3:30, SPTM-P7.1
ON OPTIMAL TRANSFORMS FOR SUBBAND DOMAIN SUPPRESSION OF COLORED NOISE
S. AKKARAKARAN, P. VAIDYANATHAN
Suppose we wish to analyze a noisy signal using a filter bank (FB) and apply noise suppression schemes such as Wiener filters in the subbands of the FB. This paper formalizes and studies the problem of finding the best FB for this purpose. The best FB depends on the class of allowed FB's, the type of subband processing, and the statistics of the input signal and additive noise. Recently we have shown the optimality of the so--called principal component filter bank (PCFB) for several signal processing problems. In particular, the PCFB is the optimum orthonormal FB for many schemes for suppression of white noise. With colored noise however, the optimization is considerably more involved, and PCFB optimality is much more restricted. Here we present several results on the colored noise suppression problem. We develop an algorithm to find the exact globally optimum unconstrained orthonormal FB for piecewise constant input signal and noise spectra. This thus allows approximation of the optimum FB for any spectra to any desired accuracy. We examine the role of PCFB's in the optimization.

3:30, SPTM-P7.2
ALPERTS MULTI-WAVELETS FROM SPLINE SUPER-FUNCTIONS
H. OZKARAMANLI, A. BHATTI, T. KABAKLI
For multi-wavelets generalized left eigenvectors of the matrix, Hf a finite portion of down-sampled convolution matrix H determine the combinations of scaling functions that produce the desired spline or scaling function from which polynomials of desired degree can be reproduced. This condition is used to construct Alpert’s multi-wavelets with multiplicity two, three and four and with approximation orders two, three and four respectively. Higher multiplicity Alpert multi-wavelets can also be constructed using this new method.

3:30, SPTM-P7.3
EFFECTING FREQUENCY SHIFTS WITH A DFT FILTERBANK
G. PARKER
It is often required to apply a shift in frequency to the channelised data within a DFT filterbank. An example application is the frequency domain implementation of the cyclic Wiener filter. A common approach is to rotate the transform through an appropriate number of bins, but this is only accurate if the frequency shift is a multiple of the bin width. A better approach is to combine the bin rotation with an approximate fine shift. In this paper the exact solution is found for an arbitrary DFT filterbank and novel, computationally efficient approximations to this are derived and compared.

3:30, SPTM-P7.4
DECIMATION BY IRRATIONAL FACTOR USING CIC FILTER AND LINEAR INTERPOLATION
D. BABIC, J. VESMA, M. RENFORS
This paper presents an efficient way to implement flexible multirate signal processing systems with high oversampling ratio and adjustable fractional or irrational sampling rate conversion ratio. One application area is a multi-standard communication receiver which should be adjustable for different symbol rates utilized in different systems. The proposed decimation filter consists of parallel CIC (cascaded integrator-comb) filters followed by a linear interpolation filter. The idea in this paper is to use two parallel CIC filters to calculate the two needed sample values for linear interpolation. These samples occur just before and after the final output sample. This corresponds to a system where the linear interpolation is done at the higher input sampling rate.

3:30, SPTM-P7.5
WAVELET BASED ESTIMATION OF A SEMI PARAMETRIC GENERALIZED LINEAR MODEL OF FMRI TIME SERIES
F. MEYER
This work provides a new approach to estimate the parameters of a semi-parametric generalized linear model in the wavelet domain. The method is illustrated with the problem of detecting significant changes in fMRI signals that are correlated to a stimulus time course. The fMRI signal is described as the sum of two effects~: a smooth trend and the response to the stimulus. The trend belongs to a subspace spanned by large scale wavelets. We have developed a scale space regression that permits to carry out the regression in the wavelet domain while omitting the scales that are contaminated by the trend. Experiments with fMRI data demonstrate that our approach can infer and remove drifts that cannot be adequately represented with low degree polynomials. Our approach results in a noticeable improvement by reducing the number of false positive and increasing the number of true positive

3:30, SPTM-P7.6
ARTIFACT FREE SIGNAL DENOISING WITH WAVELETS
J. FROMENT, S. DURAND
Recent years have seen the development of signal denoising algorithms based on the thresholding of wavelet coefficients. This approach allows to restore the smoothness of the original signal, but suffers of a main drawback : around discontinuities the reconstructed signal is smoothed, exhibiting pseudo-Gibbs phenomenon. We propose to apply a traditional wavelet denoising method followed by a total variation minimization approach. This allows to remove the Gibbs phenomena and therefore to restore sharp discontinuities, while the other structures are preserved. The main innovation of our algorithm is to constrain the total variation minimization by the knowledge of the remaining wavelet coefficients. In this way, we make sure that the restoration process does not deteriorate the information that has been considered as significant in the denoising step. With this approach we substantially improve the performance of classical wavelet denoising algorithms, both in terms of SNR and in terms of visual artifacts.

3:30, SPTM-P7.7
QUANTIZATION TO MAXIMIZE SNR IN NON-ORTHOGONAL SUBBAND CODERS
R. GANDHI, S. MITRA
Recent research in the design of filter banks has shown that non-orthogonal filter banks can potentially provide higher coding gains over orthogonal filter banks. The use of non-orthogonal filter banks, however, poses a difficulty in the quantization of subband signals. The conventional nearest-neighbor (NN) encoding rule for the quantization of subband signals is no longer optimal. In this paper, we propose two schemes for the quantization of subband signals in non-orthogonal subband coders. An optimal scheme for quantization of subband signals is proposed first. The complexity of the optimal quantization scheme is shown to grow exponentially with the length of the synthesis filters, which motivates the development of low-complexity quantization schemes when the length of the filters in the synthesis filter bank is large. The second quantization technique uses an iterative method to quantize the subband signals such that the mean square error between the input and the reconstructed output signals is minimized.

3:30, SPTM-P7.8
DESIGN OF 2-BAND ORTHOGONAL NEAR-SYMMETRIC CQF
A. ABDELNOUR, I. SELESNICK
The FIR 2-band wavelets have found wide applications in practice. One of their disadvantages, however, is that they cannot be made both symmetric and orthogonal. There have been some works on filters which are orthogonal and nearly symmetric. In this paper, Groebner methods are used to design orthogonal filters with a subset of exactly symmetric coefficients of various lengths, as opposed to nearly symmetric coefficients.

3:30, SPTM-P7.9
FABRIC DEFECT DETECTION USING ADAPTIVE WAVELET
Y. ZHI, G. PANG, N. YUNG

3:30, SPTM-P7.10
THE DESIGN OF HILBERT TRANSFORM PAIRS OF WAVELET BASES VIA THE FLAT DELAY FILTER
I. SELESNICK
This paper describes a simple procedure, based on spectral factorization, for the design of a pair of orthonormal wavelet bases where the two wavelets form a Hilbert transform pair. The two scaling filters respectively have the numerator and denominator of the flat delay all-pass filter as factors. The design procedure allows for an arbitrary number of zero wavelet moments to be specified. A Matlab program for the procedure is given, and examples are also given to illustrate the results. URL: http://taco.poly.edu/selesi/hwlet/