468 research outputs found
Wavelet and FFT Based Image Denoising Using Non-linear Filters
We propose a stationary and discrete wavelet based image denoising scheme and an FFTbased image denoising scheme to remove Gaussian noise. In the first approach, high subbands are added with each other and then soft thresholding is performed. The sum of low subbands is filtered with either piecewise linear (PWL) or Lagrange or spline interpolated PWL filter. In the second approach, FFT is employed on the noisy image and then low frequency and high frequency coefficients are separated with a specified cutoff frequency.Then the inverse of low frequency components is filtered with one of the PWL filters and the inverse of high frequency components is filtered with soft thresholding. The experimental results are compared with Liu and Liu's tensor-based diffusion model (TDM) approach
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Image interpolation using Shearlet based iterative refinement
This paper proposes an image interpolation algorithm exploiting sparse
representation for natural images. It involves three main steps: (a) obtaining
an initial estimate of the high resolution image using linear methods like FIR
filtering, (b) promoting sparsity in a selected dictionary through iterative
thresholding, and (c) extracting high frequency information from the
approximation to refine the initial estimate. For the sparse modeling, a
shearlet dictionary is chosen to yield a multiscale directional representation.
The proposed algorithm is compared to several state-of-the-art methods to
assess its objective as well as subjective performance. Compared to the cubic
spline interpolation method, an average PSNR gain of around 0.8 dB is observed
over a dataset of 200 images
Peak Transform for Efficient Image Representation and Coding
Digital Object Identifier 10.1109/TIP.2007.896599In this work, we introduce a nonlinear geometric transform, called peak transform (PT), for efficient image representation
and coding. The proposed PT is able to convert
high-frequency signals into low-frequency ones, making them much easier to be compressed. Coupled with wavelet transform
and subband decomposition, the PT is able to significantly reduce signal energy in high-frequency subbands and achieve a significant transform coding gain. This has important applications in efficient
data representation and compression. To maximize the transform coding gain, we develop a dynamic programming solution for
optimum PT design. Based on PT, we design an image encoder, called the PT encoder, for efficient image compression. Our extensive
experimental results demonstrate that, in wavelet-based subband decomposition, the signal energy in high-frequency subbands can be reduced by up to 60% if a PT is applied. The
PT image encoder outperforms state-of-the-art JPEG2000 and H.264 (INTRA) encoders by up to 2-3 dB in peak signal-to-noise ratio (PSNR), especially for images with a significant amount
of high-frequency components. Our experimental results also show that the proposed PT is able to efficiently capture and preserve high-frequency image features (e.g., edges) and yields significantly improved visual quality
FRESH – FRI-based single-image super-resolution algorithm
In this paper, we consider the problem of single image super-resolution and propose a novel algorithm that outperforms state-of-the-art methods without the need of learning patches pairs from external data sets. We achieve this by modeling images and, more precisely, lines of images as piecewise smooth functions and propose a resolution enhancement method for this type of functions. The method makes use of the theory of sampling signals with finite rate of innovation (FRI) and combines it with traditional linear reconstruction methods. We combine the two reconstructions by leveraging from the multi-resolution analysis in wavelet theory and show how an FRI reconstruction and a linear reconstruction can be fused using filter banks. We then apply this method along vertical, horizontal, and diagonal directions in an image to obtain a single-image super-resolution algorithm. We also propose a further improvement of the method based on learning from the errors of our super-resolution result at lower resolution levels. Simulation results show that our method outperforms state-of-the-art algorithms under different blurring kernels
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