques. Different techniques are used depending on whether visibility data are irregularly distributed in the u,v plane or interpolated onto a rectangular lattice prior to reconstruction. The efficiency of the fast Fourier transform provides a tremendous computational advantage with the result that maximum entropy reconstruction on a moderately large grid (64×64) is practicable at reasonable cost. Several comparative examples are shown, and some of the limitations of the present theory of maximum entropy imaging are identified.