Efficient Recursive Multichannel Blind Image Restoration
EURASIP Journal on Advances in Signal Processing
Hindawi Publishing Corporation
Efficient Recursive Multichannel Blind Image Restoration
Li Chen 0
Kim-Hui Yap 0
Yu He 0
0 Division of Information Engineering, School of Electrical and Electronic Engineering, Nanyang Technological University , 50 Nanyang Avenue , Singapore 639798
This paper presents a novel multichannel recursive filtering (MRF) technique to address blind image restoration. The primary motivation for developing the MRF algorithm to solve multichannel restoration is due to its fast convergence in joint blur identification and image restoration. The estimated image is recursively updated from its previous estimates using a regularization framework. The multichannel blurs are identified iteratively using conjugate gradient optimization. The proposed algorithm incorporates a forgetting factor to discard the old unreliable estimates, hence achieving better convergence performance. A key feature of the method is its computational simplicity and efficiency. This allows the method to be adopted readily in real-life applications. Experimental results show that it is effective in performing blind multichannel blind restoration.
1. INTRODUCTION
Image restoration deals with the estimation of the original
images from the observed blurred, degraded images using
the partial information about the imaging system. It is an
illposed problem as the uniqueness and stability of the solution
are not guaranteed [1]. In many applications such as remote
sensing and microscopy imaging, multiple degraded images
of a single scene become available while the blurring function
or point spread function (PSF) of each channel remains
unknown. Therefore, the recovery of the original scene from its
multiple observations is required and this problem is,
commonly, referred to as multichannel blind image restoration
[2].
Various researchers have investigated the problem of
multichannel image restoration over the years. With the
assumption that the multichannel PSFs are weakly coprime,
and in the absence of noise, the desired image and PSFs can
be transformed into the null space of a special matrix
constructed from the degraded images [3–6]. Centered on this
idea, several techniques have been proposed which include
greatest common divisor (GCD) [3], subspace-based [4, 5],
and eigenstructure-based approaches [6]. The GCD method
is based on the notion that the desired image can be regarded
as the polynomial GCD among the degraded images in the
z-domain. Subspace-based methods work by first estimating
the blurring function using a procedure of min-eigenvector,
followed by conventional image restoration using the
identified PSFs. In similar concept, eigenstructure-based algorithm
transforms the null space problem into a constrained
optimization framework and performs direct deconvolver
estimation. The aforementioned null space-based methods,
however, suffer from noise amplification, which often lead to
poor solutions in the noisy environments.
There are some successful works on the development
of multichannel restoration, which exploit the features of
single-channel restoration algorithms [7–15]. These
techniques develop a cost function within the framework of
constrained least squares minimization [7, 8]. The minimization
step involves two processes of blur identification and image
restoration centered on the principle of projection onto
convex sets (POCS). The alternating minimization (AM)
strategy is first proposed in [9], and later extended to double
Tikhonov regularization in [10, 11]. Double regularization
(DR) [12] and the Gauss-Markov random fields [13] have
also been applied in blind image restoration. Total
variation (TV) has been incorporated into the DR to achieve
edge preservation and noise suppression. A promising
attempt has been made by utilizing the blur null space as the
regularization term in the framework of TV [14]. Recently,
the extension of the Bussgang blind equalization algorithm
to iterative multichannel deconvolution has been proposed
in [15]. The basic idea is focused on Wiener filtering of the
observed degraded images, and updating the filters using a
nonlinear Bayesian estimation of the estimated image.
Generally speaking, these iterative methods are extensions of
single-channel blind image restorations approaches.
Therefore, if an extra degraded image becomes available at a later
stage, the iterative schemes will require a complete rerun,
rather than a recursive process to update the estimate. This
is, clearly, inflexible and computationally inefficient.
In view of this, we develop a new efficient algorithm
called multichannel recursive filtering (MRF) to solve blind
multichannel image restoration. To the best of our
knowledge, no previous work on recursive filtering has been
developed to address blind multichannel image restoration. The
estimated image is recursively updated from the previous
estimate using a regularization framework. All the operat (...truncated)