Bruce W. Suter

The multilayer perceptron as an approximation to a Bayes optimal discriminant function

The multilayer perceptron, when trained as a classifier using backpropagation, is shown to approximate the Bayes optimal discriminant function. The result is demonstrated for both the two-class problem and multiple classes. It is shown that the outputs of the multilayer perceptron approximate the a posteriori probability functions of the classes being trained. The proof applies to any number of layers and any type of unit activation function, linear or nonlinear.

Design of prefilters for discrete multiwavelet transforms

The pyramid algorithm for computing single wavelet transform coefficients is well known. The pyramid algorithm can be implemented by using tree-structured multirate filter banks. The authors propose a general algorithm to compute multiwavelet transform coefficients by adding proper premultirate filter banks before the vector filter banks that generate multiwavelets. The proposed algorithm can be thought of as a discrete vector-valued wavelet transform for certain discrete-time vector-valued signals. The proposed algorithm can be also thought of as a discrete multiwavelet transform for discrete-time signals. The authors then present some numerical experiments to illustrate the performance of the algorithm, which indicates that the energy compaction for discrete multiwavelet transforms may be better than the one for conventional discrete wavelet transforms.

Vector-valued wavelets and vector filter banks

In this paper, we introduce vector-valued multiresolution analysis and vector-valued wavelets for vector-valued signal spaces. We construct vector-valued wavelets by using paraunitary vector filter bank theory. In particular, we construct vector-valued Meyer wavelets that are band-limited. We classify and construct vector-valued wavelets with sampling property. As an application of vector-valued wavelets, multiwavelets can be constructed from vector-valued wavelets. We show that certain linear combinations of known scalar-valued wavelets may yield multiwavelets. We then present discrete vector wavelet transforms for discrete-time vector-valued (or blocked) signals, which can be thought of as a family of unitary vector transforms.

Multirate filter banks with block sampling

Multirate filter banks with block sampling were recently studied by Khansari and Leon-Garcia (1993). In this paper, we want to systematically study multirate filter banks with block sampling by studying general vector filter banks where the input signals and transfer functions in conventional multirate filter banks are replaced by vector signals and transfer matrices, respectively. We show that multirate filter banks with block sampling studied by Khansari and Leon-Garcia are special vector filter banks where the transfer matrices are pseudocirculant. We present some fundamental properties for the basic building blocks, such as Noble identities, interchangeability of down/up sampling, polyphase representations of M-channel vector filter banks, and multirate filter banks with block sampling. We then present necessary and sufficient conditions for the alias-free property, finite impulse response (FIR) systems with FIR inverses, paraunitariness, and lattice structures for paraunitary vector filter banks. We also present a necessary and sufficient condition for paraunitary multirate filter banks with block sampling. As an application of this theory, we present all possible perfect reconstruction delay chain systems with block sampling. We also show some examples that are not paraunitary for conventional multirate filter banks but are paraunitary for multirate filter banks with proper block sampling. In this paper, we also present a connection between vector filter banks and vector transforms studied by Li. Vector filter banks also play important roles in multiwavelet transforms and vector subband coding.

The Fractional Wave Packet Transform

We introduce the concept of the Fractional Wave Packet Transform(FRWPT), based on the idea of the Fractional Fourier Transform(FRFT) and Wave Packet Transform(WPT). We show a version of the resolution of the identity and some properties of FRWPT connected with those of FRFT and WPT.

FIR paraunitary filter banks given several analysis filters: factorizations and constructions

FIR paraunitary filter banks have been extensively studied and well understood. We address the following problem: how to characterize and construct an FIR paraunitary filter bank when its several analysis filters are given a priori. To study this problem is not only useful in orthogonal M-band wavelets with certain regularity where we need to construct wavelet filters when a scaling filter with certain regularity is found a priori but is also useful in the design of multirate filter banks where we have already had several desired analysis filters. One such example is multiwavelet transforms. We present a method of constructing all possible FIR paraunitary filter banks in terms of a McMillan degree when several analysis filters are given.

On a magnitude preserving iterative MAXnet algorithm

A new iterative maximum picking neural net (MAXnet) is presented. This formulation determines the value and the location either for a unique maximum or for multiple maxima. This new net converges, for many commonly occurring distributions, in O(log M) iterations using only simple computing elements.

Kernel design techniques for alias-free time-frequency distributions

This paper presents a modification of the alias-free generalized discrete time-frequency distribution (AF-GDTFD) which reduces the computations necessary to implement the algorithm from O(N/sup 3/) to O(N/sup 2/log N). With this new implementation, we examine the problem of designing/modifying kernels defined in the ambiguity plane for use with the AF-GDTFD. We present three different methods to allow the use of these kernels and demonstrate them using the Butterworth kernel.<<ETX>>

On variable overlapped windows and weighted orthonormal bases

A generalized lapped orthonormal transform (GLOT) formulation is presented for the analysis and synthesis of signals. This formulation is composed of a variable width window and a linear combination of weighted orthonormal functions. Tradeoffs in the specification of windows are examined. A sinusoidal example is considered, and a fast algorithm is provided for its evaluation. >

Wavelet detection of clustered microcalcifications

An automated method for detecting microcalcification clusters is presented. The algorithm begins with a digitized mammogram and outputs the center coordinates of regions of interest (ROIs). The method presented uses a non-linear function and a 12-tap least asymmetric Daubechies (LAD12) wavelet in a tree structured filter bank to increase the signal to noise level by 10.26 dB. The signal to noise level gain achieved by the filtering allows subsequent thresholding to eliminate on average 90% of the image from further consideration without eliminating actual microcalcification clusters 95% of the time. Morphological filtering and texture analysis are then used to identify individual microcalcifications. Altogether, the method successfully detected 44 of 53 microcalcification clusters (83%) with an average of 2.3 false positive clusters per image. A cluster is considered detected if it contains 3 or more microcalcifications within a 6.4 mm by 6.4 mm area. The method successfully detected 13 of the 14 malignant cases (93%).