Two-dimensional Recursive Filters Research Articles

Design of Two-Dimensional Recursive IIR Filters Using Cooperative Quantum Particle Swarm Optimization with Dynamic Varying Search Area and Lévy Flights

Design of Two-Dimensional Recursive IIR Filters Using Cooperative Quantum Particle Swarm Optimization with Dynamic Varying Search Area and Lévy Flights

Design of 1-D and 2-D recursive filters using crossover bacterial foraging and Cuckoo search techniques

Recently, there has been an increasing interest on the application of the evolutionary algorithms in order to solve the drawbacks of traditional filter design methods. Unlike classical methods, they offer the advantage of not requiring a good initial estimate of filter parameters to proceed. This paper presents design of one-dimensional (1-D) and two-dimensional (2-D) recursive filters using crossover bacterial foraging (COBFO) and Cuckoo Search (CS) techniques. Design of 1-D and 2-D recursive filters is considered here as a constrained optimization problem to ensure stability. The solution is obtained through convergence of a biased random search using crossover bacterial foraging optimization technique to ensure quality. A faster solution is also obtained through the convergence of a meta heuristic search technique called the Cuckoo search technique. Inbuilt constraint handling capability makes our proposal attractive in the design of recursive filters. Results are compared with genetic algorithm (GA) and bacteria foraging optimization (BFO) techniques.

Quality analysis of two-dimensional recursive filter

Данная статья посвящена анализу качества двумерного цифрового фильтра. Полученные результаты полностью согласовываются с теорией. Исследовано влияние взаимной информации на качество оценки медленно изменяющихся процессов

Design of a two-dimensional recursive filter using the bees algorithm

This paper presents the first application of the bees algorithm to the optimisation of parameters of a two-dimensional (2D) recursive digital filter. The algorithm employs a search technique inspired by the foraging behaviour of honey bees. The results obtained show clear improvement compared to those produced by the widely adopted genetic algorithm (GA).

Stabilization of 2D NSHP Recursive Digital Filters with Guaranteed Stability Using PLSI Polynomials

Two-dimensional digital filters have gained wide acceptance in recent years. For recursive filters, nonsymmetric half-plane versions (also known as semicausal) are more general than quarter-plane versions (also known as causal) in approximating arbitrary magnitude characteristics. The major problem in designing two-dimensional recursive filters is to guarantee their stability with the expected magnitude response. In general, it is very difficult to take stability constraints into account during the stage of approximation. This is the reason why it is useful to develop techniques, by which stability problem can be separated from the approximation problem. In this way, at the end of approximation process, if the filter becomes unstable, there is a need for stabilization procedures that produce a stable filter with similar magnitude response as that of the unstable filter. This paper, demonstrates a stabilization procedure for a two-dimensional nonsymmetric half-plane recursive filters based on planar least squares inverse (PLSI) polynomials. The paper's findings prove that, a new way of form-preserving transformation can be used to obtain stable PLSI polynomials. Therefore obtaining PLSI polynomial is computationally less involved with the proposed form-preserving transformation as compared to existing methods, and the stability of the resulting filters is guaranteed.

Design of two-dimensional recursive filters by using Taguchi-based immune algorithm

The Taguchi-based immune algorithm (TBIA), based on both the features of a biological immune system and the systematic reasoning ability of the Taguchi method, is applied in this work to solve the design problem of two-dimensional (2D) recursive digital filters. In the TBIA, the clonal proliferation within hypermutation for several antibody diversifications and the recombination by using the Taguchi method for the local search are integrated to improve the capabilities of exploration and exploitation. The systematic reasoning ability of the Taguchi method is implemented in the recombination operation to select the better antibody genes to achieve the potential recombination, and consequently enhance the TBIA. The design of the 2D filter is reduced to a constrained minimisation problem, the solution of which is achieved by the convergence of the presented TBIA. The computational experiments show that the presented TBIA approach can obtain better results than some previous design methods.

Image recovery under nonlinear and non-Gaussian degradations

A new two-dimensional recursive filter for recovering degraded images is proposed that is based on particle-filter theory. The main contribution of this work lies in evolving a framework that has the potential to recover images suffering from a general class of degradations such as system nonlinearity and non-Gaussian observation noise. Samples of the prior probability distribution of the original image are obtained by propagating the samples through an appropriate state model. Given the measurement model and the degraded image, the weights of the samples are computed. The samples and their corresponding weights are used to calculate the conditional mean that yields an estimate of the original image. The proposed method is validated by demonstrating its effectiveness in recovering images degraded by film-grain noise. Synthetic as well as real examples are considered for this purpose. Performance is also compared with that of an existing scheme.

Corrections to “Design of Two-Dimensional Recursive Filters Using Genetic Algorithms”

Corrections to “Design of Two-Dimensional Recursive Filters Using Genetic Algorithms”

Design of two-dimensional recursive filters using genetic algorithms

In this paper, we examine a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs). The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA. Theoretical results are illustrated by a numerical example. Also, comparison with the results of some previous design methods is attempted.

Design of two-dimensional recursive filters by using neural networks

A new design method for two-dimensional (2-D) recursive digital filters is investigated. The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate neural network. The method is tested on a numerical example and compared with previously published methods when applied to the same example. Advantages of the proposed method over the existing ones are discussed as well.

Two-dimensional recursive filtering algorithm with edge preserving properties and reduced numerical complexity

The filtering problem for noisy nonhomogeneous images is considered. A semicausal recursive filter with edge information is proposed. The filter is obtained as a combination of a one-dimensional (1-D) fixed-interval smoother and of a 1-D Kalman predictor, and involves a modest computational burden. Experimental results show the effectiveness of the new filtering scheme.

