Multi-spectral image shift-estimation error calculations using simulated phenomenology.

Registration of multi-spectral imagery is a critical pre-processing step for applications such as image fusion, but phenomenological differences between spectral bands can lead to significant estimation errors. To develop credible requirements for multi-spectral imaging systems, it is critical to characterize errors, both algorithmic and fundamental, associated with estimating registration parameters; however, attempting to quantify error using archival data sets poses a number of problems. In this paper, we demonstrate the use of commercially available graphics software and available optical property measurements to create fully synthetic, multi-spectral imagery with high-fidelity representations of emissive and reflective phenomenology. We discuss and demonstrate techniques needed to quantify error for both area- and feature-based algorithms. We further show that such synthetic data sets can be used to quantify both the Fisher information and sample errors associated with estimation of the shift between images acquired in different spectral bands and, by extension, estimation of registration model parameters. With the flexibility offered by synthetic data, such characterization can be obtained for robust domains of image brightness, sensor parameters, and differences in image phenomenology.

Intrinsic bias in Fisher information calculations for multi-mode image registration.

To address the need for the analysis of image processing and optical requirements in multi-mode imaging systems, such as multi-spectral and polarimetric imagers, I have developed a Fisher information matrix to quantify errors in estimating the shift between images with non-transformational feature differences. If images of the same field have differences not attributable to a geometric transformation, as is common for images acquired using different spectral or polarization filters, uncertainty in estimating the parameters of the transformation will be increased by intrinsic bias, or bias inherent in the data itself, as opposed to bias originating in the estimation algorithm. The approach to shift-estimation error analysis described in this Letter accounts for intrinsic bias, has intuitively expected properties and, given planned system sensitivity and operating conditions, can be used with simulated multi-mode imagery to estimate image registration error and develop realistic requirements.

Airlight-imposed errors for space-object polarimetric observations from the ground.

We discuss and characterize how polarimetric sensing is contaminated by various "airlight" phenomena, as well as unpolarized light from the target, when space objects are observed with a ground-based telescope. Estimates of the polarization state are limited by unpolarized target light regardless of sensor technology or estimator algorithm, and increased target brightness actually degrades estimation of the S1, S2, and S3 Stokes parameters if the added light is unpolarized. Unpolarized airlight in the field of view has an identical degrading effect. Atmospheric scattering can significantly polarize airlight, so airlight polarization must be calibrated and subtracted from the estimated target polarization. We derive an expression for the mean-square Stokes estimation error when noisy, biased estimates for the airlight polarization state are subtracted from noisy, biased estimates of the target polarization state; this expression shows that target and airlight Stokes estimation noise and bias generally sum in the ms estimation error for airlight-calibrated target Stokes. While SNR for the estimate of a given Stokes parameter increases with the magnitude of that parameter, estimation bias also appears to be correlated with magnitude. We note that when the linear Stokes reference is not arbitrary, requiring a rotational transformation of the estimated Stokes vector, the SNRs of the S1 and S2 estimates vary with the rotation angle. Finally, we show that measured data can be used in numerical calculations described here to approximate the errors associated with Stokes estimation, with or without airlight calibration.

Cramér-Rao lower bound calculations for image registration using simulated phenomenology.

The Cramér-Rao lower bound (CRLB) is a valuable tool to quantify fundamental limits to estimation problems associated with imaging systems, and has been used previously to study image registration performance bounds. Most existing work, however, assumes constant-variance noise; for many applications, noise is signal-dependent. Further, linear filters applied after detection can potentially yield reduced registration error, but prior work has not treated the CRLB behavior caused by filter-imposed noise correlation. We have developed computational methods to efficiently generalize existing image registration CRLB calculations to account for the effect of both signal-dependent noise and linear filtering on the estimation of rigid-translation ("shift") parameters. Because effective use of the CRLB requires radiometrically realistic simulated imagery, we have also developed methods to exploit computer animation software and available optical properties databases to conveniently build and modify synthetic objects for radiometric image simulations using DIRSIG. In this paper, we present the generalized expressions for the rigid shift Fisher information matrix and discuss the properties of the associated CRLB. We discuss the methods used to synthesize object "sets" for use in DIRSIG, and then demonstrate the use of simulated imagery in the CRLB code to choose an error-minimizing filter and optimal integration time for an image-based tracker in the presence of random platform jitter.

Signal, noise, and bias for a broadband, division-of-amplitude Stokes polarimeter.

We analyze estimation error as a function of spectral bandwidth for division-of-amplitude (DoAm) Stokes polarimeters. Our approach allows quantitative assessment of the competing effects of noise and deterministic error, or bias, as bandwidth is varied.We use the signal-to-rms error (SRR) as a metric. Rather than calculating the SRR of the estimated Stokes parameters themselves, we use the singular-value decomposition to calculate the SRRs of the coefficients of the measured data vector projected onto the measurement matrix left singular vectors.We argue that calculating the SRRs for left singular vector coefficients will allow development of reconstruction filters to minimize Stokes estimation error. For the example case of a source with constant polarization over a relatively wide band, we show that as the spectral filter bandwidth is increased to include wavelengths significantly different than the design wavelength, the SRRs of the estimated left singular vector coefficients will a.) increase monotonically if relatively few photo-detection events (PDEs) are recorded, b.) after a sharp peak close to the design wavelength, decrease monotonically if relatively many PDEs are recorded, and c.) have well-defined maxima for nominal PDE counts. Given some idea of the source brightness relative to detector noise, one can specify a spectral filter bandwidth minimizing the variance and bias effects and optimizing Stokes parameter estimation. Our approach also allows one to specify the bandwidth over which the response of "achromatic" optics must be reasonably invariant with wavelength for rms Stokes estimation error to remain below some desired maximum. Finally, we point out that our method can be generalized not only to other types of polarimeters, but also to any sensing scheme that can be represented by a linear system for limiting values of a certain parameter.

Primary and secondary superresolution by data inversion.

Superresolution by data inversion is the extrapolation of measured Fourier data to regions outside the measurement bandwidth using post processing techniques. Here we characterize superresolution by data inversion for objects with finite support using the twin concepts of primary and secondary superresolution, where primary superresolution is the essentially unbiased portion of the superresolved spectra and secondary superresolution is the remainder. We show that this partition of superresolution into primary and secondary components can be used to explain why some researchers believe that meaningful superresolution is achievable with realistic signal-to-noise ratios, and other researchers do not.