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This paper proposes a low-complexity convolutional neural network (CNN) for super-resolution (SR). The proposed deep-learning model for SR has two layers to deal with horizontal, vertical, and diagonal visual information. The front-end layer extracts the horizontal and vertical high-frequency signals using a CNN with one-dimensional (1D) filters. In the high-resolution image-restoration layer, the high-frequency signals in the diagonal directions are processed by additional two-dimensional (2D) filters. The proposed model consists of 1D and 2D filters, and as a result, we can reduce the computational complexity of the existing SR algorithms, with negligible visual loss. The computational complexity of the proposed algorithm is 71.37%, 61.82%, and 50.78% lower in CPU, TPU, and GPU than the very-deep SR (VDSR) algorithm, with a peak signal-to-noise ratio loss of 0.49 dB.

В статье определена связь между базовыми апертурами фильтра и их различными конфигурациями. Показано, как для фильтра заданной конфигурации выбираются отсчеты коэффициента автокорреляции входного изображения. The connection between the basic filter apertures and their various configurations is determined. It is shown how samples of the autocorrelation coefficient of the input image are selected for a filter of a given configuration.

In this paper, we present a general approximation for 2D filters by using only power-of-two terms. This enables to easily implement these filters in electronic devices such as FPGA and ASIC just by using simple hardware shifters and adders/subtractors. Consequently, no division and no multiplication operators are required, which can reduce the memory and the power needed for computing operations such as convolution. Instead of using only additions and power-of-two terms for representing a number like in the standard binary decomposition, our model also uses subtractions for representing and approximating numbers. In addition, we propose a binary tree structure for computing a minimal representation in power-of-two terms in such a way that hardware shifters used for performing a convolution with a low-pass filter for example are well reduced to their minimum. Based on some experiments performed for contrast enhancement, which is a common image processing operation, we have noticed that good results can be obtained using our approximation in terms of image quality, hardware resources, and power consumption when compared to some other binary representations.

In this paper state space realizations for all-pole and all-zero two-dimensional (2D) lattice discrete ®lters are presented. The proposed realizations are based on the corresponding circuit implementations. For the realizations, the 2D state space model of the Roesser type was used. The dimension of the state vector was minimal. Three low-order examples are presented to illustrate the proposed results.

We investigated channel estimation with scattered pilots (SPs) in digital terrestrial television broadcasting (DTTB) and the performance of a receiver with a two-dimensional (2D) filter. High-accuracy interpolation is necessary because we perform channel equalization with SPs, which are inserted in transmit signals nonrectangularly. This interpolation is performed with a 2D filter that has a nonrectangular spectrum. However, the generation of the 2D filter involves heavy computational complexity. We propose a method of reducing the computational complexity by designing separable 2D filters. Then the 2D filters are generated from 1D prototype filters. We'll also indicate the effectiveness of some methods of generating 1D prototype filters. In addition, we present simulation results that compare our method with some conventional methods and show its effectiveness.

It is well known that, unlike the 1D case, it is not always possible to find a minimal state-space realization for a general 2D filter or system described by a transfer function except for some particular categories. The purpose of this paper is to explore the possibility of minimal Roesser model realization for a class of 2D filters or systems which does not belong to the clarified categories. As main results, a constructive realization procedure is first proposed, which can be viewed as a kind of generalization of the well-known 1D realization approaches. Based on the proposed procedure, a sufficient condition for the existence of minimal realization of the considered class of 2D filters is derived, and the construction of such a minimal realization is shown. In addition, some further possible variations and applications of the obtained results are discussed and several illustrative examples are presented to show the details and effectiveness of the proposed approach.

Various two-dimensional weight functions (windows) are applied to processing and the analysis of radar images in millimeter range. For construction of two-dimensional filters it is necessary to synthesize them on some basic areas which geometry has essential value. It influences physical characteristics of filters, and also results of processing of multivariate signals. We shall notice, that classical methods allow to synthesize 2D filters only on the elementary basic areas. On the basis of the theory of R-functions it is possible to describe the equation of basic area of the reference areas of the any shape at an analytical level. Such approach allows to build two-dimensional weight functions (windows) on reference areas of non-standard geometry.

Symmetry properties of phase responses of 2D filters are reported. The classes of functions that possess the various types of symmetries in their phase responses are determined. The relationships between the magnitude symmetry and phase symmetry that a filter frequency response may possess are also established. Characteristics of the factors that possess the different standard symmetries in their magnitude response are also discussed. >

The purpose of this paper is to establish a new constructive procedure for realization of 2D systems by Fornasini-Marchesini second (F-MII) local state-space model which can further reduce the order of the resultant realization to about half of that obtained by the procedure given recently by the authors. Nontrivial illustrative examples are given.

Meta-materials are characterised using a modal technique for the analysis of 2N- port two dimensional filter networks. It will be shown that in general, all such networks support N modes of propagation each with different propagation constants unless as with the TEM multi-wire transmission line, the inductance matrix is the inverse of the capacitance matrix. Furthermore a simple equivalent circuit for these 2N port networks is derived, enabling complete network analysis for any combination of modal excitations. An explicit formula is derived for the propagation constants of a quasi lowpass filter. This demonstrates that there are always N modes even when the transverse network is infinite in extent.

