Maximum Entropy Image Research Articles

Maximum-entropy image reconstruction using wavelets

The maximum-entropy method (MEM) is often used for enhancing astronomical images and, in particular, has recently been applied to cosmic microwave background (CMB) observations. Wavelet functions are also now used widely in astronomy, since they allow the sparse and efficient representation of a signal at different scales, and the application of wavelets to the denoising of CMB maps has been investigated. In this paper, we give a systematic discussion of how to combine these two approaches by the use of the MEM in wavelet bases for the denoising and deconvolution of general images and, in particular, CMB maps. We find that the MEM in the à trous wavelet basis has lower reconstruction residuals than conventional pixel-basis MEM in the case when the signal-to-noise ratio is low and the point spread function is narrow. Furthermore, the Bayesian evidence for the wavelet MEM reconstructions is generally higher for a wide range of images. From a Bayesian point of view, the wavelet basis thus provides a better model of the image.

Maximum Entropy Reconstruction Methods in Electron Paramagnetic Resonance Imaging

Electron Paramagnetic Resonance (EPR) is a spectroscopic technique that detects and characterizes molecules with unpaired electrons (i.e., free radicals). Unlike the closely related nuclear magnetic resonance (NMR) spectroscopy, EPR is still under development as an imaging modality. Athough a number of physical factors have hindered its development, EPR's potential is quite promising in a number of important application areas, including in vivo oximetry. EPR images are generally reconstructed using a tomographic imaging technique, of which filtered backprojection (FBP) is the most commonly used. We apply two iterative methods for maximum-entropy image reconstruction in EPR. The first is the multiplicative algebraic reconstruction technique (MART), a well-known row-action method. We propose a second method, known as LSEnt (least-squares entropy), that maximizes entropy and performs regularization by maintaining a desired distance from the measurements. LSEnt is in part motivated by the barrier method of interior-point programming. We present studies in which images of two physical phantoms, reconstructed using FBP, MART, and LSEnt, are compared. The images reconstructed using MART and LSEnt have lower variance, better contrast recovery, subjectively better resolution, and reduced streaking artifact than those reconstructed using FBP. These results suggest that maximum-entropy reconstruction methods (particularly the more flexible LSEnt) may be critical in overcoming some of the physical challenges of EPR imaging.

Surface differential rotation and prominences of the Lupus post T Tauri star RX J1508.6-4423

We present in this paper a spectroscopic monitoring of the Lupus post T Tauri star RX J1508.6-4423 carried out at two closely separated epochs (1998 May 06 and 10) with the UCL Echelle Spectrograph on the 3.9-m Anglo-Australian Telescope. Applying least-squares convolution and maximum entropy image reconstruction techniques to our sets of spectra, we demonstrate that this star features on its surface a large cool polar cap with several appendages extending to lower latitudes, as well as one spot close to the equator. The images reconstructed at both epochs are in good overall agreement, except for a photospheric shear that we interpret in terms of latitudinal differential rotation. Given the spot distribution at the epoch of our observations, differential rotation could only be investigated between latitudes 15° and 60°. We find in particular that the observed differential rotation is compatible with a solar-like law (i.e., with rotation rate decreasing towards high latitudes proportionally to sin2l, where l denotes the latitude) in this particular latitude range. Assuming that such a law can be extrapolated to all latitudes, we find that the equator of RX J1508.6-4423 does one more rotational cycle than the pole every 50±10 d, implying a photospheric shear 2 to 3 times stronger than that of the Sun. We also discover that the Hα emission profile of RX J1508.6-4423 is most of the time double-peaked and strongly modulated with the rotation period of the star. We interpret this rotationally modulated emission as being caused by a dense and complex prominence system, the circumstellar distribution of which is obtained through maximum entropy Doppler tomography. These maps show in particular that prominences form a complete and inhomogeneous ring around the star, precisely at the corotation radius. We use the total Hα and Hβ emission flux to estimate that the mass of the whole prominence system is about 1020 g. From our observation that the whole cloud system surrounding the star is regenerated in less than 4 d, we conclude that the braking time-scale of RX J1508.6-4423 is shorter than 1 Gyr, and that prominence expulsion is thus likely to contribute significantly to the rotational spindown of young low-mass stars.

Improvement of Yohkoh HXT imaging and an analysis of the 1997 November 6, X9 flare

The imaging capability of the Hard X-ray Telescope (HXT) on board Yohkoh has been drastically improved by (1) adopting new instrumental response functions (modulation patterns) derived from a self-calibration procedure that makes use of solar flares themselves as calibration sources, (2) revising the Maximum Entropy (MEM) image synthesis procedure for better total flux estimation, and (3) incorporating in MEM properly estimated observation errors. One of the most intense flares so far observed with HXT, the 1997 November 6, X9 flare, has been analyzed with the new HXT imaging program. Two footpoint sources are clearly seen and show systematic motions during the impulsive phase. This may provide a new clue to understand the coronal magnetic field structure involved in the energy release process of flares.