Behaviour of stability tests for two-dimensional digital recursive filters when faced with rounding errors

In this paper, the behaviour of four recent algorithms, which test the stability of two-dimensional (2-D) real recursive filters, are compared when faced with rounding errors in floating point arithmetic. Experimental results, comparing the data given by these algorithms when they are implemented either in floating point arithmetic, or with infinite precision in formal calculus, are presented. It appears with this comparison, that this behaviour is a very important point for choosing such an algorithm among all the existing ones.

A Framework for Two-Dimensional Hyperstability Theory Based Provably Convergent Adaptive Two-Dimensional IIR Filtering

A set of results for two-dimensional quarter plane causal systems reminiscent of one-dimensional hyperstability theory have been reported. The key to this development is a little known result of Landau [Math. Ann., 62 (1906), p. 272], which asserts that a positive polynomial in two variables can be expressed as the sum of squares of polynomials in one variable whose coefficients are real rational functions of the other variable. The tools used are largely based on notions of passivity and the results obtained can be interpreted as a two-dimensional quarter plane causal generalization of the fact that if the total flow of energy into a dissipative system is upper bounded then both input and output asymptotically die out to zero. An adaptive two-dimensional recursive filtering scheme potentially useful in propagating wave type two-dimensional problems is considered next. It is then shown via our two-dimensional hyperstability results that the adaptive scheme converges in an appropriate sense.

High speed architectures for two-dimensional state-space recursive filtering

A description is given of 2-D state-space filter algorithms, and two VLSI architectures for high-speed applications are proposed. The advanced state update architecture trades increased throughput rate and a simple input-output scheme for increased hardware. The technique is based on block processing. The state update matrix is changed by recursive multiplications, and the advanced state vector can be calculated. This architecture is a two-dimensional systolic array. It can process one pixel during each multiplication/addition clock period with a regular line-by-line scanning method. To achieve very high speed, the global speedup architecture is utilized by exploiting the inherent spatial concurrency. This architecture consists of a number of column array processors. Based on the computational independence between the samples along the diagonal lines in a first-quadrant 2-D system, it works on multiple columns of images concurrently. The architecture is very modular and flexible. The throughput rate can be very high and is adjustable by changing the number of column processors. Different high-speed architectures for image processing are compared. >

Design of highly selective two-dimensional recursive fan filters by relaxing symmetry constraints

We show for the design of quadrantally symmetric 2-D fan filters that it is unnecessarily restrictive to prescribe exact quadrantal symmetry, which requires that the denominator of the Z-transform transfer function be product-separable. Superior approximately symmetric fan filter designs can be achieved using nonseparable denominators.

Formation of the block toeplitz matrix for two-dimensional PLSI Polynomials

The planar least-squares inverse (PLSI) polynomials are used for stabilization of two-dimensional unstable recursive filters. In order to obtain the PLSI polynomials, the main work involved consists in forming a set of linear equations and then solving them. In this paper we present an efficient and simple method to form the necessary set of linear equations (i.e., the required coefficient matrix) for a chosen pattern and order of the desired PLSI polynomial, starting from the denominator polynomial of a two-dimensional unstable recursive filter.

Using Canny's criteria to derive a recursively implemented optimal edge detector

A highly efficient recursive algorithm for edge detection is presented. Using Canny's design [1], we show that a solution to his precise formulation of detection and localization for an infinite extent filter leads to an optimal operator in one dimension, which can be efficiently implemented by two recursive filters moving in opposite directions. In addition to the noise truncature immunity which results, the recursive nature of the filtering operations leads, with sequential machines, to a substantial saving in computational effort (five multiplications and five additions for one pixel, independent of the size of the neighborhood). The extension to the two-dimensional case is considered and the resulting filtering structures are implemented as two-dimensional recursive filters. Hence, the filter size can be varied by simply changing the value of one parameter without affecting the time execution of the algorithm. Performance measures of this new edge detector are given and compared to Canny's filters. Various experimental results are shown.

A portable high-speed digital image processing instrument for the enhancement of television images

It is known that digital images may be usefully enhanced using two-dimensional (2D) recursive filters. The associated digital filter algorithms must have acceptable word lengths and be implement-able over the entire image at an acceptable processing speed. Spatial-integrator 2D filtering algorithms and recursion along diagonal lines of pixels are used to permit the design and construction of a fast, portable, and low-cost television image-enhancement instrument. Menu-driven software permits the nonspecialist user to enhance television images in less than 4 s using any of 27 different 2D filter transfer functions.

A fast filter for real-time image processing

In this paper, a new digital filter structure is developed for the implementation of two-dimensional (2-D) recursive filters for realtime image processing. The proposed structure has a short clock cycle time or a high data throughput rate, independent of the order of the filter. Parallelism and pipelining are the two features of the proposed filter structure that contribute to its high-speed performance. The filter can be implemented without multipliers. Using standard integrated circuits and memories, the new filter is capable of filtering images of size up to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">512 {\times} 512</tex> pixels with a TV scan rate of 30 frames/s in real time. The effects of the finite precision arithmetic have been considered. Scaling and overflow problems are studied to give insight into the choice of a proper scaling factor, so that an adequate signal-to-noise ratio at the filter output can be obtained.

On the proof of stabilization of two-dimensional recursive filters via discrete Hilbert transform

In this paper, we prove that the two-dimensional recursive digital filters stabilized via the discrete Hilbert transform (DHT) would be stable, with a constraint on the amplitude of the frequency spectrum of the original unstable filter. It is pointed out in the discussion that the finer the grid <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">(w_1, w_2)</tex> is, the better will be the matching of the magnitude spectrum with that of the original unstable filter.