Meredith Kupinski

Scanning linear estimation: improvements over region of interest (ROI) methods

In tomographic medical imaging, a signal activity is typically estimated by summing voxels from a reconstructed image. We introduce an alternative estimation scheme that operates on the raw projection data and offers a substantial improvement, as measured by the ensemble mean-square error (EMSE), when compared to using voxel values from a maximum-likelihood expectation-maximization (MLEM) reconstruction. The scanning-linear (SL) estimator operates on the raw projection data and is derived as a special case of maximum-likelihood estimation with a series of approximations to make the calculation tractable. The approximated likelihood accounts for background randomness, measurement noise and variability in the parameters to be estimated. When signal size and location are known, the SL estimate of signal activity is unbiased, i.e. the average estimate equals the true value. By contrast, unpredictable bias arising from the null functions of the imaging system affect standard algorithms that operate on reconstructed data. The SL method is demonstrated for two different tasks: (1) simultaneously estimating a signals size, location and activity; (2) for a fixed signal size and location, estimating activity. Noisy projection data are realistically simulated using measured calibration data from the multi-module multi-resolution small-animal SPECT imaging system. For both tasks, the same set of images is reconstructed using the MLEM algorithm (80 iterations), and the average and maximum values within the region of interest (ROI) are calculated for comparison. This comparison shows dramatic improvements in EMSE for the SL estimates. To show that the bias in ROI estimates affects not only absolute values but also relative differences, such as those used to monitor the response to therapy, the activity estimation task is repeated for three different signal sizes.

Method for optimizing channelized quadratic observers for binary classification of large-dimensional image datasets

We present a new method for computing optimized channels for channelized quadratic observers (CQO) that is feasible for high-dimensional image data. The method for calculating channels is applicable in general and optimal for Gaussian distributed image data. Gradient-based algorithms for determining the channels are presented for five different information-based figures of merit (FOMs). Analytic solutions for the optimum channels for each of the five FOMs are derived for the case of equal mean data for both classes. The optimum channels for three of the FOMs under the equal mean condition are shown to be the same. This result is critical since some of the FOMs are much easier to compute. Implementing the CQO requires a set of channels and the first- and second-order statistics of channelized image data from both classes. The dimensionality reduction from M measurements to L channels is a critical advantage of CQO since estimating image statistics from channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier. In a simulation study we compare the performance of ideal and Hotelling observers to CQO. The optimal CQO channels are calculated using both eigenanalysis and a new gradient-based algorithm for maximizing Jeffreys divergence (J). Optimal channel selection without eigenanalysis makes the J-CQO on large-dimensional image data feasible.

Relating the statistics of the angle of linear polarization to measurement uncertainty of the Stokes vector

Abstract. This work shows an analytic solution to the central moments of the angle of linear polarization (AoLP) when the linear Stokes parameters are independent and Gaussian distributed with different means but equal variance. Such a result is useful for distinguishing AoLP features from noise in polarimetry. When the DoLP is high relative to the measurement uncertainty of the linear Stokes vector, AoLP statistics have been shown to be well approximated by a Gaussian distribution. When the DoLP is zero, AoLP values are uniformly distributed. In general, the probability density function (PDF) of AoLP does not have a closed-form solution and this is the first report, to our knowledge, on an exact analytic form for the central moments of the AoLP. This analytic form will be useful when the AoLP is of interest even when the DoLP is low and the corresponding PDF on the AoLP is in between the extreme cases of a Gaussian or a uniform distribution. We also show that a simple propagation of error (PE) analysis underestimates the AoLP variance at extremely low DoLP but is verified for cases of DoLP that are high relative to the Stokes measurement uncertainty. An example use of the AoLP variance in imaging polarimetry is presented.

