47 research outputs found
A Method for Finding Structured Sparse Solutions to Non-negative Least Squares Problems with Applications
Demixing problems in many areas such as hyperspectral imaging and
differential optical absorption spectroscopy (DOAS) often require finding
sparse nonnegative linear combinations of dictionary elements that match
observed data. We show how aspects of these problems, such as misalignment of
DOAS references and uncertainty in hyperspectral endmembers, can be modeled by
expanding the dictionary with grouped elements and imposing a structured
sparsity assumption that the combinations within each group should be sparse or
even 1-sparse. If the dictionary is highly coherent, it is difficult to obtain
good solutions using convex or greedy methods, such as non-negative least
squares (NNLS) or orthogonal matching pursuit. We use penalties related to the
Hoyer measure, which is the ratio of the and norms, as sparsity
penalties to be added to the objective in NNLS-type models. For solving the
resulting nonconvex models, we propose a scaled gradient projection algorithm
that requires solving a sequence of strongly convex quadratic programs. We
discuss its close connections to convex splitting methods and difference of
convex programming. We also present promising numerical results for example
DOAS analysis and hyperspectral demixing problems.Comment: 38 pages, 14 figure
A Homotopy-based Algorithm for Sparse Multiple Right-hand Sides Nonnegative Least Squares
Nonnegative least squares (NNLS) problems arise in models that rely on
additive linear combinations. In particular, they are at the core of
nonnegative matrix factorization (NMF) algorithms. The nonnegativity constraint
is known to naturally favor sparsity, that is, solutions with few non-zero
entries. However, it is often useful to further enhance this sparsity, as it
improves the interpretability of the results and helps reducing noise. While
the -"norm", equal to the number of non-zeros entries in a vector, is a
natural sparsity measure, its combinatorial nature makes it difficult to use in
practical optimization schemes. Most existing approaches thus rely either on
its convex surrogate, the -norm, or on heuristics such as greedy
algorithms. In the case of multiple right-hand sides NNLS (MNNLS), which are
used within NMF algorithms, sparsity is often enforced column- or row-wise, and
the fact that the solution is a matrix is not exploited. In this paper, we
first introduce a novel formulation for sparse MNNLS, with a matrix-wise
sparsity constraint. Then, we present a two-step algorithm to tackle
this problem. The first step uses a homotopy algorithm to produce the whole
regularization path for all the -penalized NNLS problems arising in
MNNLS, that is, to produce a set of solutions representing different tradeoffs
between reconstruction error and sparsity. The second step selects solutions
among these paths in order to build a sparsity-constrained matrix that
minimizes the reconstruction error. We illustrate the advantages of our
proposed algorithm for the unmixing of facial and hyperspectral images.Comment: 20 pages + 7 pages supplementary materia
Image Processing and Machine Learning for Hyperspectral Unmixing: An Overview and the HySUPP Python Package
Spectral pixels are often a mixture of the pure spectra of the materials,
called endmembers, due to the low spatial resolution of hyperspectral sensors,
double scattering, and intimate mixtures of materials in the scenes. Unmixing
estimates the fractional abundances of the endmembers within the pixel.
Depending on the prior knowledge of endmembers, linear unmixing can be divided
into three main groups: supervised, semi-supervised, and unsupervised (blind)
linear unmixing. Advances in Image processing and machine learning
substantially affected unmixing. This paper provides an overview of advanced
and conventional unmixing approaches. Additionally, we draw a critical
comparison between advanced and conventional techniques from the three
categories. We compare the performance of the unmixing techniques on three
simulated and two real datasets. The experimental results reveal the advantages
of different unmixing categories for different unmixing scenarios. Moreover, we
provide an open-source Python-based package available at
https://github.com/BehnoodRasti/HySUPP to reproduce the results
スペクトルの線形性を考慮したハイパースペクトラル画像のノイズ除去とアンミキシングに関する研究
This study aims to generalize color line to M-dimensional spectral line feature (M>3) and introduce methods for denoising and unmixing of hyperspectral images based on the spectral linearity.For denoising, we propose a local spectral component decomposition method based on the spectral line. We first calculate the spectral line of an M-channel image, then using the line, we decompose the image into three components: a single M-channel image and two gray-scale images. By virtue of the decomposition, the noise is concentrated on the two images, thus the algorithm needs to denoise only two grayscale images, regardless of the number of channels. For unmixing, we propose an algorithm that exploits the low-rank local abundance by applying the unclear norm to the abundance matrix for local regions of spatial and abundance domains. In optimization problem, the local abundance regularizer is collaborated with the L2, 1 norm and the total variation.北九州市立大
A convex model for non-negative matrix factorization and dimensionality reduction on physical space
A collaborative convex framework for factoring a data matrix into a
non-negative product , with a sparse coefficient matrix , is proposed.
