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)
technique.
One of the main goals of the STAP-BOY program has been the implementation of a space-time adaptive processing (STAP) algorithm on graphics processing units (GPUs) with the goal of reducing the processing time. Within the context of GPU implementation, we have further developed algorithms that exploit data redundancy
inherent in particular STAP applications. Integration of these algorithms with GPU architecture is of primary importance for fast algorithmic processing times. STAP algorithms involve solving a linear system in which the transformation matrix is a covariance matrix. A standard method involves estimating a covariance matrix from a data matrix, computing its Cholesky factors by one of several methods, and then solving the system by substitution. Some STAP applications have redundancy in successive data matrices from which the covariance matrices are formed. For STAP applications in which a data matrix is updated with the addition of a new data row at
the bottom and the elimination of the oldest data in the top of the matrix, a sequence of data matrices have multiple rows in common. Two methods have been developed for exploiting this type of data redundancy when computing Cholesky factors. These two methods are referred to as
1) Fast QR factorizations of successive data matrices
2) Fast Cholesky factorizations of successive covariance matrices.
We have developed GPU implementations of these two methods. We show that these two algorithms exhibit reduced computational complexity when compared to benchmark algorithms that do not exploit data redundancy. More importantly, we show that when these algorithmic improvements are optimized for the GPU architecture,
the processing times of a GPU implementation of these matrix factorization algorithms may be greatly improved.
This paper reviews the implementation of DARPA MTO STAP-BOY program for both Phase I and II conducted
at Science Applications International Corporation (SAIC). The STAP-BOY program conducts fast covariance
factorization and tuning techniques for space-time adaptive process (STAP) Algorithm Implementation on Graphics
Processor unit (GPU) Architectures for Embedded Systems.
The first part of our presentation on the DARPA STAP-BOY program will focus on GPU implementation and
algorithm innovations for a prototype radar STAP algorithm. The STAP algorithm will be implemented on the
GPU, using stream programming (from companies such as PeakStream, ATI Technologies' CTM, and NVIDIA)
and traditional graphics APIs. This algorithm will include fast range adaptive STAP weight updates and
beamforming applications, each of which has been modified to exploit the parallel nature of graphics architectures.
KEYWORDS: Signal processing, Visualization, Detection and tracking algorithms, Data modeling, 3D modeling, 3D image processing, Computer architecture, Fourier transforms, Object recognition, Computer programming
This paper reviews the DARPA MTO STAP-BOY program for both Phase I and II. The STAP-BOY program
conducts fast covariance factorization and tuning techniques for space-time adaptive process (STAP) Algorithm
Implementation on Graphics Processor unit (GPU) Architectures for Embedded Systems.
Emerging capabilities in stream and multi-core computation, along with high speed memory bandwidths in
commercial GPU architectures, are enabling breakthrough low-cost and low-power teraflop computing solutions to
DoD-embedded computing challenges. Under the DARPA MTO STAP-BOY program, SAIC and Duke University,
in cooperation with commercial graphics processor companies, have been mapping complex signal processing
algorithms to GPU architectures. Algorithms undergoing implementation include STAP applications for radar
adaptive beamforming and spin-image surface matching applications for object recognition in 3-D range-image
data.
Accurate image registration (with subpixel accuracy) techniques are critical components for many advanced image
processing systems such as the time-differencing system and the super-resolution imaging system. In this paper,
several image registration methods are compared and evaluated. Performance of registration accuracy is evaluated
using several LWIR and CCD video imagery by two metrics: RMSE (root mean square error) and SCNR (signal-to-clutter
noise-ratio) gain (improvement of SCNR). Promising applications for iris biometric identification, super-resolution
image enhancements, heavy background clutter suppression for improving moving target detection have
been presented in this paper.
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.
Measuring the similarity between discretely sampled intensity values of different images as a function of geometric transformations is necessary for performing automatic image registration. Arbitrary spatial transformations require a continuous model for the intensity values of the discrete images. Because of computation cost most researchers choose to use low order basis functions, such as the linear hat function or low order B-splines, to model the discrete images. Using the theory of random processes we show that low order interpolators cause undesirable local optima artifacts in similarity measures based on the L2 norm, linear correlation coefficient, and mutual information. We show how these artifacts can be significantly reduced, and at times completely eliminated, by using sinc approximating kernels.
KEYWORDS: Deconvolution, Radon transform, Signal to noise ratio, Convolution, Wavelets, Lab on a chip, Radon, Rutherfordium, Algorithm development, Point spread functions
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.