Applying a microfacet model to polarized light scattering measurements of the Earth's surface

Representative examples from three-years of measurements from JPLs Ground-based Multiangle SpectroPolarimetric Imager (Ground-MSPI)[1] are compared to a model for the surface polarized bidirectional reflectance distribution matrix (BRDM). Ground-MSPI is an eight-band spectropolarimetric camera mounted on a rotating gimbal to acquire push-broom imagery of outdoor landscapes. The camera uses a photoelastic-modulator-based polarimetric imaging technique to measure linear Stokes parameters in three wavebands (470, 660, and 865 nm) with a ±0.005 uncertainty in degree of linear polarization (DoLP). Comparisons between MSPI measurements, BRDM models, and common modifications to the model are made over a range of scattering angles determined from a fixed viewing geometry and varying sun positions over time. The BRDM model is comprised of a volumetric reflection term plus a specular reflection term of Fresnel-reflecting micro-facets. We consider modifications to this model using a shadowing function and two different micro-facet scattering density functions. We report the root-mean-square error (RMSE) between the Ground-MSPI measurements and BRDM model. The BRDM model predicts an angle of the linear polarization (AoLP) that is perpendicular to the scattering plane. This is usually, but not always, observed in Ground-MSPI measurements and in this work we offer explanations for some of the deviations from the model.

Spectral invariance hypothesis study of polarized reflectance with Ground-based Multiangle SpectroPolarimetric Imager (GroundMSPI)

Many models used to represent the boundary condition for the separation of atmospheric scattering from the surface reflectance in polarized remote sensing measurements assume that the polarized surface reflectance is spectrally neutral. The Spectral Invariance Hypothesis asserts that the magnitude and shape of the polarized bidirectional reflectance factor (pBRF) is equal for all wavelengths. In order to test this hypothesis, JPLs Ground-based Multiangle SpectroPolarimetric Imager (GroundMSPI) is used to measure polarization information of different outdoor surface types. GroundMSPI measures the linear polarization Stokes parameters (I, Q, U), at three wavelengths, 470 nm, 660 nm, and 865 nm. The camera is mounted on a two-axis gimbal to accurately select the view azimuth and elevation directions. On clear sky days we acquired day-long scans of scenes that contain various surface types such as grass, dirt, cement, brick, and asphalt and placed a Spectralon panel in the camera field of view to provide a reflectance reference. Over the course of each day, changing solar position in the sky provides a large range of scattering angles for this study. The polarized bidirectional reflectance factor (pBRF) is measured for the three wavelengths and the best fit slope of the spectral correlation is reported. This work reports the range of best fit slopes measured for five region types.

Comparison of the scanning linear estimator (SLE) and ROI methods for quantitative SPECT imaging

In quantitative emission tomography, tumor activity is typically estimated from calculations on a region of interest (ROI) identified in the reconstructed slices. In these calculations, unpredictable bias arising from the null functions of the imaging system affects ROI estimates. The magnitude of this bias depends upon the tumor size and location. In prior work it has been shown that the scanning linear estimator (SLE), which operates on the raw projection data, is an unbiased estimator of activity when the size and location of the tumor are known. In this work, we performed analytic simulation of SPECT imaging with a parallel-hole medium-energy collimator. Distance-dependent system spatial resolution and non-uniform attenuation were included in the imaging simulation. We compared the task of activity estimation by the ROI and SLE methods for a range of tumor sizes (diameter: 1-3 cm) and activities (contrast ratio: 1-10) added to uniform and non-uniform liver backgrounds. Using the correct value for the tumor shape and location is an idealized approximation to how task estimation would occur clinically. Thus we determined how perturbing this idealized prior knowledge impacted the performance of both techniques. To implement the SLE for the non-uniform background, we used a novel iterative algorithm for pre-whitening stationary noise within a compact region. Estimation task performance was compared using the ensemble mean-squared error (EMSE) as the criterion. The SLE method performed substantially better than the ROI method (i.e. EMSE(SLE) was 23-174 times lower) when the background is uniform and tumor location and size are known accurately. The variance of the SLE increased when a non-uniform liver texture was introduced but the EMSE(SLE) continued to be 5-20 times lower than the ROI method. In summary, SLE outperformed ROI under almost all conditions that we tested.

