359,251 research outputs found
Spectral Representations of One-Homogeneous Functionals
This paper discusses a generalization of spectral representations related to
convex one-homogeneous regularization functionals, e.g. total variation or
-norms. Those functionals serve as a substitute for a Hilbert space
structure (and the related norm) in classical linear spectral transforms, e.g.
Fourier and wavelet analysis. We discuss three meaningful definitions of
spectral representations by scale space and variational methods and prove that
(nonlinear) eigenfunctions of the regularization functionals are indeed atoms
in the spectral representation. Moreover, we verify further useful properties
related to orthogonality of the decomposition and the Parseval identity.
The spectral transform is motivated by total variation and further developed
to higher order variants. Moreover, we show that the approach can recover
Fourier analysis as a special case using an appropriate -type
functional and discuss a coupled sparsity example
Modeling Land-Cover Types Using Multiple Endmember Spectral Mixture Analysis in a Desert City
Spectral mixture analysis is probably the most commonly used approach among sub-pixel analysis techniques. This method models pixel spectra as a linear combination of spectral signatures from two or more ground components. However, spectral mixture analysis does not account for the absence of one of the surface features or spectral variation within pure materials since it utilizes an invariable set of surface features. Multiple endmember spectral mixture analysis (MESMA), which addresses these issues by allowing endmembers to vary on a per pixel basis, was employed in this study to model Landsat ETM+ reflectance in the Phoenix metropolitan area. Image endmember spectra of vegetation, soils, and impervious surfaces were collected with the use of a fine resolution Quickbird image and the pixel purity index. This study employed 204 (=3x17x4) total four-endmember models for the urban subset and 96 (=6x6x2x4) total five-endmember models for the non-urban subset to identify fractions of soil, impervious surface, vegetation, and shade. The Pearson correlation between the fraction outputs from MESMA and reference data from Quickbird 60 cm resolution data for soil, impervious, and vegetation were 0.8030, 0.8632, and 0.8496 respectively. Results from this study suggest that the MESMA approach is effective in mapping urban land covers in desert cities at sub- pixel level.
Exponential convergence to quasi-stationary distribution for absorbed one-dimensional diffusions with killing
This article studies the quasi-stationary behaviour of absorbed
one-dimensional diffusion processes with killing on . We obtain
criteria for the exponential convergence to a unique quasi-stationary
distribution in total variation, uniformly with respect to the initial
distribution. Our approach is based on probabilistic and coupling methods,
contrary to the classical approach based on spectral theory results. Our
general criteria apply in the case where is entrance and 0 either
regular or exit, and are proved to be satisfied under several explicit
assumptions expressed only in terms of the speed and killing measures. We also
obtain exponential ergodicity results on the -process. We provide several
examples and extensions, including diffusions with singular speed and killing
measures, general models of population dynamics, drifted Brownian motions and
some one-dimensional processes with jumps.Comment: arXiv admin note: text overlap with arXiv:1506.0238
Expressions for the nonlinear transmission performance of multi-mode optical fiber
We develop an analytical theory which allows us to identify the information spectral density limits of multimode optical fiber transmission systems. Our approach takes into account the Kerr-effect induced interactions of the propagating spatial modes and derives closed-form expressions for the spectral density of the corresponding nonlinear distortion. Experimental characterization results have confirmed the accuracy of the proposed models. Application of our theory in different FMF transmission scenarios has predicted a ~10% variation in total system throughput due to changes associated with inter-mode nonlinear interactions, in agreement with an observed 3dB increase in nonlinear noise power spectral density for a graded index four LP mode fiber
Hyperspectral Image Restoration via Total Variation Regularized Low-rank Tensor Decomposition
Hyperspectral images (HSIs) are often corrupted by a mixture of several types
of noise during the acquisition process, e.g., Gaussian noise, impulse noise,
dead lines, stripes, and many others. Such complex noise could degrade the
quality of the acquired HSIs, limiting the precision of the subsequent
processing. In this paper, we present a novel tensor-based HSI restoration
approach by fully identifying the intrinsic structures of the clean HSI part
and the mixed noise part respectively. Specifically, for the clean HSI part, we
use tensor Tucker decomposition to describe the global correlation among all
bands, and an anisotropic spatial-spectral total variation (SSTV)
regularization to characterize the piecewise smooth structure in both spatial
and spectral domains. For the mixed noise part, we adopt the norm
regularization to detect the sparse noise, including stripes, impulse noise,
and dead pixels. Despite that TV regulariztion has the ability of removing
Gaussian noise, the Frobenius norm term is further used to model heavy Gaussian
noise for some real-world scenarios. Then, we develop an efficient algorithm
for solving the resulting optimization problem by using the augmented Lagrange
multiplier (ALM) method. Finally, extensive experiments on simulated and
real-world noise HSIs are carried out to demonstrate the superiority of the
proposed method over the existing state-of-the-art ones.Comment: 15 pages, 20 figure
- …