Richard A. Haddad

Adaptive median filters: new algorithms and results

Based on two types of image models corrupted by impulse noise, we propose two new algorithms for adaptive median filters. They have variable window size for removal of impulses while preserving sharpness. The first one, called the ranked-order based adaptive median filter (RAMF), is based on a test for the presence of impulses in the center pixel itself followed by a test for the presence of residual impulses in the median filter output. The second one, called the impulse size based adaptive median filter (SAMF), is based on the detection of the size of the impulse noise. It is shown that the RAMF is superior to the nonlinear mean L(p) filter in removing positive and negative impulses while simultaneously preserving sharpness; the SAMF is superior to Lins (1988) adaptive scheme because it is simpler with better performance in removing the high density impulsive noise as well as nonimpulsive noise and in preserving the fine details. Simulations on standard images confirm that these algorithms are superior to standard median filters.

A class of fast Gaussian binomial filters for speech and image processing

The authors present an efficient, in-place algorithm for the batch processing of linear data arrays. These algorithms are efficient, easily scaled, and have no multiply operations. They are suitable as front-end filters for a bank of quadrature mirror filters and for pyramid coding of images. In the latter application, the binomial filter was used as the low-pass filter in pyramid coding of images and compared with the Gaussian filter devised by P.J. Burt (Comput. Graph. Image Processing, vol.16, p.20-51, 1981). The binomial filter yielded a slightly larger signal-to-noise ratio in every case tested. More significantly, for an (L+1)*(L+1) image array processed in (N+1)*(N+1) subblocks, the fast Burt algorithm requires a total of 2(L+1)/sup 2/N adds and 2(L+1)/sup 2/ (N/2+1) multiplies. The binomial algorithm requires 2L/sup 2/N adds and zero multiplies. >

The Binomial QMF-Wavelet Transform for Multiresolution Signal Decomposition

Perfect reconstruction quadrature mirror filters (PR QMF’s) have been proposed as structures suitable for hierarchical subband coding [ ll-[4], and also for multiresolution signal decomposition as might be used in image pyramid coding [5]. More recently, multiresolution signal decomposition methods are being examined from the standpoint of the discrete wavelet transform for continuous-time signals [6]-[8]. In this paper, we describe a class of orthogonal binomial filters that provide basis functions for a perfect reconstruction bank of finite impulse response QMF’s. The orthonormal wavelet filters derived by Daubechies 171 from a discrete wavelet transform approach are shown to be the same as the solutions inherent in the binomial-based filters. The energy compaction performance of the binomial QMF decomposition is computed and shown to be better than the DCT for the Markov source models, as well as real-world images considered. The proposed binomial structure is efficient, simple to implement on VLSI, and suitable for multiresolution signal decomposition and coding applications.

A new look at digital orthogonal transmultiplexers for CDMA communications

Orthogonal transmultiplexers have been successfully utilized for multiuser communications. They are of the FDMA type in their most common version. The transmultiplexers using frequency selective PR-QMFs as their user codes were reported in the literature. This approach conflicts with the requirements of a CDMA communications system. We introduce novel spread spectrum PR-QMF codes, wherein the orthogonality is distributed over both time and frequency domains. It is shown that the proposed multivalued spread spectrum PR-QMF codes with minimized auto and cross-correlation properties outperform the conventional binary Gold codes in CDMA communication scenarios considered in the article.

Modeling, analysis, and optimum design of quantized M-band filter banks

This paper provides a rigorous modeling and analysis of quantization effects in M-band subband codecs, followed by optimal filter bank design and compensation. The codec is represented by a polyphase decomposition of the analysis/synthesis filter banks and an embedded nonlinear gain-plus-additive noise model for the pdf-optimized scalar quantizers. We construct an equivalent time-invariant but nonlinear structure operating at the slow clock rate that allows us to compute the exact expression for the mean square quantization error in the reconstructed output. This error is shown to consist of two components: a distortion component and a dominant random noise component uncorrelated with the input signal. We determine the optimal paraunitary and biorthogonal FIR filter coefficients, compensators, and integer bit allocation to minimize this MSE subject to the constraints of filter length, average bit rate, and perfect reconstruction (PR) in the absence of quantizers. The biorthogonal filter bank results in a smaller MSE but the filter coefficients are very sensitive to signal statistics and to average bit constraints. By comparison, the paraunitary structure is much more robust. We also show that the null-compensated design that eliminates the distortion component is more robust than the optimally-compensated case that minimizes the total MSE, but only at nominal conditions. Both modeling and optimal design are validated by simulation in the two-channel case.