Estimating the relative water content of leaves in a cotton canopy

Remotely sensing plant canopy water status remains a long term goal of remote sensing research. Established approaches to estimating canopy water status — the Crop Water Stress Index, the Water Deficit Index and the Equivalent Water Thickness — involve measurements in the thermal or reflective infrared. Here we report plant water status estimates based upon analysis of polarized visible imagery of a cotton canopy measured by ground Multi-Spectral Polarization Imager (MSPI). Such estimators potentially provide access to the plant hydrological photochemistry that manifests scattering and absorption effects in the visible spectral region.

Binary classification of Mueller matrix images from an optimization of Poincaré coordinates

A new binary classification method for Mueller matrix images is presented which optimizes the polarization state analyzer (PSA) and the polarization state generator (PSG) using a statistical divergence between pixel values in two regions of an image. This optimization generalizes to multiple PSA/PSG pairs so that the classification performance as a function of number of polarimetric measurements can be considered. Optimizing PSA/PSG pairs gives insight into which polarimetric measurements are most useful for the binary classification. For example, in scenes with strong diattenuation, retardance, or depolarization certain PSA/PSG pairs would make two regions in an image look very similar and other pairs would make the regions look very different. The method presented in this paper provides a quantitative method for ensuring the images acquired can be classified optimally.

Comparison of the scanning linear estimator (SLE) and ROI uptake estimation for quantitative 111In-Octreotide SPECT imaging of signals embedded in random backgrounds

In quantitative PET and SPECT imaging signal activity is typically estimated from calculations in a 3D region of interest (ROI) of the reconstructed slices. In these calculations, unpredictable bias arising from the null functions of the imaging system (e.g. signal size and location) affects ROI estimates. An alternative to the ROI method is the scanning linear estimator (SLE), which operates on the raw projection data. In this work, we compared the ROI and SLE methods through analytic simulations of a realistic NCAT human phantom modeling 111In-Octreotide studies. The task was to estimate the signal activity of a spherical lesion in the liver, and its size and location are known. The performance of SLE and ROI methods were compared for two assumptions about the activity in the liver: 1) a uniform distribution of known value and 2) a non-uniform and random distribution. For all imaging scenarios in this simulation study the SLE estimated the uptake values better than the ROI estimation when compared using the ensemble-mean-squared error (EMSE).

HabEx polarization ray trace and aberration analysis

The flux difference between a terrestrial exoplanet and a much brighter nearby star creates an enormous optical design challenge for space-based imaging systems. Coronagraphs are designed to block the star’s flux and obtain a high-dynamic-range image of the exoplanet. The contrast of an optical system is calculated using the point spread function (PSF). Contrast quantifies starlight suppression of an imaging system at a given separation of the two objects. Contrast requirements can be as small as 10−10 for earth-like planets. This work reports an analysis of the September 2017 Habitable Exoplanet Imaging Mission (HabEx) end-to-end optical system prescription for geometric and polarization aberrations across the 450 to 550 nm channel. The Lyot coronagraph was modeled with a vector vortex charge 6 mask but without adaptive optics (AO) to correct the phase of the Jones pupil. The detector plane irradiance was calculated for three states of the telescope/coronagraph system: (1) free of geometric and polarization aberrations; (2) isotropic mirror coatings throughout the end-toend system; and (3) isotropic mirrors with form birefringence on the primary mirror. For each of these three states the system response both with and without a coronagraph mask was calculated. Two merit functions were defined to quantify the system’s ability to attenuate starlight: (1) normalized polychromatic irradiance (NPI), and (2) starlight suppression factor (SSF). Both of these are dimensionless and their values are functions of position across the focal plane. The NPI is defined as the irradiance point-by-point across the detector plane with a coronagraph mask divided by the value of the on-axis irradiance without a coronagraph mask. The SSF is the irradiance point-by-point across the detector plane with a coronagraph mask divided by the pointby-point value of the irradiance across the detector plane without a coronagraph mask. Both the NPI and the SSF provide insights into coronagraph performance. Deviations from the aberration-free case are calculated and summarized in table 2. The conclusions are: (1) the HabEx optical system is well-balanced for both geometric and polarization aberrations; (2) the spatially dependent polarization reflectivity for the HabEx primary mirror should be specified to ensure the coating is isotropic; (3) AO to correct the two orthogonal polarization-dependent wavefront errors is essential.