23-05-2012, 12:06 PM
Image Resolution Enhancement Using Dual-tree
Complex Wavelet Transform
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Abstract
In this letter, a complex wavelet-domain image resolution enhancement algorithm based on the estimation of wavelet
coefficients is proposed. The method uses forward and inverse dual-tree complex wavelet transform (DT-CWT) to construct
the high-resolution (HR) image from the given low-resolution (LR) image. The HR image is reconstructed from the LR image
together with a set of wavelet coefficients using the inverse dual-tree complex wavelet transform (IDT-CWT). The set of wavelet
coefficients is estimated from the DT-CWT decomposition of the rough estimation of the HR image. Results are presented and
discussed on very high-resolution QuickBird data, through comparisons between state-of-the-art resolution enhancement methods.
INTRODUCTION
Image resolution enhancement is a usable preprocess for many satellite image processing applications, such as vehicle
recognition, bridge recognition, and building recognition to name a few. Image resolution enhancement techniques can be
categorized into two major classes according to the domain they are applied in: 1) image-domain; and 2) transform-domain.
The techniques in image-domain use the statistical and geometric data directly extracted from the input image itself [1], [2],
while transform-domain techniques use transformations such as decimated discrete wavelet transform to achieve the image
resolution enhancement [3]–[6].
The decimated discrete wavelet transform (DWT) has been widely used for performing image resolution enhancement [3]–
[5]. A common assumption of DWT-based image resolution enhancement is that the low-resolution (LR) image is the low-pass
filtered subband of the wavelet-transformed high-resolution (HR) image. This type of approach requires the estimationof wavelet
coefficients in subbands containing high-pass spatial frequency information in order to estimate the HR image from the LR
image.
EXPERIMENTAL RESULTS
In the experiments, the natural colour (R, G, and B), 60 centimeter (2 foot) high-resolution QuickBird satellite image data
is used. The QuickBird data was acquired over Wall Street and the southern tip of Manhattan on April 24, 2009. A test
image of size 256 × 512 pixel at the resolution of 60 cm are cropped from the raw image as shown in Fig. 1 (a), and is
used as the reference image. In order to obtain a performance metric in addition to visual assessment of the results using
different resolution enhancement methods, we take a 256×512 image, XH, filter it with 3×3 averaging (low-pass) filter, and
down-sample it to obtain two available LR images X
(2)
L and X
(4)
L of sizes 128 × 256 and 64 × 128 pixels, respectively. The
available LR images are shown in Fig. 1 (b) and 1 ©. The superscripts 2 and 4 denote the down-sample factor. The resolution
enhancement methods are applied on LR images X
(2)
L and X
(4)
L to reconstruct an estimate ˆX H of the known HR image XH.
The original HR image XH and the reconstructed HR image ˆX H are then compared qualitatively and quantitatively. In this
letter, images consisting of three spectral bands that correspond to R, G and B channels in natural colour image representation,
are used and resolution enhancement methods are applied to
each spectral band of LR image XL independently to reconstruct an estimate of the reference image.
CONCLUSION
A method for image resolution enhancement from a single low-resolution image using the dual-tree complex wavelet is
presented. The initial rough estimate of the high-resolution image is decomposed to estimate the complex-valued high-pass
wavelet coefficients for the input low-resolution image. Estimated complex wavelet coefficients are used together with the
input low-resolution image to reconstruct the resultant high-resolution image by employing inverse dual-tree complex wavelet
transform.
Extensive tests and comparisons with the state-of-the-art methods show the superiority of the method presented in this letter.
The proposed resolution enhancement method retains both intensity and geometric features of the low-resolution image.