10,737 research outputs found
Sparse kernel density estimation technique based on zero-norm constraint
A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance
Recent Progress in Image Deblurring
This paper comprehensively reviews the recent development of image
deblurring, including non-blind/blind, spatially invariant/variant deblurring
techniques. Indeed, these techniques share the same objective of inferring a
latent sharp image from one or several corresponding blurry images, while the
blind deblurring techniques are also required to derive an accurate blur
kernel. Considering the critical role of image restoration in modern imaging
systems to provide high-quality images under complex environments such as
motion, undesirable lighting conditions, and imperfect system components, image
deblurring has attracted growing attention in recent years. From the viewpoint
of how to handle the ill-posedness which is a crucial issue in deblurring
tasks, existing methods can be grouped into five categories: Bayesian inference
framework, variational methods, sparse representation-based methods,
homography-based modeling, and region-based methods. In spite of achieving a
certain level of development, image deblurring, especially the blind case, is
limited in its success by complex application conditions which make the blur
kernel hard to obtain and be spatially variant. We provide a holistic
understanding and deep insight into image deblurring in this review. An
analysis of the empirical evidence for representative methods, practical
issues, as well as a discussion of promising future directions are also
presented.Comment: 53 pages, 17 figure
Bayesian Estimation for Continuous-Time Sparse Stochastic Processes
We consider continuous-time sparse stochastic processes from which we have
only a finite number of noisy/noiseless samples. Our goal is to estimate the
noiseless samples (denoising) and the signal in-between (interpolation
problem).
By relying on tools from the theory of splines, we derive the joint a priori
distribution of the samples and show how this probability density function can
be factorized. The factorization enables us to tractably implement the maximum
a posteriori and minimum mean-square error (MMSE) criteria as two statistical
approaches for estimating the unknowns. We compare the derived statistical
methods with well-known techniques for the recovery of sparse signals, such as
the norm and Log (- relaxation) regularization
methods. The simulation results show that, under certain conditions, the
performance of the regularization techniques can be very close to that of the
MMSE estimator.Comment: To appear in IEEE TS
Regularized linear system identification using atomic, nuclear and kernel-based norms: the role of the stability constraint
Inspired by ideas taken from the machine learning literature, new
regularization techniques have been recently introduced in linear system
identification. In particular, all the adopted estimators solve a regularized
least squares problem, differing in the nature of the penalty term assigned to
the impulse response. Popular choices include atomic and nuclear norms (applied
to Hankel matrices) as well as norms induced by the so called stable spline
kernels. In this paper, a comparative study of estimators based on these
different types of regularizers is reported. Our findings reveal that stable
spline kernels outperform approaches based on atomic and nuclear norms since
they suitably embed information on impulse response stability and smoothness.
This point is illustrated using the Bayesian interpretation of regularization.
We also design a new class of regularizers defined by "integral" versions of
stable spline/TC kernels. Under quite realistic experimental conditions, the
new estimators outperform classical prediction error methods also when the
latter are equipped with an oracle for model order selection
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