We restrict the columns of the dictionary matrix to coincide with certain
columns of the data matrix , thereby guaranteeing a physically meaningful
dictionary and dimensionality reduction. We use regularization
to select the dictionary from the data and show this leads to an exact convex
relaxation of in the case of distinct noise free data. We also show how
to relax the restriction-to- constraint by initializing an alternating
minimization approach with the solution of the convex model, obtaining a
dictionary close to but not necessarily in . We focus on applications of the
proposed framework to hyperspectral endmember and abundances identification and
also show an application to blind source separation of NMR data.Comment: 14 pages, 9 figures. EE and JX were supported by NSF grants
{DMS-0911277}, {PRISM-0948247}, MM by the German Academic Exchange Service
(DAAD), SO and MM by NSF grants {DMS-0835863}, {DMS-0914561}, {DMS-0914856}
and ONR grant {N00014-08-1119}, and GS was supported by NSF, NGA, ONR, ARO,
DARPA, and {NSSEFF.
Recommended from our members
Hyperspectral unmixing: a theoretical aspect and applications to CRISM data processing
Hyperspectral imaging has been deployed in earth and planetary remote sensing, and has contributed the development of new methods for monitoring the earth environment and new discoveries in planetary science. It has given scientists and engineers a new way to observe the surface of earth and planetary bodies by measuring the spectroscopic spectrum at a pixel scale.
Hyperspectal images require complex processing before practical use. One of the important goals of hyperspectral imaging is to obtain the images of reflectance spectrum. A raw image obtained by hyperspectral remote sensing usually undergoes conversion to a physical quantity representing the intensity of light energy, called radiance. In order to obtain the reflectance spectrum of surface, the contribution of atmosphere needs to be addressed and then divided by a spectrum of ``white reference.\u27\u27 Furthermore, the obtained reflectance spectra of image pixels are likely to be the mixtures of multiple species due to limited spatial resolution from orbits around planets.
Hyperspectral unmixing is an attempt to unmix those pixels - to identify substantial components and estimate their fractional abundances. Hyperspectral unmixing has been widely explored in the literature, but there are still many aspects yet to be studied. The majority of research focuses on the development of methods to retrieve correct substantial components and accurate fractional abundances. Their theoretical aspects are rarely investigated. Chapter 2 will pursue a theoretical aspect of sparse unmixing, one of the hyperspectral unmixing problems and derive its theoretical conditions that guarantee the correct identification of substantial components.
Hyperspectral unmixing can also be used for other stages of hyperspectral data processing. Chapter 3 explores the application of hyperspectral unmixing to the processing of hyperspectral image acquired by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) onboard the Mars Reconnaissance Orbiter (MRO). In particular, new atmospheric correction and de-noising methods for the CRISM data that use a hyperspectral unmixing to model surface spectra, are introduced. The new methods remove most of the problematic systematic artifacts present in CRISM images and significantly improve signal quality.
Chapter 4 investigates how hyperspectral images acquired from orbits can be combined with ground exploration. In the recent rush of the launch of many Martian ground rover missions, it is important to effectively integrate knowledge obtained by hyperspectral remote sensing from orbits into ground exploration for facilitating Martian exploration. In specific, this dissertation solves the problem of matching hyperspectral image pixels obtained by the CRISM with ground mega-pixel images acquired by the Mast Camera (Mastcam) installed on the Curiosity rover on Mars. A new systematic methodology to map the CRISM and Mastcam images onto high resolution surface topography is developed
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1