Per-pixel Errors Research Articles

Full-sky Cosmic Microwave Background Foreground Cleaning Using Machine Learning

Abstract In order to extract cosmological information from observations of the millimeter and submillimeter sky, foreground components must first be removed to produce an estimate of the cosmic microwave background (CMB). We developed a machine-learning approach for doing so for full-sky temperature maps of the millimeter and submillimeter sky. We constructed a Bayesian spherical convolutional neural network architecture to produce a model that captures both spectral and morphological aspects of the foregrounds. Additionally, the model outputs a per-pixel error estimate that incorporates both statistical and model uncertainties. The model was then trained using simulations that incorporated knowledge of these foreground components that was available at the time of the launch of the Planck satellite. On simulated maps, the CMB is recovered with a mean absolute difference of <4 μK over the full sky after masking map pixels with a predicted standard error of >50 μK; the angular power spectrum is also accurately recovered. Once validated with the simulations, this model was applied to Planck temperature observations from its 70 GHz through 857 GHz channels to produce a foreground-cleaned CMB map at a Healpix map resolution of nside = 512. Furthermore, we demonstrate the utility of the technique for evaluating how well different simulations match observations, particularly in regard to the modeling of thermal dust.

Remote Sensing of Seagrass Leaf Area Index and Species: The Capability of a Model Inversion Method Assessed by Sensitivity Analysis and Hyperspectral Data of Florida Bay

The capability for mapping two species of seagrass, Thalassia testudinium and Syringodium filiforme, by remote sensing using a physics based model inversion method was investigated. The model was based on a three-dimensional canopy model combined with a model for the overlying water column. The model included uncertainty propagation based on variation in leaf reflectances, canopy structure, water column properties and the air-water interface. The uncertainty propagation enabled both a-priori predictive sensitivity analysis of potential capability and the generation of per-pixel error bars when applied to imagery. A primary aim of the work was to compare the sensitivity analysis to results achieved in a practical application using airborne hyperspectral data, to gain insight on the validity of sensitivity analyses in general. Results showed that while the sensitivity analysis predicted a weak but positive discrimination capability for species, in a practical application the relevant spectral differences were extremely small compared to discrepancies in the radiometric alignment of the model with the imagery – even though this alignment was very good. Complex interactions between spectral matching and uncertainty propagation also introduced biases. Ability to discriminate LAI was good, and comparable to previously published methods using different approaches. The main limitation in this respect was spatial alignment with the imagery with in situ data, which was heterogeneous on scales of a few meters. The results provide insight on the limitations of physics based inversion methods and seagrass mapping in general. Complex models can degrade unpredictably when radiometric alignment of the model and imagery is not perfect and incorporating uncertainties can have non-intuitive impacts on method performance. Sensitivity analyses are upper bounds to practical capability, incorporating a term for potential systematic errors in radiometric alignment may be advisable. While Thalassia testudinium and Syringodium filiforme were too spectrally similar to be discriminated purely on spectral grounds, mapping of these and other species may be achievable by exploiting co-incident factors based on ecological zonation.

Adaptive rendering with non-local means filtering

We propose a novel approach for image space adaptive sampling and filtering in Monte Carlo rendering. We use an iterative scheme composed of three steps. First, we adaptively distribute samples in the image plane. Second, we denoise the image using a non-linear filter. Third, we estimate the residual per-pixel error of the filtered rendering, and the error estimate guides the sample distribution in the next iteration. The effectiveness of our approach hinges on the use of a state of the art image denoising technique, which we extend to an adaptive rendering framework. A key idea is to split the Monte Carlo samples into two buffers. This improves denoising performance and facilitates variance and error estimation. Our method relies only on the Monte Carlo samples, allowing us to handle arbitrary light transport and lens effects. In addition, it is robust to high noise levels and complex image content. We compare our approach to a state of the art adaptive rendering technique based on adaptive bandwidth selection and demonstrate substantial improvements in terms of both numerical error and visual quality. Our framework is easy to implement on top of standard Monte Carlo renderers and it incurs little computational overhead.

Iterative Spectral Unmixing for Optimizing Per-Pixel Endmember Sets

Fractional abundances predicted for a given pixel using spectral mixture analysis (SMA) are most accurate when only the endmembers that comprise it are used, with larger errors occurring if inappropriate endmembers are included in the unmixing process. This paper presents an iterative implementation of SMA (ISMA) to determine optimal per-pixel endmember sets from the image endmember set using two steps: 1) an iterative unconstrained unmixing, which removes one endmember per iteration based on minimum abundance and 2) analysis of the root-mean-square error as a function of iteration to locate the critical iteration defining the optimal endmember set. The ISMA was tested using simulated data at various signal-to-noise ratios (SNRs), and the results were compared with those of published unmixing methods. The ISMA method correctly selected the optimal endmember set 96% of the time for SNR of 100 : 1. As a result, per-pixel errors in fractional abundances were lower than for unmixing each pixel using the full endmember set. ISMA was also applied to Airborne Visible/Infrared Imaging Spectrometer hyperspectral data of Cuprite, NV. Results show that the ISMA is effective in obtaining abundance fractions that are physically realistic (sum close to one and nonnegative) and is more effective at selecting endmembers that occur within a pixel as opposed to those that are simply used to improve the goodness of fit of the model but not part of the mixture

Error analysis and performance optimization of fast hierarchical backprojection algorithms

We recently proposed a novel fast backprojection algorithm for reconstruction of an N x N pixel object from O(N) projections in O(N(2)log(2)N) operations. In this paper, we analyze a simplified version of that algorithm, to determine the effects of various parameter choices on the algorithm's theoretical performance. We derive a bound on the variance of the per-pixel error introduced by using hierarchical backprojection. This bound is with respect to an ensemble of input sinograms, and allows us to construct confidence intervals (for any specified level) for the per-pixel errors. The bound has a simple form, and we show how to use it to select algorithm parameters for different cost versus error tradeoffs. Simulation results show that the bound accurately predicts the performance of the algorithm over a wide range of parameter choices. These results are verified for different images, including a tomographic reconstruction from the visual human dataset (VHD). The analysis therefore provides an effective tool for the selection of parameters and operating point for the fast hierarchical backprojection algorithm.