1,980 research outputs found
Adaptive Fractal and Wavelet Image Denoising
The need for image enhancement and restoration is encountered in many practical applications. For instance, distortion due to additive white Gaussian noise (AWGN) can be caused by poor quality image acquisition, images observed in a noisy environment or noise inherent in communication channels. In this thesis, image denoising is investigated. After reviewing standard image denoising methods as applied in the spatial, frequency and wavelet domains of the noisy image, the thesis embarks on the endeavor of developing and experimenting with new image denoising methods based on fractal and wavelet transforms. In particular, three new image denoising methods are proposed: context-based wavelet thresholding, predictive fractal image denoising and fractal-wavelet image denoising. The proposed context-based thresholding strategy adopts localized hard and soft thresholding operators which take in consideration the content of an immediate neighborhood of a wavelet coefficient before thresholding it. The two fractal-based predictive schemes are based on a simple yet effective algorithm for estimating the fractal code of the original noise-free image from the noisy one. From this predicted code, one can then reconstruct a fractally denoised estimate of the original image. This fractal-based denoising algorithm can be applied in the pixel and the wavelet domains of the noisy image using standard fractal and fractal-wavelet schemes, respectively. Furthermore, the cycle spinning idea was implemented in order to enhance the quality of the fractally denoised estimates. Experimental results show that the proposed image denoising methods are competitive, or sometimes even compare favorably with the existing image denoising techniques reviewed in the thesis. This work broadens the application scope of fractal transforms, which have been used mainly for image coding and compression purposes
Simultaneous denoising and enhancement of signals by a fractal conservation law
In this paper, a new filtering method is presented for simultaneous noise
reduction and enhancement of signals using a fractal scalar conservation law
which is simply the forward heat equation modified by a fractional
anti-diffusive term of lower order. This kind of equation has been first
introduced by physicists to describe morphodynamics of sand dunes. To evaluate
the performance of this new filter, we perform a number of numerical tests on
various signals. Numerical simulations are based on finite difference schemes
or Fast and Fourier Transform. We used two well-known measuring metrics in
signal processing for the comparison. The results indicate that the proposed
method outperforms the well-known Savitzky-Golay filter in signal denoising.
Interesting multi-scale properties w.r.t. signal frequencies are exhibited
allowing to control both denoising and contrast enhancement
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
A statistical reduced-reference method for color image quality assessment
Although color is a fundamental feature of human visual perception, it has
been largely unexplored in the reduced-reference (RR) image quality assessment
(IQA) schemes. In this paper, we propose a natural scene statistic (NSS)
method, which efficiently uses this information. It is based on the statistical
deviation between the steerable pyramid coefficients of the reference color
image and the degraded one. We propose and analyze the multivariate generalized
Gaussian distribution (MGGD) to model the underlying statistics. In order to
quantify the degradation, we develop and evaluate two measures based
respectively on the Geodesic distance between two MGGDs and on the closed-form
of the Kullback Leibler divergence. We performed an extensive evaluation of
both metrics in various color spaces (RGB, HSV, CIELAB and YCrCb) using the TID
2008 benchmark and the FRTV Phase I validation process. Experimental results
demonstrate the effectiveness of the proposed framework to achieve a good
consistency with human visual perception. Furthermore, the best configuration
is obtained with CIELAB color space associated to KLD deviation measure
Denoising by multiwavelet singularity detection
Wavelet denoising by singularity detection was proposed as an algorithm that combines Mallat and Donoho’s denoising approaches. With wavelet transform modulus sum, we can avoid the error and ambiguities of tracing the modulus maxima across scales and the complicated and computationally demanding reconstruction process. We can also avoid the visual artifacts produced by shrinkage. In this paper, we investigate a multiwavelet denoising algorithm based on a modified singularity detection approach. Improved signal denoising results are obtained in comparison to the single wavelet case
Fractal Image Coding as Projections Onto Convex Sets
Abstract. We show how fractal image coding can be viewed and gen-eralized in terms of the method of projections onto convex sets (POCS). In this approach, the fractal code denes a set of spatial domain sim-ilarity constraints. We also show how such a reformulation in terms of POCS allows additional contraints to be imposed during fractal image decoding. Two applications are presented: image construction with an incomplete fractal code and image denoising.
- …