Doppler Imaging of Two Zero‐Age Main‐Sequence Stars in the Pleiades: HII 686 and HII 3163

Maximum entropy image reconstruction (Doppler imaging) is applied to HII 686 (K4 V, v sin i = 64 km s-1) and HII 3163 (K0 V, v sin i = 70 km s-1), two zero-age main-sequence stars of the Pleiades cluster. Their surface temperature distributions are determined in order to study the nature of magnetic activity in ultrafast rotators of known evolutionary status. Specific intensity line profiles used in the Doppler imaging (DI) algorithm are synthesized. The sensitivity of the reconstructions to the choice of input stellar and atomic data is investigated. The quality of the fit to the average disk-integrated line profile is found to be more important to DI analysis than the exact parameters used to generate the fit when the shape of the disk-integrated line profile is dominated by rotational broadening. Fifteen absorption lines are used to generate 15 individual reconstructions of each Pleiades target. Averaging reduces noise in the reconstructions. However, simulations reveal that spurious features tend to cluster systematically at subobserver longitudes and can therefore persist in the images even after averaging several reconstruction together. Such phase-ghosting becomes more severe as the signal-to-noise ratio decreases and does not appear to depend on the spot morphology. HII 686 shows one predominant feature at 77° latitude, which is 860 K cooler than the surrounding photosphere. HII 3163 shows a predominant feature centered at approximately 70° latitude, which has two temperature minima (780 K cooler than the photosphere) separated by approximately 130° in longitude. However, photometric observations suggest that this double-lobed morphology is a consequence of poor phase sampling. One temperature minimum located midway in longitude better reproduces the observed light curve. We are unable to make any reliable detections of low-latitude features on the surface of either star. The results are discussed in light of recent theoretical observations and existing image reconstructions of similar objects. No correlations are found among reconstructions that could be attributed to line characteristics: equivalent width, excitation potential, or depth of formation. This is also true for the Li I and K I resonance lines. Despite their temperature sensitivity, they yield results that are consistent with those determined from lines that are not temperature sensitive. For each object, the chromospheric residual emission (Hα, Ca II 8498 A) is measured as a function of rotational phase. Maximum emission does not consistently occur at the phase of spot transit.

A new approach for ME image restoration based on CNN

A new approach for image restoration by cellular neural network (CNN) is developed in this paper. Based on the statistical characteristics of Gibbs image model and the analysis of maximum entropy (ME) image restoration, a reasonable template for binary image restoration is proposed. To process multilevel image, a multi-layer cellular neural network is employed and an extensive algorithm for multilevel image restoration is proposed. The results of computer simulation prove the effectiveness of this approach and show that we can get the effective template of CNN for some special image questions if we apply the statistical characteristics of Gibbs image model and analyse the physical meaning of the questions. Copyright © 1999 John Wiley & Sons, Ltd.

Magnetic cycles of HR 1099 and LQ Hydrae

We present in this paper a 6-yr time series of magnetic (and brightness) surface images of the K1 subgiant of the RS CVn system HR 1099 (=V711 Tauri) and of the young K0 dwarf LQ Hydrae, reconstructed (with the help of a dedicated maximum entropy image reconstruction software) from Zeeman--Doppler imaging observations collected at the Anglo-Australian Telescope. All the stellar magnetic images that we reconstruct host at least one high-contrast feature in which the field is predominantly azimuthal, thus confirming that such surface structures (already detected in previous similar studies) are indeed real. We take this as strong evidence that dynamo processes of late-type rapid rotators operate throughout the whole stellar convective envelope, rather than being confined to an interface layer between the convective and radiative zones as in the Sun. The latitudinal polarity pattern of azimuthal and radial fields that we observe at the surface of both stars suggests that these magnetic regions respectively reveal the toroidal and poloidal components of the large-scale dynamo field. The spatial structure of these two magnetic field components becomes increasingly more complex (with higher axisymmetric spherical harmonic degrees) for larger rotation rates and deeper convective zones. The strength of the toroidal and poloidal components is typically a few hundred G, more than two orders of magnitude stronger than in the Sun. Long-term evolution of the toroidal and poloidal components of the large-scale field is clearly detected in our time series. We also report the detection of small fluctuations in the orbital period of HR 1099, with a peak-to-peak amplitude of about 36±1 s (i.e. 0.015 per cent) and a period of about 18±2 yr (assuming sinusoidal variations around the nominal value). The most plausible way of explaining such fluctuations is that the quadrupole moment of the K1 subgiant is varying with time, and that this modulation is driven by the magnetic activity cycle of the primary star itself (through a periodic exchange between kinetic and magnetic energy within the convective zone). It provides in particular an independent confirmation that a dynamo operates within the whole convective zone, and suggests that the average azimuthal field in the convective envelope is of the order of 6 kG.

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.

Closed-form maximum entropy image restoration

The use of maximum entropy image restoration has, heretofore, required recursive, or iterative, search routines. This paper, by contrast, describes a one-pass, closed-form maximum entropy algorithm. The approach derives from minimization of a log L 2-error norm between object and reconstruction. The resulting output has the form of the exponential of a Wiener-type filtering of the image data. The logarithmic nature of the norm gives rise to a tendency toward constant relative error across the output field.

