242 research outputs found
FastMMD: Ensemble of Circular Discrepancy for Efficient Two-Sample Test
The maximum mean discrepancy (MMD) is a recently proposed test statistic for
two-sample test. Its quadratic time complexity, however, greatly hampers its
availability to large-scale applications. To accelerate the MMD calculation, in
this study we propose an efficient method called FastMMD. The core idea of
FastMMD is to equivalently transform the MMD with shift-invariant kernels into
the amplitude expectation of a linear combination of sinusoid components based
on Bochner's theorem and Fourier transform (Rahimi & Recht, 2007). Taking
advantage of sampling of Fourier transform, FastMMD decreases the time
complexity for MMD calculation from to , where and
are the size and dimension of the sample set, respectively. Here is the
number of basis functions for approximating kernels which determines the
approximation accuracy. For kernels that are spherically invariant, the
computation can be further accelerated to by using the Fastfood
technique (Le et al., 2013). The uniform convergence of our method has also
been theoretically proved in both unbiased and biased estimates. We have
further provided a geometric explanation for our method, namely ensemble of
circular discrepancy, which facilitates us to understand the insight of MMD,
and is hopeful to help arouse more extensive metrics for assessing two-sample
test. Experimental results substantiate that FastMMD is with similar accuracy
as exact MMD, while with faster computation speed and lower variance than the
existing MMD approximation methods
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
Multispectral and Hyperspectral Image Fusion by MS/HS Fusion Net
Hyperspectral imaging can help better understand the characteristics of
different materials, compared with traditional image systems. However, only
high-resolution multispectral (HrMS) and low-resolution hyperspectral (LrHS)
images can generally be captured at video rate in practice. In this paper, we
propose a model-based deep learning approach for merging an HrMS and LrHS
images to generate a high-resolution hyperspectral (HrHS) image. In specific,
we construct a novel MS/HS fusion model which takes the observation models of
low-resolution images and the low-rankness knowledge along the spectral mode of
HrHS image into consideration. Then we design an iterative algorithm to solve
the model by exploiting the proximal gradient method. And then, by unfolding
the designed algorithm, we construct a deep network, called MS/HS Fusion Net,
with learning the proximal operators and model parameters by convolutional
neural networks. Experimental results on simulated and real data substantiate
the superiority of our method both visually and quantitatively as compared with
state-of-the-art methods along this line of research.Comment: 10 pages, 7 figure
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