Acquisition of full-polarimetric millimeter-wave, or microwave, moving target signature sets sufficient for developing ATR algorithms have proven to be costly and difficult to achieve operationally. Thorough investigations involving moving targets are often hindered by the lack of rigorously consistent signature data for a sufficient number of targets across requisite viewing angles, articulations and environmental conditions. Under the support of DARPA's TRUMPETS and AMSTE programs in conjunction with the US Army National Ground Intelligence Center, X-band far-field turntable signature data has been acquired on 1/16th scaled models of the Bradley and BTR-70 vehicles specifically constructed for moving target investigations using ERADS' 160 GHz fully polarimetric compact range. The tracks/wheels of the scale models were translated incrementally as the radar's transmit frequency was stepped across a 10.5 Ghz bandwidth. By acquiring a full frequency sweep at each track/wheel position with appropriate translation resolution, HRR RCS profiles of Doppler-shifted body/track components were generated. HRR profiles of the equivalent stationary vehicle were also generated for analysis using the vehicle's HRR profiles for any given track position.
In the work, we describe a method for constructing non- separable multidimensional folding operators and discuss preliminary obtained with a discrete rhomboidal local cosine transform. Our construction extends related work by Xia and Suter and Bernardini and Kovacevic by generalizing the definition of folding operators to include the use of non- abelian symmetry groups. A family of prototypical dihedral folding operators allows one to decompose L2(R2) into n subspaces supported on approximate equiangular sectors. We draw directly on the representation theory of finite groups, making use of the group algebra structure. The folding operators do not incorporate windows. Instead, the folding operators are constructed directly by using elements of the matrix group SO(2n).
We have applied techniques from differential motion estimation in the context of automatic registration of medical images. This method uses optical-flow and Fourier technique for local/global registration. A six parameter affine model is used to estimate shear, rotation, scale and translation. We show the efficacy of this method with images of similar and different contrasts.
We present an automatic, multi-resolution correlation based approach for elastic image registration. The technique presented assumes no a priori information (such as landmarks or segmentation), which makes it suitable for a wide class of image registration tasks. We also present preliminary results of the technique on a variety of images.
A multi-resolution approach to problems of the identification of classes of ballistic missile objects is outlined. This approach is based on the utilization of features estimated from time-varying infrared signatures and the subsequent discrimination of different objects using unique time-frequency patterns obtained from a multi- resolution decomposition of the training and observation (performance evaluation) data. For example, we have identified four features that show some promise for discrimination: the intensity in the second lowest sub-band, the temporal profile in the lowest frequency sub-band, the modulation intensity, and the DC level of each observed object. The multi-resolution discrimination algorithm's performance can be evaluated by comparing with more traditional Fourier based approaches. The multi-resolution discrimination algorithms were applied to simulated data and were shown, by using L1 or L2 norms as distance metrics, to provide good classification performance and to reduce the temporal data length by half. The features extracted using the discrete wavelet packet transform can help to further improve classification performance. The robustness of the algorithm in the presence of noise is also studied. All data sets were generated with Raytheon Missile Systems Company's high fidelity simulation.
In many applications one wishes to perform an analysis of the homogeneity of a point process, often as a precursor to more advanced analysis. In general, rejection of the null hypothesis of homogeneity may imply a requirement for further analysis. In remote sensing for minefield detection, for example, homogeneity may correspond to the 'no minefield' case while regions of nonhomogeneity warrant closer inspection. This paper considers a version of the spatial scan process which uses stochastic and disjoint scan regions. The associated test for nonhomogeneity has the potential for improved power over conventional alternative sin applications where the point process is embedded in a general random field. Specifically, when the locations of any subregions of nonhomogeneity in the point process correspond to regions in the underlying field which can be segmented as distinct from their surroundings, the test derived here is recommended. The application to the detection of point clusters in gray-scale imagery, particularly minefields in multispectral imagery, is investigated.
KEYWORDS: Image processing, Convolution, Wavelets, Linear filtering, Magnetic resonance imaging, Data modeling, Data processing, Computer programming, Signal processing, Data communications
Adaptive signal representations, such as those determined by best-basis type algorithms, have found extensive application in image processing, although their use in real time applications may be limited by the complexity of the algorithm. In contrast to the wavelet transform which can be computed in O(n) time, the full wavelet packet expansion required for the standard best basis search takes O(n log n) time to compute. In the parallel work, however, the latter transform becomes attractive to implement, due to a theoretical speedup of O(log n) when the number of processors equal the number of data elements. This note describes near real-time performance obtained with a parallel implementation of best basis algorithms for wavelet packet bases. The platform for our implementation is a DECmpp 12000/Sx 2000, a parallel machine identical to the MasPar MP-2. The DECmpp is a single instruction, multiple data system; such systems support a data parallel programming model, a model well suited to the task at hand. We have implemented the 1D and the 2D WPT on this machine and our results show a significant speedup over the sequential counterparts. In the 1D case we almost attain the theoretical speedup, while in the 2D case we increase execution speed by about two orders of magnitude. The current implementation of the 1D transform is limited to signals of length 2048, and the 2D transform is limited to images of size: 32 X 32, 64 X 64, and 128 X 128. We are currently working on extending our transform to handle signals and images of larger size.
