Dick E. Boekee

Regularized iterative image restoration with ringing reduction

Linear space-invariant image restoration algorithms often introduce ringing effects near sharp intensity transitions. It is shown that these artifacts are attributable to the regularization of the ill-posed image restoration problem. Two possible methods to reduce the ringing effects in restored images are proposed. The first method incorporates deterministic a priori knowledge about the original image into the restoration algorithm. The second method locally regulates the severity of the noise magnification and the ringing phenomenon, depending on the edge information in the image. A regularized iterative image restoration algorithm is proposed in which both ringing reduction methods are included by making use of the theory of the projections onto convex sets and the concept of norms in a weighted Hilbert space. Both the numerical performance and the visual evaluation of the results are improved by the use of ringing reduction. >

Subband coding of images using vector quantization

A novel two-dimensional subband coding technique is presented that can be applied to images as well as speech. A frequency-band decomposition of the image is carried out by means of 2D separable quadrature mirror filters, which split the image spectrum into 16 equal-rate subbands. These 16 parallel subband signals are regarded as a 16-dimensional vector source and coded as such using vector quantization. In the asymptotic case of high bit rates, a theoretical analysis yields that a lower bound to the gain is attainable by choosing this approach over scalar quantization of each subband with an optimal bit allocation. It is shown that vector quantization in this scheme has several advantages over coding the subbands separately. Experimental results are given, and it is shown the scheme has a performance that is comparable to that of more complex coding techniques. >

An optimal bit allocation algorithm for sub-band coding

An optimal bit allocation algorithm is presented that is suitable for all practical situations. Each source to be coded is assumed to have its own set of admissible quantizers (which can be either scalar or vector quantizers) which do not need to have integer bit rates. The distortion versus rate characteristic of each quantizer set may have an arbitrary shape. The algorithm is very simple in structure and can be applied to any practical coding scheme (such as a subband coder) that needs dynamic bit allocation.<<ETX>>

The R-norm information measure

The R -norm information measure is discussed and its properties, as well as an axiomatic characterization, are given. The measure is extended to conditional and joint measures. Applications to coding and hypothesis testing are given. The R -norm information measure includes Shannons information measure as a special case.

Scalar quantization error analysis for image subband coding using QMFs

The authors analyze the coding errors due to quantization by explicitly incorporating a mathematical model for a Lloyd-Max quantizer into a quadrature mirror filter (QMF) splitting and reconstruction scheme (P. H. Westerink et al., 1988). This approach explicitly incorporates quantization errors into a QMF system by means of a quantizer model. This makes it possible to discriminate between different types of coding errors, such as the aliasing error. Other errors that can be distinguished are a QMF design error, a signal error, and a random error, which is uncorrelated with the original image. Both a mean-squared error calculation and a subjective judgment of the coding errors show that the aliasing errors can be neglected for filter lengths of 12 taps or more. The signal error determines the sharpness of the reconstructed image, while the random error is most visible in the flat areas. >

Some aspects of error bounds in feature selection

Abstract In this paper we discuss various bounds on the Bayesian probability of error, which are used for feature selection, and are based on distance measures and information measures. We show that they are basically of two types. One type can be related to the f -divergence, the other can be related to information measures. This also clarifies some properties of these measures for the two-class problem and for the multiclass problem. We give some general bounds on the Bayesian probability of error and discuss various aspects of the different approaches.

Bounds and constructions for binary codes of length less than 24 and asymmetric distance less than 6

Upper bounds to the maximum number of codewords in a binary code of length n and asymmetric distance Delta are derived for some values of n and Delta . A method is given in which a code of length n-m and asymmetric distance at least t+1 is constructed by expurgating and puncturing a code of length n and Hamming distance at least 2t+1. Novel asymmetric error-correcting codes are constructed by applying this method to some celebrated symmetric error-correcting codes. a table is presented on the size of optimal asymmetric error-correcting codes of length less than 24 and asymmetric distance less than 6. >

The shortest feedback shift register that can generate a given sequence

In this paper the problem of finding the absolutely shortest (possibly nonlinear) feedback shift register, which can generate a given sequence with characters from some arbitrary finite alphabet, is considered. To this end, a new complexity measure is denned, called the maximum order complexity. A new theory of the nonlinear feedback shift register is developed, concerning elementary complexity properties of transposed and reciprocal sequences, and feedback functions of the maximum order feedback shift register equivalent. Moreover, Blumers algorithm is identified as a powerful tool for determining the maximum order complexity profile of sequences, as well as their period, in linear time and memory. The typical behaviour of the maximum order complexity profile is shown and the consequences for the analysis of given sequences and the synthesis of feedback shift registers are discussed.

Subband Coding of Color Images

The digital encoding of color images has received considerably less attention than the coding of monochrome images. And although most image coding algorithms indeed concentrate on the case of monochrome images, it is clear that color pictures are generally far more preferred and appreciated than monochrome images by the human observer. Modern image compression schemes therefore will all be suitable for color images, while for typical monochrome applications such as medical image data storage and the transmission of newspaper pictures, they will also be compatible with monochrome image compression. For example, both in present analog color television (NTSC/PAL/SECAM) and in the color television standard for digital television (the CCIR recommendation 601, [8]), the system is compatible with monochrome systems. Thus we will first discuss the encoding of monochrome images using subband coding. Then we will extend the technique to color images.

An efficient algorithm for the generation of DeBruijn cycles

An algorithm is presented for the generation of binary DeBruijn sequences using feedback shift registers (FSRs). The algorithm is based on the principle of cycle joining, through which all the cycles in the cycle structure of a FSR can be joined together to one complete cycle, thereby producing a DeBruijn sequence of period 2/sup n/, where n is the length of the FSR. By a proper choice of the feedback function of the FSR O(2/sup 2n///sup log2n/) DeBruijn sequences of period 2/sup n/ can be generated, requiring only 3n bits of storage and at most 4n FSR shifts for the generation of the next bit in the sequence. >