9:30, IMDSP-P5.1
LOSSLESS 2D DISCRETE WALSH-HADAMARD TRANSFORM
K. KOMATSU, K. SEZAKI
The 64-point separable lossless two dimensional (2D) WHT is composed of the 8-point lossless one dimensional WHT. The latter is obtained by first decomposing the 8-point WHT into the 2-point WHTs and second replacing every 2-point WHT by a ladder network. Since the coefficients in the ladder network then become real, the advantage of multiplier-free vanishes. This paper therefore proposes a 64-point nonseparable lossless 2D WHT without multiplication as follows. First the 64-point separable 2D WHT is decomposed into the 4-point 2D WHTs. Second every 4-point 2D WHT is replaced by a 2D ladder network which is multiplier-free. It is also shown that the transform coefficients of the proposed transform are closer to those of the 64-point lossy 2D WHT than those of the 64-point separable lossless 2D WHT.

9:30, IMDSP-P5.2
2-D SINUSOIDAL AMPLITUDE ESTIMATION WITH APPLICATION TO 2-D SYSTEM IDENTIFICATION
H. LI, W. SUN, P. STOICA, J. LI
In [1], we studied amplitude estimation of one-dimensional (1-D) sinusoidal signals from measurements corrupted by possibly colored observation noise. We herein extend the results for two-dimensional (2-D) amplitude estimation. In particular, we investigate the 2-D sinusoidal amplitude estimation within the general frameworks of least squares (LS), weighted least squares (WLS), and MAtched FIlterbank (MAFI) estimation. A variety of 2-D amplitude estimators are presented, which are all asymptotically statistically efficient. The performances of these estimators in finite samples are compared numerically with one another. Making use of amplitude estimation techniques, we introduce a new scheme for 2-D system identification, which is shown to be computationally simpler and statistically more accurate than the conventional output error method (OEM), when the observation noise is colored.

9:30, IMDSP-P5.3
STABILITY OF THE 2-D FORNASINI-MARCHESINI MODEL WITH PERIODIC COEFFICIENTS
T. BOSE, R. THAMVICHAI, M. RADENKOVIC
The stability of two-dimensional (2-D) periodically shift varying (PSV) filters is considered. These filters have applications in filtering video signals with cyclostationary noise, image and video scrambling, and design of multiplierless filters. The considered system is represented in state space by the first model of Fornasini-Marchesini with periodic coefficients. Then the stability of this model is studied. Two necessary conditions and two sufficient conditions are established for asymtotic stability. The conditions are easy to use and computationally simple.

9:30, IMDSP-P5.4
A FAST ALGORITHM FOR TOEPLITZ-BLOCK-TOEPLITZ LINEAR SYSTEMS
A. YAGLE
A Toeplitz-block-Toeplitz (TBT) matrix is block Toeplitz with Toeplitz blocks. TBT systems of equations arise in 2-D interpolation, 2-D linear prediction and 2-D least squares deconvolution problems. Although the doubly Toeplitz structure should be exploitable in a fast algorithm, existing fast algorithms only exploit the block Toeplitz structure, not the Toeplitz structure of the blocks. Iterative algorithms can employ the 2-D FFT, but usually take thousands of iterations to converge. We develop a new fast algorithm that assumes a smoothness constraint (described in the text) on the matrix entries. For an M^2-by-M^2 TBT matrix with M M-by-M Toeplitz blocks along wach edge, the algorithm requires only O(6M^3) operations to solve an M^2-by-M^2 linear system of equations; parallel computing on 2M parallel processors can be performed on the algorithm as given. Two examples show the operation and performance of the algorithm.

9:30, IMDSP-P5.5
IMAGE PROCESSING USING SINGULARITIES AND WAVELETS
A. LANGI, W. KINSNER
The paper develops a singularity image model as an alternative to linear models for processing many complicated but important images. The model is effective because it provides image characterization, image decomposition, and image reconstruction. For a given measure, one can nonlinearly transform an image into a singularity domain, where each pixel has a singular coefficient. For everywhere singular images, the coefficients are equivalent to fractal dimensions. The image can be decomposed into subimages such that pixels in each subimage have the same singularity coefficients. Since each subimage is fractal, the overall image can have singularity spectrum. For a wavelet-based measure, it is possible to reconstruct the image from the singularity information. The paper shows application examples including image denoising, image compression, and analysis on natural and biomedical images.