Several methods have been used to obtain complete MR images from a reduced set of measured encodes. All of these techniques use some sort of a priori information to complete the incomplete data set. These techniques have had varying degrees of success in a variety of applications: imaging contrast uptake, interventional procedures, spectroscopy, fMRI contrast changes, and routine scans of a given population. In this paper we make three points: First, significant effort has been made toward finding the set of phase encodes that minimizes the expected L2 norm of the encoding error. We show that in experiments many sets of phase encodes come close to attaining the Karhunen-Loeve (K-L) limit. However, second, we show that other image quality metrics result in much more pleasing images that have much better detail than images where the L2 norm is optimized. For this purpose we use best basis algorithms to find a local trigonometric and wavelet packet bases which optimizes several cost functions including the Lp norms and entropy; the L0.25 norm gave the most pleasing results. Lastly, we show that although ringing produced by undersampling cannot be eliminated it can be effectively controlled when the general shape of the object is known. Ringing renders techniques like SLIM impractical. We are able to control ringing by fitting the reconstructed signal to a piecewise monotonic function. The larger peaks are kept and the fast oscillations characteristic of ringing are eliminated. The signal can be pulled out of noise or fast oscillations when the signal energy is only one quarter of the noise energy.
In this paper we will begin by presenting basic background material concerning the propagation of pulses through optical fibers, and current transmission schemes for optical fiber communication networks. We will then propose a time-frequency network design for high bandwidth fiber optic communications. We will discuss the crucial links in the system, which are: (1) an optical temporal Fourier transform which enables the optical computation of signal correlations, (2) the design of the input waveforms in order to avoid the harmful effects of Brillouin scattering and phase noise, and (3) the use of time frequency bases to lower the requirements on electronic modulators and detectors in high bandwidth communications.
KEYWORDS: Magnetic resonance imaging, Computer programming, Signal to noise ratio, Magnetism, Fourier transforms, Data acquisition, Wavelets, Brain, Phase measurement, Head
We discuss the advantages and disadvantages of using a Karhunen-Loeve (K-L) expansion of a training set of images to reduce the number of encodes required for a magnetic resonance (MR) image of a new object. One form of this technique has been proposed and another implemented. We evaluate the error likely to be achieved as a function of the number of encodes and two technical problems: reduced SNR in the images and smoothing of the K-L functions in practice. As an alternative, we propose the use of joint best bases derived from the local trigonometric library as an approximation to the K-L basis. These bases approach the rate-distortion characteristic achieved by the K-L basis, but they are easier to use in MRI and can be applied with existing methods for fast acquisition.
In this paper we present basic background material concerning the propagation of pulses through fiber optics, and current transmission schemes in fiber optics. We discuss the value of using different signal processing techniques, and time-frequency bases in fiber optic transmission. Finally we outline issues which we believe to be of current interest in fiber optic transmission.
We propose a new experimental data acquisition method which acquires multiple exposures through a windowed x-ray radiation profile. The tapered profile is localized at the target region with a reduced radiation dosage but must be repeated at a few discrete shifts outside the target region to cover the whole slice. Such an approximated spatial window-convolution projection, a weighted-shifted radon transform, is ideally suited for the wavelet transform (WT) which is a bank of constant-Q matched filters creating a local space-scale joint representation. It is more efficient than the Fourier transform (FT) for any local signal analysis. It requires fewer basis terms and provides better signal-to-noise ratio enhancement than FT. Thus, the WT version of the central slice theorem (CST) yields an image reconstruction method. Because of the compact support and the design flexibility of the wavelet bases, this new approach has the potential of requiring fewer of the weighted x-ray projections, in which a lower radiation dosage is used, than standard tomography. Despite the sparser data set, a reconstructed image of similar quality to that created by standard FT tomography can be achieved. Moreover, the WT using the tapered radiation cuts can provide a multi-resolution feature extraction for use in artificial neural network-based automatic pattern classification.
