401 research outputs found
Partially Linear Estimation with Application to Sparse Signal Recovery From Measurement Pairs
We address the problem of estimating a random vector X from two sets of
measurements Y and Z, such that the estimator is linear in Y. We show that the
partially linear minimum mean squared error (PLMMSE) estimator does not require
knowing the joint distribution of X and Y in full, but rather only its
second-order moments. This renders it of potential interest in various
applications. We further show that the PLMMSE method is minimax-optimal among
all estimators that solely depend on the second-order statistics of X and Y. We
demonstrate our approach in the context of recovering a signal, which is sparse
in a unitary dictionary, from noisy observations of it and of a filtered
version of it. We show that in this setting PLMMSE estimation has a clear
computational advantage, while its performance is comparable to
state-of-the-art algorithms. We apply our approach both in static and dynamic
estimation applications. In the former category, we treat the problem of image
enhancement from blurred/noisy image pairs, where we show that PLMMSE
estimation performs only slightly worse than state-of-the art algorithms, while
running an order of magnitude faster. In the dynamic setting, we provide a
recursive implementation of the estimator and demonstrate its utility in the
context of tracking maneuvering targets from position and acceleration
measurements.Comment: 13 pages, 5 figure
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
Data-Driven Image Restoration
Every day many images are taken by digital cameras, and people
are demanding visually accurate and pleasing result. Noise and
blur degrade images captured by modern cameras, and high-level
vision tasks (such as segmentation, recognition, and tracking)
require high-quality images. Therefore, image restoration
specifically, image
deblurring and image denoising is a critical preprocessing step.
A fundamental problem in image deblurring is to recover reliably
distinct spatial frequencies that have been suppressed by the
blur kernel. Existing image deblurring techniques often rely on
generic image priors that only help recover part of the frequency
spectrum, such as the frequencies near the high-end. To this end,
we pose the following specific questions: (i) Does class-specific
information offer an advantage over existing generic priors for
image quality restoration? (ii) If a class-specific prior exists,
how should it be encoded into a deblurring framework to recover
attenuated image frequencies? Throughout this work, we devise a
class-specific prior based on the band-pass filter responses and
incorporate it into a deblurring strategy. Specifically, we show
that the subspace of band-pass filtered images and their
intensity distributions serve as useful priors for recovering
image frequencies.
Next, we present a novel image denoising algorithm that uses
external, category specific image database. In contrast to
existing noisy image restoration algorithms, our method selects
clean image “support patches” similar to the noisy patch from
an external database. We employ a content adaptive distribution
model for each patch where we derive the parameters of the
distribution from the support patches. Our objective function
composed of a Gaussian fidelity term that imposes category
specific information, and a low-rank term that encourages the
similarity between the noisy and the support patches in a robust
manner.
Finally, we propose to learn a fully-convolutional network model
that consists of a Chain of Identity Mapping Modules (CIMM) for
image denoising. The CIMM structure possesses two distinctive
features that are important for the noise removal task. Firstly,
each residual unit employs identity mappings as the skip
connections and receives pre-activated input to preserve the
gradient magnitude propagated in both the forward and backward
directions. Secondly, by utilizing dilated kernels for the
convolution layers in the residual branch, each neuron in the
last convolution layer of each module can observe the full
receptive field of the first layer
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
Convolutional Deblurring for Natural Imaging
In this paper, we propose a novel design of image deblurring in the form of
one-shot convolution filtering that can directly convolve with naturally
blurred images for restoration. The problem of optical blurring is a common
disadvantage to many imaging applications that suffer from optical
imperfections. Despite numerous deconvolution methods that blindly estimate
blurring in either inclusive or exclusive forms, they are practically
challenging due to high computational cost and low image reconstruction
quality. Both conditions of high accuracy and high speed are prerequisites for
high-throughput imaging platforms in digital archiving. In such platforms,
deblurring is required after image acquisition before being stored, previewed,
or processed for high-level interpretation. Therefore, on-the-fly correction of
such images is important to avoid possible time delays, mitigate computational
expenses, and increase image perception quality. We bridge this gap by
synthesizing a deconvolution kernel as a linear combination of Finite Impulse
Response (FIR) even-derivative filters that can be directly convolved with
blurry input images to boost the frequency fall-off of the Point Spread
Function (PSF) associated with the optical blur. We employ a Gaussian low-pass
filter to decouple the image denoising problem for image edge deblurring.
Furthermore, we propose a blind approach to estimate the PSF statistics for two
Gaussian and Laplacian models that are common in many imaging pipelines.
Thorough experiments are designed to test and validate the efficiency of the
proposed method using 2054 naturally blurred images across six imaging
applications and seven state-of-the-art deconvolution methods.Comment: 15 pages, for publication in IEEE Transaction Image Processin
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