428 research outputs found
ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing
We present directional operator splitting schemes for the numerical solution of a fourth-order, nonlinear partial differential evolution equation which arises in image processing. This equation constitutes the H−1-gradient flow of the total variation and represents a prototype of higher-order equations of similar type which are popular in imaging for denoising, deblurring and inpainting problems. The efficient numerical solution of this equation is very challenging due to the stiffness of most numerical schemes. We show that the combination of directional splitting schemes with implicit time-stepping provides a stable and computationally cheap numerical realisation of the equation
Evolution-Operator-Based Single-Step Method for Image Processing
This work proposes an evolution-operator-based single-time-step
method for image and signal processing. The key component of the
proposed method is a local spectral evolution kernel (LSEK) that
analytically integrates a class of evolution partial differential
equations (PDEs). From the point of view PDEs, the LSEK provides
the analytical solution in a single time step, and is of spectral
accuracy, free of instability constraint. From the point of
image/signal processing, the LSEK gives rise to a family of
lowpass filters. These filters contain controllable time delay and
amplitude scaling. The new evolution operator-based method is
constructed by pointwise adaptation of anisotropy to the
coefficients of the LSEK. The Perona-Malik-type of anisotropic
diffusion schemes is incorporated in the LSEK for image denoising.
A forward-backward diffusion process is adopted to the LSEK for
image deblurring or sharpening. A coupled PDE system is modified
for image edge detection. The resulting image edge is utilized for
image enhancement. Extensive computer experiments are carried out
to demonstrate the performance of the proposed method. The major
advantages of the proposed method are its single-step solution and
readiness for multidimensional data analysis
Fast nonnegative least squares through flexible Krylov subspaces
Constrained least squares problems arise in a variety of applications, and
many iterative methods are already available to compute their solutions. This
paper proposes a new efficient approach to solve nonnegative linear least
squares problems. The associated KKT conditions are leveraged to form an
adaptively preconditioned linear system, which is then solved by a flexible
Krylov subspace method. The new method can be easily applied to image
reconstruction problems affected by both Gaussian and Poisson noise, where the
components of the solution represent nonnegative intensities. {Theoretical
insight is given, and} numerical experiments and comparisons are displayed in
order to validate the new method, which delivers results of equal or better
quality than many state-of-the-art methods for nonnegative least squares
solvers, with a significant speedup
Super Resolution of Wavelet-Encoded Images and Videos
In this dissertation, we address the multiframe super resolution reconstruction problem for wavelet-encoded images and videos. The goal of multiframe super resolution is to obtain one or more high resolution images by fusing a sequence of degraded or aliased low resolution images of the same scene. Since the low resolution images may be unaligned, a registration step is required before super resolution reconstruction. Therefore, we first explore in-band (i.e. in the wavelet-domain) image registration; then, investigate super resolution. Our motivation for analyzing the image registration and super resolution problems in the wavelet domain is the growing trend in wavelet-encoded imaging, and wavelet-encoding for image/video compression. Due to drawbacks of widely used discrete cosine transform in image and video compression, a considerable amount of literature is devoted to wavelet-based methods. However, since wavelets are shift-variant, existing methods cannot utilize wavelet subbands efficiently. In order to overcome this drawback, we establish and explore the direct relationship between the subbands under a translational shift, for image registration and super resolution. We then employ our devised in-band methodology, in a motion compensated video compression framework, to demonstrate the effective usage of wavelet subbands. Super resolution can also be used as a post-processing step in video compression in order to decrease the size of the video files to be compressed, with downsampling added as a pre-processing step. Therefore, we present a video compression scheme that utilizes super resolution to reconstruct the high frequency information lost during downsampling. In addition, super resolution is a crucial post-processing step for satellite imagery, due to the fact that it is hard to update imaging devices after a satellite is launched. Thus, we also demonstrate the usage of our devised methods in enhancing resolution of pansharpened multispectral images
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