In this paper we introduce an algorithm for imaging a time varying object f(x,t) from its projections at different fixed times. We show that the reconstruction of coarse features, corresponding to low spatial-frequency data, can be made nearly instantaneously in time from the evolving data. A temporal sequence of these low spatial-frequency reconstructions can be used to estimate the motion of the object. Once the motion is estimated, we may use the estimate to compensate for some of the motion of fine scale features. This enables accurate reconstructions of the time varying fine structure in several cases. The algorithm is demonstrated for a selection of phantoms and actual MRI studies. In general, this technique shows promise for a wide variety of applications in MRI, as well as for heart imaging using x- ray CT. Clinical applications should include both functional MRI such as dynamic imaging of oxygen usage and blood flow in the brain, and motion imaging of joints, angiography in the lungs, and heart imaging.
Experience suggests the existence of a connection between the contrast of a gray-scale image and the gradient magnitude of intensity edges in the neighborhood where the contrast is measured. This observation motivates the development of edge-based contrast enhancement techniques. We present a simple and effective method for
image contrast enhancement based on the multiscale edge representation of images. The contrast of an image can be enhanced simply by stretching or upscaling the multiscale gradient maxima of the image. This method offers flexibility to selectively enhance features of different sizes and ability to control noise magnification. We present some experimental results from enhancing medical images and discuss the advantages of this wavelet approach over other edge-based techniques.
In this paper we introduce an algorithm for imaging a time- varying object from its projections at different fixed times. We show that the reconstruction of coarse features, corresponding to low spatial-frequency data, can be made nearly instantaneously in time from the evolving data. A temporal sequence of these low spatial-frequency reconstructions can be used to estimate the motion of the object. Once the motion is estimated, we may use the estimate to compensate for some of the motion of fine scale features. This enables accurate reconstructions of the time varying fine structure in several cases. The algorithm is demonstrated for a selection of phantoms and actual MRI studies. In general, this technique shows promise for a wide variety of applications in MRI, as well as for heart imaging using X-ray CT. Clinical applications should include both functional MRI such as dynamic imaging of oxygen usage and blood flow in the brain, and motion imaging of joints, angiography in the lungs, and heart imaging.
In this paper we present background material concerning the propagation of pulses through fiber optics, and current transmission schemes in fiber optics. We discuss the value of using different signal processing techniques, and time-frequency bases in fiber optic transmission. Finally we will outline methods which allow one to send optical pulses with arbitrary shapes through fiber optics.
One of the primary visual properties used by radiologists in classifying masses is the sharpness of the edge of the mass. Wavelet transforms can be thought of as multiscale edge detectors. We report using the edge detection and classification properties of wavelet transforms to help classify masses on mammograms. We digitized six masses from mammograms: three benign and three malignant. Our preliminary results indicate that edge properties of masses in mammograms can be obtained from features in the wavelet transform domain. These edge properties can be used to help classify masses prior to biopsy. In particular, the change in the direction of the edge gradient at intermediate scales is indicative of malignancy. This work must be extended to a much larger sample size. The larger sample size will allow other measures to be used. More importantly the interaction between measures can then be observed. Undoubtedly a combination of measures will be required to classify masses accurately.
We demonstrate a simple and effective method for image contrast enhancement based on the multiscale edge representation of images. The contrast of an image can be enhanced simply by stretching or scaling the multiscale gradient maxima of the image. This method offers flexibility to selectively enhance features of different sizes and ability to control noise magnification. Experimental results from enhanced medical images are presented.
We present a new approach to studying a discrete Gabor expansion (DGE). We show that, in general, DGE is not the usual biorthogonal decomposition, but belongs to a larger and looser decomposition scheme which we call pseudo frame decomposition. It includes the DGE scheme proposed as a special case. The standard dual frame decomposition is also a special case. We derive algorithms using techniques for Gabor sequences to compute 'biorthogonal' sequences through proper matrix representation. Our algorithms involve solutions to a linear system to obtain the 'biorthogonal' windows. This approach provides a much broader mathematical view of the DGE, and therefore, establishes a wider mathematical foundation towards the theory of DGE. The general algorithm derived also provides a whole class of discrete Gabor expansions, among which 'good' ones can be generated. Simulation results are also provided.
In this paper we introduce an algorithm for fast updating of projection reconstruction MRI images. This algorithm makes use of range characterizations of the Radon transform, and sampling techniques of computerized tomography. Our algorithm differs from other attempts to image time-varying phenomena in that it does not average over time, but rather localizes in time for 'snap-shot' imaging. This uses the fact that image features from different scales can be updated at different rates. We also introduce a technique for spatial localization of MRI data. This technique shows promise for fast updating of locally changing phenomena in MR. Clinical applications of this technique include dynamic imaging of time dependent physiological processes like oxygen usage and blood flow in the brain.
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