9:30, IMDSP-P5.6
AFFINE INVARIANT WAVELET TRANSFORM
V. HA, J. MOURA
We present a two-dimensional wavelet transform that is invariant to affine distortions of the input signal. Affine distortions include geometric effects such as translation, reflection, uniform and anisotropic scaling, rotation, and shearing of the input signal. Invariance of the wavelet transform to affine distortions is achieved in our work by developing an algorithm that reduces replicas of a signal related by affine distortions to a unique prototype signal. The affine invariant wavelet transform is then defined as the two-dimensional wavelet transform of the prototype signal, which provides the wavelet coefficients that are invariant to affine distortions of the input signal. We describe our algorithm and show examples that demonstrate our claims.

9:30, IMDSP-P5.7
A 3D ACQUISITION AND MODELLING SYSTEM
S. MAHADEVAN, H. PANDZO, M. BENNAMOUN, J. WILLIAMS
This paper presents our implementation of an integrated 3D acquisition and modelling system. The proposed system consists of an acquisition module, a registration algorithm proposed by the last two authors and a reconstruction module. Techniques for addressing the implementation of the modules are first briefly followed by a more detailed discussion of the techniques implemented in the system is given. Results are also presented to demonstrate the system's operation.

9:30, IMDSP-P5.8
FAST ALGORITHM FOR THE 3-D DCT
S. BOUSSAKTA, O. ALSHIBAMI
The three-dimensional discrete Cosine transform (3-D DCT) has been used in many 3-D applications such as video coding and compression. Many fast algorithms have been developed for the calculation of 1-D DCT. These algorithms are then used for the calculation of 3-D DCT using the row-column approach. However, 3-D algorithms involve less arithmetic operations and can be faster. In this paper, the 3-D vector-radix algorithm (3-D VR), for the 3-D DCT, is developed and its arithmetic complexity analysed and compared to similar algorithms. Compared to the familiar row-column approach, the 3-D vector-radix reduces the number of multiplications significantly while keeping the number of additions the same and hence can be used for fast 3-D image and video coding and compression.

9:30, IMDSP-P5.9
ADAPTIVE, OPTIMAL-RECOVERY IMAGE INTERPOLATION
D. MURESAN, T. PARKS
We consider the problem of image interpolation using adaptive optimal recovery. We adaptively estimate the local quadratic signal class of our image pixels. We then use optimal recovery to estimate the missing local samples based on this quadratic signal class. This approach tends preserve edges, interpolating along edges and not across them.

9:30, IMDSP-P5.10
BRIDGING SCALE-SPACE TO MULTISCALE FRAME ANALYSES
Y. BAO, H. KRIM
We address a well known problem of nonlinear image diffusion techniques, namely the loss of texture information. We do so by first determining that it is due to unaccounted correlation structure in the image which we subsequently mitigate by proposing a wavelet frame-based technique. This, by the same token establishes a theoretical bridge between the scale space methodology and the multiscale analysis approach. We provide examples to illustrate the effectiveness of the proposedapproach. http://www4.ncsu.edu/~yfbao/personal/publication.html

9:30, IMDSP-P5.11
IMAGE INTERPOLATION USING WAVELET-BASED HIDDEN MARKOV TREES
K. KINEBUCHI, D. MURESAN, T. PARKS
Hidden Markov trees in the wavelet domain are capable of accurately modeling the statistical behavior of real world signals by exploiting relationships between coefficients in different scales. The model is used to interpolate images by predicting coefficients at finer scales. Various optimizations and post-processing steps are also investigated to determine their effect on the performance of the interpolation. The interpolation algorithm was found to produce noticeably sharper images with PSNR values which outperform many other interpolation techniques on a variety of images.

9:30, IMDSP-P5.12
ESTIMATION OF MORPHOLOGICAL DEGRADATION MODEL PARAMETERS
T. KANUNGO, Q. ZHENG
Noise models are crucial for designing image restoration algorithms, generating synthetic training data, and predicting algorithm performance. However, to accomplish any of these tasks, an estimate of the noise model parameters is essential. In this paper we describe a parameter estimation algorithm for a morphological, binary image degradation model. Inputs to the estimation algorithm are the ideal and degraded images. We search for the optimal parameter by looking for a parameter value for which the corresponding noise pattern distribution in the simulated image and the given degraded image are most similar. The parameter space is searched using the simplex algorithm proposed by Nelder and Mead. We use the the p-value of the Kolmogorov-Smirnov test of difference between the two pattern distributions as the objective function value. We show results of applying our algorithm on document images.