Projection-Based and Look Ahead Strategies for Atom Selection

In this paper, we improve iterative greedy search algorithms in which atoms are selected serially over iterations, i.e., one-by-one over iterations. For serial atom selection, we devise two new schemes to select an atom from a set of potential atoms in each iteration. The two new schemes lead to two new algorithms. For both the algorithms, in each iteration, the set of potential atoms is found using a standard matched filter. In case of the first scheme, we propose an orthogonal projection strategy that selects an atom from the set of potential atoms. Then, for the second scheme, we propose a look ahead strategy such that the selection of an atom in the current iteration has an effect on the future iterations. The use of look ahead strategy requires a higher computational resource. To achieve a trade-off between performance and complexity, we use the two new schemes in cascade and develop a third new algorithm. Through experimental evaluations, we compare the proposed algorithms with existing greedy search and convex relaxation algorithms.Comment: sparsity, compressive sensing; IEEE Trans on Signal Processing 201

Optimized kernel minimum noise fraction transformation for hyperspectral image classification

This paper presents an optimized kernel minimum noise fraction transformation (OKMNF) for feature extraction of hyperspectral imagery. The proposed approach is based on the kernel minimum noise fraction (KMNF) transformation, which is a nonlinear dimensionality reduction method. KMNF can map the original data into a higher dimensional feature space and provide a small number of quality features for classification and some other post processing. Noise estimation is an important component in KMNF. It is often estimated based on a strong relationship between adjacent pixels. However, hyperspectral images have limited spatial resolution and usually have a large number of mixed pixels, which make the spatial information less reliable for noise estimation. It is the main reason that KMNF generally shows unstable performance in feature extraction for classification. To overcome this problem, this paper exploits the use of a more accurate noise estimation method to improve KMNF. We propose two new noise estimation methods accurately. Moreover, we also propose a framework to improve noise estimation, where both spectral and spatial de-correlation are exploited. Experimental results, conducted using a variety of hyperspectral images, indicate that the proposed OKMNF is superior to some other related dimensionality reduction methods in most cases. Compared to the conventional KMNF, the proposed OKMNF benefits significant improvements in overall classification accuracy

A new kernel method for hyperspectral image feature extraction

Hyperspectral image provides abundant spectral information for remote discrimination of subtle differences in ground covers. However, the increasing spectral dimensions, as well as the information redundancy, make the analysis and interpretation of hyperspectral images a challenge. Feature extraction is a very important step for hyperspectral image processing. Feature extraction methods aim at reducing the dimension of data, while preserving as much information as possible. Particularly, nonlinear feature extraction methods (e.g. kernel minimum noise fraction (KMNF) transformation) have been reported to benefit many applications of hyperspectral remote sensing, due to their good preservation of high-order structures of the original data. However, conventional KMNF or its extensions have some limitations on noise fraction estimation during the feature extraction, and this leads to poor performances for post-applications. This paper proposes a novel nonlinear feature extraction method for hyperspectral images. Instead of estimating noise fraction by the nearest neighborhood information (within a sliding window), the proposed method explores the use of image segmentation. The approach benefits both noise fraction estimation and information preservation, and enables a significant improvement for classification. Experimental results on two real hyperspectral images demonstrate the efficiency of the proposed method. Compared to conventional KMNF, the improvements of the method on two hyperspectral image classification are 8 and 11%. This nonlinear feature extraction method can be also applied to other disciplines where high-dimensional data analysis is required

Linearized iterative least-squares (LIL): A parameter fitting algorithm for component separation in multifrequency CMB experiments such as Planck

We present an efficient algorithm for the least squares parameter fitting optimized for component separation in multi-frequency CMB experiments. We sidestep some of the problems associated with non-linear optimization by taking advantage of the quasi-linear nature of the foreground model. We demonstrate our algorithm, linearized iterative least-squares (LIL), on the publicly available Planck sky model FFP6 simulations and compare our result with the other algorithms. We work at full Planck resolution and show that degrading the resolution of all channels to that of the lowest frequency channel is not necessary. Finally we present results for the publicly available Planck data. Our algorithm is extremely fast, fitting 6 parameters to 7 lowest Planck channels at full resolution (50 million pixels) in less than 160 CPU-minutes (or few minutes running in parallel on few tens of cores). LIL is therefore easily scalable to future experiments which may have even higher resolution and more frequency channels. We also naturally propagate the uncertainties in different parameters due to noise in the maps as well as degeneracies between the parameters to the final errors on the parameters using Fisher matrix. One indirect application of LIL could be a front-end for Bayesian parameter fitting to find the maximum of the likelihood to be used as the starting point for the Gibbs sampling. We show for rare components, such as the carbon-monoxide emission, present in small fraction of sky, the optimal approach should combine parameter fitting with model selection. LIL may also be useful in other astrophysical applications which satisfy the quasi-linearity criteria.Comment: Accepted versio

CMBPol Mission Concept Study: Prospects for polarized foreground removal

In this report we discuss the impact of polarized foregrounds on a future CMBPol satellite mission. We review our current knowledge of Galactic polarized emission at microwave frequencies, including synchrotron and thermal dust emission. We use existing data and our understanding of the physical behavior of the sources of foreground emission to generate sky templates, and start to assess how well primordial gravitational wave signals can be separated from foreground contaminants for a CMBPol mission. At the estimated foreground minimum of ~100 GHz, the polarized foregrounds are expected to be lower than a primordial polarization signal with tensor-to-scalar ratio r=0.01, in a small patch (~1%) of the sky known to have low Galactic emission. Over 75% of the sky we expect the foreground amplitude to exceed the primordial signal by about a factor of eight at the foreground minimum and on scales of two degrees. Only on the largest scales does the polarized foreground amplitude exceed the primordial signal by a larger factor of about 20. The prospects for detecting an r=0.01 signal including degree-scale measurements appear promising, with 5 sigma_r ~0.003 forecast from multiple methods. A mission that observes a range of scales offers better prospects from the foregrounds perspective than one targeting only the lowest few multipoles. We begin to explore how optimizing the composition of frequency channels in the focal plane can maximize our ability to perform component separation, with a range of typically 40 < nu < 300 GHz preferred for ten channels. Foreground cleaning methods are already in place to tackle a CMBPol mission data set, and further investigation of the optimization and detectability of the primordial signal will be useful for mission design.Comment: 42 pages, 14 figures, Foreground Removal Working Group contribution to the CMBPol Mission Concept Study, v2, matches AIP versio

Robust Inversion Methods for Aerosol Spectroscopy

The Fast Aerosol Spectrometer (FASP) is a device for spectral aerosol measurements. Its purpose is to safely monitor the atmosphere inside a reactor containment. First we describe the FASP and explain its basic physical laws. Then we introduce our reconstruction methods for aerosol particle size distributions designed for the FASP. We extend known existence results for constrained Tikhonov regularization by uniqueness criteria and use those to generate reasonable models for the size distributions. We apply a Bayesian model-selection framework on these pre-generated models. We compare our algorithm with classical inversion methods using simulated measurements. We then extend our reconstruction algorithm for two-component aerosols, so that we can simultaneously retrieve their particle-size distributions and unknown volume fractions of their two components. Finally we present the results of a numerical study for the extended algorithm.Comment: 37 pages, 3 figure