Cyclostationary modeling, analysis, and optimal compensation of quantization errors in subband codecs

The paper is concerned with the analysis and modeling of the effects of quantization of subband signals in subband codecs. Using cyclostationary representations, the authors derive equations for the autocorrelation and power spectral density (PSD) of the reconstructed signal y(n) in terms of the analysis/synthesis filters, the PSD of the input, and the pdf-optimized quantizer model. Formulas for the mean-square error (MSE) and for compaction gain are obtained in terms of these parameters. The authors constrain the filter bank to be perfect reconstruction (PR) (but not necessarily paraunitary) in the absence of quantization and transmission errors. These formulas set the stage for filter optimization (maximization of compaction gain and minimization of MSE) subject to PR and bit constraints. Optimal filters are designed, optimal compensation is performed, and the theoretical results are confirmed with simulations. The floating-point quantizer wherein only the mantissa is uniformly quantized is also analyzed and compared with the fixed point, pdf-optimized filter bank. For high bit rates, their performance is comparable. >

Multilevel nonlinear filters for edge detection and noise suppression

Two new classes of multilevel nonlinear filters are introduced for simultaneous edge detection and noise suppression, which the authors call a nested median filter/median averaging filter (NMF/MAF) pair and a delayed decision filter/embedded median trimmed filter (DDF/EMTF) pair. Median filters and median-related filter cause an edge shift in the presence of an impulse near the edge. The proposed filters reduce such edge shifting while suppressing impulsive as well as nonimpulsive noise. It is shown that at the noisy edge point the NMF and the DDF are substantially superior both theoretically and experimentally to the median filter, the /spl alpha/-TM filter, and the STM filter in two respects: (1) the output bias error and (2) the output mean square error. It is also shown that in the noisy homogeneous region (nonedge point), the bias errors of the MAF are zero and the output mean square errors of the MAF are substantially close to those of the optimized single-level filters: the averager, the median filter, and the min-max filter under Gaussian, Laplacian, and uniform noise, respectively. Test results confirm that the NMF/MAF pair and the DDF/EMTF structure are each robust in preserving sharp edges, inhibiting edge shifting, and suppressing a wide variety of noise. >

A new orthogonal transform for signal coding

The authors propose an orthogonal, unitary transformation called the modified Hermite transformation (MHT) and its extension, which is called the modular modified Hermite transformation (MMHT). The MHT algorithm, which is an efficient algorithm, is explained and explored. The MHT is compared to the discrete cosine transform (DCT) for various AR(1) input signal source models using the performance criterion of gain over PCM, denoted by /sup N/G/sub TC/. The MHT algorithm requires only 2N real multiplications or divisions for a transformation of a signal block of N samples. It is also used for the inverse transformation, IMHT, and makes this new transform attractive. It is efficient computationally and comparable to the DCT for AR(1) source models with positive correlation coefficients, it is somewhat better than the DCT for negative correlation coefficients. >

Modeling, analysis, and compensation of quantization effects in M-band subband codecs

The authors present a rigorous modeling and analysis of quantization effects in PDF-optimized quantizers for the M-band case. They develop a technique for nulling out the signal distortion and for minimizing quantization noise in the reconstructed output, while imposing perfect reconstruction constraints. The present analysis and compensation are important in situations requiring low average bit per channel allocation.<<ETX>>

Modeling and analysis of quantization errors in two-channel subband filter structures

This paper is concerned with the analysis and modeling of the effects of quantization of subband signals in a two channel filter bank. We derive equations for the autocorrelation and power spectral density (PSD) of the reconstructed signal y(n) in terms of the analysis/synthesis filters, the PSD of the input, and the quantizer model. Formulas for the mean-square error (MSE) and for compaction gain are obtained in terms of these parameters. We assume the filter bank is perfect reconstruction (PR) (but not necessarily paraunitary) in the absence of quantization and transmission errors. These formulas set the stage for filter optimization (maximization of compaction gain and minimization of MSE) subject to PR and bit constraints.