Sos S. Agaian

Multidimensional discrete unitary transforms : representation, partitioning, and algorithms

This reference presents a more efficient, flexible, and manageable approach to unitary transform calculation and examines novel concepts in the design, classification, and management of fast algorithms for different transforms in one-, two-, and multidimensional cases. Illustrating methods to construct new unitary transforms for best algorithm selection and development in real-world applications, the book contains a wide range of examples to compare the efficacy of different algorithms in a variety of one-, two-, and three-dimensional cases. Multidimensional Discrete Unitary Transforms builds progressively from simple representative cases to higher levels of generalization.

Decompositional methods for stack filtering using Fibonacci p -codes

Abstract Stack filters form a wide class of nonlinear filters which has received a great deal of attention during recent years. In this paper new decompositional methods based on Fibonacci p-codes for computing the output for different stack filters are presented. The computational complexities of these methods are also studied and numerical examples illustrating the benefits of using different values of p for different situations.

On rank selection probabilities

The concept of rank selection probabilities for stack filters has previously been introduced. If the probabilities are known, then the output distribution for i.i.d. input follows easily. There is another expression for the output distribution of a stack filter using certain quantities called A/sub i/. The authors utilize the different forms of output distribution to derive a simple connection between the quantities A/sub i/ and the rank selection probabilities. This also leads to a new fast method for the computation of rank selection probabilities. >

Accelerated predictive-transform

This paper presents a novel accelerated predictive-transform (APT) modeling methodology for use in compression. The APT scheme is illustrated with a monochrome 2D image compression application yielding very promising results. For example, when the Lena image is compressed to 0.056 bits per pixel and the pixel blocks are of dimension 16×16, it is shown that both the design and implementation computational complexity of the prior predictive-transform (PT) modeling art is improved by a factor of 12 without any loss in the visual quality of the compressed image. The APT methodology can also be used in other application areas such as estimation; detection, identification, channel and source integrated coding, and control and other related areas.

SBNR processor for stack filters

The signed binary number representation (SBNR) is used to reduce the number of PBF calculation stages in stack filters. The approach is based on the possibility of minimization of signed power-of-two terms in the SBNR representation of input data. A coder and a decoder for the mutual transformation of binary-weighted code and the minimal SBNR are proposed. An efficient algorithm and a processor structure for stack filtering based on the minimal SBNR are presented. The time complexity of the proposed filter is of order kT/sub PBF/, where k is the number of bits in the input signals and T/sub PBF/ is the delay in the incorporated circuit for the positive Boolean function (PBF). A stack filtering algorithm for the generalized nonadjacent form (GNAF) of signed digit number representation (SDNR) is also presented.

A unified approach to implementation of stack filters

New stack filter architectures are proposed. Known architectures are considered from new positions and combined to obtain new structures with suitable complexities and throughputs. It is shown that all stack filters can be used without changes when the input data is represented in one of the binary lexicographic codes. Stack filters are also proposed for the cases where the data are represented in multiple-value lexicographic codes. The class of pipeline-parallel structures for common stack filters is simple and modular in structure, and suitable for VLSI implementation. The time-area complexity of the proposed filters is O(k), where k is the number of bits in the input signals.<<ETX>>

Parametric family of discrete trigonometric transforms

In this paper, we introduce a new class of discrete parametric trigonometric transforms. We establish the conditions of unitarity of the discrete parametric trigonometric transform matrices, by which we construct a wide range of orthonormal transform matrices. Analysis of proposed unitary trigonometric (cosine, sine and combined sine-cosine) transforms is performed, and efficient algorithms for their computation are developed.

Spectral approach to logical distribution-free classification problem

A spectral approach to logical distribution-free classification is presented. The discriminant function is based on logical conjunctions which are called descriptors of the classes. The main steps of the algorithm are: (1) finding a minimal descriptor for each pattern class, (2) computing a local discriminant function for each minimal descriptor and (3) making the actual classification of the observed pattern into a class. For constructing minimal descriptors we utilize spectral algorithms to extract the prime implicants of the Boolean function corresponding: to a prototype class. The spectral algorithms involve computing Walsh and conjunctive (need-Muller) spectra for which there exists fast algorithms.

Edge-protection nonlinear filters for removing compression block artifacts and noise

JPEG is perhaps the most commonly used still-image standard due to its good compression rate, flexibility in choosing image quality and fast algorithm for implementation. In JPEG, the DCT is used for 8 by 8 block transforms. However the notorious block artifacts caused by the DCT are of great concern. In this article, we focus on the DCT and try different filters to smooth the annoying block boundaries which are very visible under a high compression rate. A new nonlinear filter is proposed which outperforms which are very visible under a high compression rate. A new nonlinear filter is proposed which outperforms existing techniques. The results are demonstrated for images with a comparison of mean-square-errors. For a general application, the new filter is used to cancel gaussian noise added to an image and the performance is compared with that of other commonly used filters.

Spectral approach to classification based on generalized unconditional tests

Spectral approach to distribution-free classification is presented. The discriminant function is based on generalized unconditional tests. The main steps of the algorithms are: (1) finding a set of deadlock generalized tests, (2) computing a local discriminant function for each such a test, and (3) performing the actual classification of the observed pattern into a class. The spectral algorithms involve computation of the Walsh and Reed-Muller (conjunctive) spectra using fast algorithms.