Tor A. Ramstad

Digital methods for conversion between arbitrary sampling frequencies

The paper presents filtering methods for interfacing time-discrete systems with different sampling frequencies. The methods are applicable for sampling rate conversion between any two sampling frequencies; the conversion ratio may even be irrational or slowly time varying. Interpolation by irrational factors requires digital filters with nonperiodically varying coefficients. This is dealt with in two ways. 1) All possible coefficient values are precalculated. This is, in a sense, possible because of the finite resolution needed. Or 2), the coefficients can be updated in real time using either FIR or IIR filters. The first solution requires a huge coefficient memory; the second scheme, on the other hand, is computationally intensive. While discussing both of these solutions, more practical intermediate schemes incorporating both FIR-and IIR-type filters are suggested. The suggested practical implementations are either based on analog reconstruction filters where the derived digital filter coefficients are functions of the distances between current input and output samples or digital interpolators combined with simple analog interpolation schemes for finding the desired values in between the uniform output samples from the digital interpolator.

Cosine-modulated analysis-synthesis filterbank with critical sampling and perfect reconstruction

The authors present a simple derivation of a parallel filterbank based on cosine-modulated versions of a model low-pass filter. With a nonuniform channel separation an efficient implementation consisting of a DFT (discrete Fourier transform) related transform and subfilters is possible. Using critical sampling of each channel and FIR (finite impulse response) filters, the conditions for perfect reconstruction are given. The computational complexity of the derived FIR filterbank is much lower than for a tree-structured FIR filterbank but cannot compete with the most efficient IIR filterbanks.<<ETX>>

An inner product space approach to image coding by contractive transformations

Consideration is given to modeling of arbitrary digital gray tone images as the fixed points of contractive transformations on the image space. The transformation is designed to exploit a form of image redundancy called piecewise self-similarity. Results from inner product space theory are used to optimize the transformation within a class of affine transformations. The resulting transformation is described by a small amount of information compared to the original image, and its piecewise self-similar fixed point, found by successively iterating the transformation from any initial image, is close to the original image. Results are improved compared to earlier results with this technique.<<ETX>>

IIR filterbank for subband coding of images

The author presents a simple derivation of a separable two-dimensional uniform filterbank for subband coding of images. Each one-dimensional filterbank is tree-structured where the individual quadrature mirror filters are of the infinite-impulse response (IIR) type. Through the use of a combination of causal and anticausal filtering in the analysis and synthesis filter banks, respectively, perfect signal reconstruction is obtained. A subband coder model including quantization is given, and results concerning optimal filtering in a subjective sense are presented.<<ETX>>

Attractor image compression with a fast non-iterative decoding algorithm

The problem of decoder convergence speed in an attractor (fractal-based) image compression system is considered. The general principles of such a system are described in the context of discrete linear spaces. A problem with previous implementations is that the decoding rests on an iterative procedure whose complexity is image-dependent. It is shown how this problem can be sidestepped by introducing a modification providing an iteration-free decoder. The coding results are not affected by this modification. The new decoding algorithm requires only one multiplication and three additions per pixel. The algorithm is suitable for applications where fast display of images is essential, such as retrieval of images from compressed databases.<<ETX>>

Application of an efficient parallel IIR filter bank to image subband coding

The principle of subband coding has recently been successfully applied for the purpose of image data compression. The analysis/synthesis filter banks and the subband signal encoder/decoder are the main parts of a subband coder. Previously the filter banks in image subband coders have been designed with FIR filters organized in a tree structure. In this paper we propose a novel structure that deviates from previously reported structures in these respects: (1) The filter bank is organized as a parallel structure. (2) The filters employed are 1st order IIR allpass filters featuring very low computational complexity. (3) The resulting subbands are complex. (4) The filter bank features exact reconstruction in the absence of encoding/decoding. In the paper we give a detailed derivation of the filter bank structure. The computational complexity is evaluated and shown to be considerably less than that of existing structures. We have incorporated this filter bank structure into a complete image subband coder. Finally, coding results obtained by computer simulation are presented.

Efficient multirate realization for narrow transition-band FIR filters

A filtering technique for reducing the computational complexity in FIR (finite-impulse-response) filters at any bandwidth is described. This technique uses a combination of multirate and complementary filters. It is shown that the resulting computational complexity is almost independent of the transition bandwidth of the filter, but depends somewhat on the cutoff frequency. It is concluded that any reasonable filter specification can be met by using about 45 multiplications per sample.<<ETX>>

Some considerations on coefficient sensitivity and noise in direct form IIR interpolators and decimators

Direct form implementation of IIR filters for sample rate alteration has been shown (1) to be efficient when the recursive part of the filters work at the low sampling frequency. In this paper we suqgest to generalize the IIR interpolators/decimators by introducting partial zero-forming of their passband. A design method based on the Remez exchange algorithm is proposed. The advantage of these filters is that the coefficient sensitivity as well as the quantization noise can be reduced. An illustrative design example is presented.

Robust image communication using subband coding and multilevel modulation

Visual communication systems can exploit the advantages of analog transmission and digital compression: Analog transmission allows the quality of the recovered data to vary gracefully as the channel conditions vary, whereas digital compression allows for powerful data reduction. In this paper, a system optimized for bandwidth- and power-limited channels which combines analog and digital communication principles is proposed. The system achieves a high bandwidth compression efficiency by combining subband signal decomposition and dynamic bandwidth allocation with 81-PAM transmission. Furthermore, graceful degradation is obtained by finding mappings from the subband samples to the channel space which minimize the impact of channel errors in the reconstructed signal. The optimized mapping system outperforms a conventional system using random mappings. In addition, it is shown that the proposed system performs better, in a rate-distortion sense for a given channel signal- to-noise ratio, than a similar subband system using conventional bit allocation, optimized mappings, and 64-PAM. A novel definition for measuring system efficiency, based on comparisons to pure analog PAM transmission, is used to evaluate the proposed system. The ideas presented in this paper can be used for future terrestrial TV broadcasting and mobile communication systems.

Ringing reduction in low bit-rate image subband coding using projection onto a space of paraboloids

Abstract This paper considers the well known problem of ringing distortion in subband coded images. Exploiting the fact that ringing artifacts are masked by edges and textures we propose a new method designed to remove all ringing distortion within the smooth image areas. The original image is used for classification purposes and the subband coded image is postprocessed using blockwise paraboloid fitting algorithms in the smooth image areas. Experimental results comparing subband coded images with and without application of the proposed method are presented. The results indicate that significant visual improvements can be made at the expense of a very small increase in bit-rat.