In this paper, we present an algorithm for image registration utilizing the shearlet representation. The shearlet framework allows one to collect multi-scale and multi-directional feature information from multidimensional data that can be used to create key feature vectors that are scale, rotation, and shift invariant. These key feature vectors produce a transformation that will align the sensed image to the source image. We demonstrate our registration algorithm on various medical databases.
An experimental investigation of super-resolution imaging from measurements of projections onto a random
basis is presented. In particular, a laboratory imaging system was constructed following an architecture that
has become familiar from the theory of compressive sensing. The system uses a digital micromirror array
located at an intermediate image plane to introduce binary matrices that represent members of a basis set.
The system model was developed from experimentally acquired calibration data which characterizes the system
output corresponding to each individual mirror in the array. Images are reconstructed at a resolution limited
by that of the micromirror array using the split Bregman approach to total-variation regularized optimization.
System performance is evaluated qualitatively as a function of the size of the basis set, or equivalently, the
number of snapshots applied in the reconstruction.
In a recent work, it was shown that the shearlet representation provides a useful formula for the reconstruction of 3D objects from their X-ray projections. One major advantage of this approach is that it yields a near-optimal rate of convergence in estimating piecewise smooth objects from 3D X-ray projections which are corrupted by white Gaussian noise. In this work, we provide numerical demonstrations to illustrate the effectiveness of this method and its performance as compared with other X-ray data restoration algorithms.
In this work, we present a new approach to image denoising derived from the general framework of wavelets
with composite dilations. This framework extends the traditional wavelet approach by allowing for waveforms
to be defined not only at various scales and locations but also according to various orthogonal transformations
such as shearing transformations. The shearlet representation is, perhaps, the most widely known example of
wavelets with composite dilations. However, many other representations are obtained within this framework,
where directionality properties are controlled by different types of orthogonal matrices, such as the newly defined
hyperbolets. In this paper, we show how to take advantage of different wavelets with composite dilations to
sparsely represent important features such as edges and texture independently, and apply these techniques to
derive improved algorithms for image denoising.
Volumetric data acquisition and increasingly massive data storage have increased the need to develop better
analysis tools for three-dimensional data sets. These volumetric data sets can provide information beyond that
contained in standard two-dimensional images. Common strategies to deal with such data sets have been based
on sequential use of two-dimensional analysis tools. In this work, we propose using an extension of the wavelet
transform known as the shearlet transform for the purpose of edge analysis and detection in three-dimensions.
This method takes advantage of the shearlet transform's improved capability to identify edges compared to
In this work, we present a new approach for the problem of interferometric phase noise reduction in synthetic
aperture radar interferometry based on the shearlet representation. Shearlets provide a multidirectional and
multiscale decomposition that have advantages when dealing with noisy phase fringes over standard filtering
methods. Using a shearlet decomposition of a noisy phase image, we can adaptively estimate a phase representation
in a multiscale and anisotropic fashion. Such denoised phase interferograms can be used to provide
much better digital elevation maps (DEM). Experiments show that this method performs significantly better
than many competitive methods.
In this paper, we present a new approach for inverse halftoning of error diffused halftones using a shearlet representation.
We formulate inverse halftoning as a deconvolution problem using Kite et al.'s linear approximation
model for error diffusion halftoning. Our method is based on a new M-channel implementation of the shearlet
transform. By formulating the problem as a linear inverse problem and taking advantage of unique properties
of an implementation of the shearlet transform, we project the halftoned image onto a shearlet representation.
We then adaptively estimate a gray-scaled image from these shearlet-toned or shear-tone basis elements in a
multi-scale and anisotropic fashion. Experiments show that, the performance of our method improves upon
many of the state-of-the-art inverse halftoning routines, including a wavelet-based method and a method that
shares some similarities to a shearlet-type decomposition known as the local polynomial approximation (LPA)
Many imaging modalities, such as Synthetic Aperture Radar (SAR), can be described mathematically as collecting
data in a Radon transform domain. The process of inverting the Radon transform to form an image can be unstable when the data collected contain noise so that the inversion needs to be regularized in some way. In this work, we develop a method for inverting the Radon transform using a shearlet-based decomposition, which provides a regularization that is nearly optimal for a general class of images. We then show through a variety of examples that this technique performs better than similar competitive methods based on the use of the wavelet and the curvelet transforms.
In this work, we present new methods for creating M-channel directional filters to construct multiresolution
and multidirectional orthogonal/biorthogonal transforms. A key feature of these methods is the ability to solve
the polynomial Bezout equation in higher dimensions by taking advantage of solutions that have been proposed
for solving a related equation known as the analytic Bezout equation. These new techniques are capable of
creating directional filters that yield spatial-frequency tilings equivalent to those of the contourlet and the
shearlet transforms. Such directional filter banks can create sparse representations for a large class of images
and can be used for various restoration problems, compression schemes, and image enhancements.
Many improvements of wavelet-based restoration techniques suggest the use of the total variation (TV) algorithm.
The concept of combining wavelet and total variation methods seems effective but the reasons for the success
of this combination have been so far poorly understood. We propose a variation of the total variation method
designed to avoid artifacts such as oil painting effects and is more suited than the standard TV techniques to be
implemented with wavelet-based estimates. We then illustrate the effectiveness of this new TV-based method
using some of the latest wavelet transforms such as contourlets and shearlets.
We present techniques for performing image reconstruction based on
deconvolution in the Radon domain. To deal with a variety of possible
boundary conditions, we work with a corresponding generalized discrete
Radon transform in order to obtain projection slices for deconvolution. By estimating the projections using wavelet techniques, we are able to do deconvolution directly in a ridgelet domain. We also show how this method can be carried out locally, so that deconvolution can be done in a curvelet domain as well. These techniques suggest a whole new paradigm for developing deconvolution algorithms, which can incorporate leading deconvolution schemes. We conclude by showing experimental results indicating that these new algorithms can significantly improve upon current leading deconvolution methods.
We introduce a method for classifying objects based on special cases of the generalized discrete Radon transform. We adjust the transform and the corresponding ridgelet transform by means of circular shifting and a singular value decomposition (SVD) to obtain a translation, rotation and scaling invariant set of feature vectors. We then use a back-propagation neural network to classify the input feature vectors. We conclude with experimental results and compare these with other invariant recognition methods.
Recently, curvelets, finite ridgelets, bandlets, and beamlets have been suggested as transforms that capture more information than traditional wavelet transforms for two or higher dimensional images. In this work, we explore several of these transforms with some new variants. In particular, we study the effectiveness of these transforms in reducing a particular type of noise known as speckle that is present in synthetic aperture radar (SAR) imagery.