Maximum entropy image reconstruction from sparsely sampled coherent field data

There are many practical problems in which it is required to detect and characterize hidden structures or remote objects by virtue of the scattered acoustic or electromagnetic fields they generate. It remains an open question, however, as to which reconstruction algorithms offer the most informative images for a given set of field measurements. Commonly used time-domain beamforming techniques, and their equivalent frequency-domain implementations, are conceptually simple and stable in the presence of noise, however, large proportions of missing measurements can quickly degrade the image quality. We apply a new algorithm based on the maximum entropy method (MEM) to the reconstruction of images from sparsely sampled coherent field data. The general principles and limitations of the new method are discussed in the framework of regularization theory, and the results of monostatic imaging experiments confirm that superior resolution and artifact suppression are obtained relative to a commonly used linear inverse filtering approach.

An Imaging Algorithm Using the Bispectrum in Radio Interferometry

We present a maximum-entropy imaging algorithm using the bispectrum observed with radio interferometers. It is iterative and based on the steepest-ascent method. Imaging simulation tests show that this algorithm can reconstruct more reliable images of weak, extended sources than can the conventional self-calibration method. An example application of this algorithm to data of the Nobeyama Millimeter Array is given.

Information, Language, and Pixon‐Based Image Reconstructiona

From an information theoretic point of view, the in verse problem and the problem of data compression a re intimately related. Optimal compression seeks the most concis e representation of a data set, while Bayesian prob ability theory favors image reconstruction algorithms which minimally model the information present in the data. This shoul d not be surprising. It is in keeping with a scientists intuitive need to s atisfy the precepts of Occam’s Razor, i.e. not to over interpret one’s data. Information scientists might describe this process as quantifying the Algorithmic Information Content (AIC) of the image, and then using this “coordinate system” for optimal ima ge reconstruction. The present paper describes pixon-based image recon struction, a technique based upon AIC minimal image models. Because AIC is language dependent (description length and language complexity are inversely related) w e have based the practical implementation of our method on concise ( descriptive) languages for generic images, e.g. mul tiresolution basis functions. The present paper describes both the theory of pixon-based reconstruction and presents practic al examples demonstrating that pixon-based reconstruction produces result s consistently superior (often by large factors) to those of other methods, including the best examples of Maximum Likelihood and Maximum Entropy image reconstruction.

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.

Multiple solution in maximum entropy deconvolution of high resolution electron microscope images

The origin of multiple solution in maximum entropy image deconvolution has been analyzed for simple crystal structures. It is illustrated that the entropy-defocus curves contain two kinds of peaks. The sharp peaks originate in the loss of at least one diffracted beam due to the defined threshold for contrast transfer function. There are several smooth peaks, and the deconvoluted images corresponding to these peaks are closely related to one another. It is illustrated how to select the correct solution from among all deconvoluted images.

Using spatial information as an aid to maximum entropy image threshold selection

Many image grey-level thresholding methods based on the theory of maximum entropy have been proposed in the past. However, the exact definition of what is meant by “image entropy” has varied considerably, with measures based on the image itself, its histogram or other related distributions being proposed. Most of these ignore the spatial component of the image, assuming pixels within the image to be independent of each other. This is convenient, but it is also counter-intuitive. The inclusion of context-related information can be a simple matter, as is demonstrated in this article. A common measure of image entropy is based on the notion of viewing the image itself as a probability distribution (often referred to as the “monkey model” of the image). Direct application of this measure as a criterion function for grey-level threshold selection yields generally unsatisfactory results. With the inclusion of spatial information in the entropy measure, the results improve dramatically.

Extended dust shells around carbon stars resolved by “HIRAS”

We have examined forty-two carbon stars which show excess emission at 60 and/or 100 μm by applying maximum-entropy image reconstruction techniques to the IRAS 60 μm survey data. Thirteen stars are found to be extended in the reconstructed images. Four of them show a detached ring centered on the stellar position. In particular, U Ant may have a double detached dust shell. The implications of our results are discussed concerning the variation of mass loss on the AGB evolution.

最大エントロピー法を用いた投射角制限下回折トモグラフィ画像復元法の実験的検討

最大エントロピー法を用いた投射角制限下回折トモグラフィ画像復元法の実験的検討

Direct Sub-Lattice Imaging of Interface Dislocation Structures in CdTe/GaAs(001)

This paper presents directly interpretable atomic resolution images of dislocation structures at interfaces in CdTe/GaAs(001) systems. This is achieved using the technique of Z-contrast imaging in a 300 kV scanning transmission electron microscope in conjunction with maximum entropy image analysis. In addition to being used to further the understanding of the relation between growth conditions and exhibited properties, the data presented provides direct information on the atomic arrangements at dislocation cores.

最大エントロピー法を用いた投射角制限下回折トモグラフィ画像復元法の検討

最大エントロピー法を用いた投射角制限下回折トモグラフィ画像復元法の検討