Frequently in character recognition, there is a need to correlate or convolve purely real 2D inputs and real 2D filters. We propose two optical correlators. The first, basic real-input-real-filter optical correlator, adds x and y mirror images adjacent to the image to generate real and even images. This avoids the need for an offset reference to capture phase. Therefore, we have greater diffraction efficiency and a reduction in filter LCD pixel size. The second, Hilbert transform basic real-input-real-filter optical correlator, uses a Hilbert transform by masking in the filter plane to reduce the number elements in the filter LCD to that of the number of pixels in a filter image. An optical system can generate the mirror images in real time so that both the input LCD and the filter LCD can have only the same number of elements as their respective number of image pixels. We show how a spatial filter can be used to remove the intensity offset produced in the Hilbert transform and restore shift invariance if required. Finally, if desired, some rotation invariance can be achieved by overlapping the mirror images with the basic correlator. Advantages and disadvantages of the proposed correlators are discussed.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

In this paper, we investigate the problem of stability of a class of linear two-dimensional (2D) digital filters when implemented on finite word-length machines and subject to uncertain variations in the parameters. A necessary and sufficient robust stability condition is developed and expressed in terms of a system of linear matrix inequalities (LMIs). Two examples are presented to illustrate the developed theory.

In a media with laterally-varying velocity, wavefield extrapolation can be realized by the recursive application of 2-D spatially varying convolutional filters on all frequency components at all spatial locations in the temporal frequency and spatial (F-X) domain. This explicit method is intuitively clear and is relatively simple in algorithm. For a given temporal frequency, the effect of lateral velocity variations in extrapolation process can be handled by using velocity dependent extrapolators. Furthermore, the method is parallel in nature. On a multiprocessor system, instead of extrapolate the wavefield in depth for one frequency at a time, the procedure is actually performed concurrently on all frequency components within all available processors. Therefore, the computational scheme is very suitable to be implemented on various parallel architecture systems such as the Cray T3D Massively Parallel Processors.

A method of reconstruction sea wave heights spectra using the nonlinear model of transfer function relating wave slopes with sea surface images is developed. The method includes the numerical simulation of optical images under various illumination conditions and the synthesis of the spatial-frequency 2-D filters for reconstruction ofsea-surface slope spectra from optical images spectra. The developed filters have been approximated with a. para-metric function. The dependencies of the approximation parameters on various imaging conditions are discussed. 1 . Introduction.The problem of remote measurement of the two-dimensional spatial spectra of sea wave heightsarises in studying series of phenomena on the ocean-atmosphere boundary: (wind-driven wavesand the interaction of internal and surface waves) in the ecological monitoring of the sea surface (for example, concerning the estimation of the degree of pollution of the sea surface by oilproducts) etc. [ I I. A considerable number of papers published in recent years [2- 1 1 ]

From the point of view of reflection signal fidelity, the best way of removing strong regular noise from a common shot gather is to estimate the noise and then subtract it from the data. This minimizes the distortion of the signal. The Karhunen±Loeive (K±L) transform is the basis of such a method, and may be used to extract high-amplitude coherent noise from common shot gathers acquired in seismic reflection surveys on land. In this paper we compare the results of filtering synthetic and real data examples in the frequency±wavenumber (f±k) domain, by hyperbolic velocity filtering in the intercept-slowness (tau-p) domain, and by extracting the noise using the K±L transform. The f±k and hyperbolic velocity filters cause serious distortion of the reflection signals, especially when the difference between the apparent velocities of signal and noise is small. In contrast, the K±L transform enables the noise to be extracted with minimal distortion of the reflection signals. It is a common experience in processing land seismic reflection data to be confronted with data containing weak reflection signals submerged by strong, regular noise such as groundroll or air waves. Although the stack-array approach to the choice of acquisition parameters is a powerful technique for suppressing these types of noise in processed sections, applications such as AVO analysis of the prestack data require that the noise be suppressed with minimum distortion of the reflection signals. For such prestack applications, the choice of filtering method to remove the noise is very important. Other types of source-generated noise, commonly observed in land data, are reverberant refraction events parallel to the first breaks. They are even more difficult to suppress than groundroll and airwaves because their apparent velocities are close to the apparent velocities of the reflection events at far offsets. We show synthetic examples to evaluate the performance of the three filtering methods when the apparent velocities of strong, regular noise are similar to, and different from, the apparent velocities of reflection signals. We then show a real data example which illustrates the superiority of the K±L transform method of noise extraction for suppressing the reverberant refracted arrivals.

In this paper we propose some techniques to design several types of 2D band-pass filters based on an ID prototype filter of a Gaussian type. First, a low-pass 2D Gaussian filter is obtained. Then, we show how a circular 2D IIR band-pass filter is derived. A band-pass filter with two symmetric bands centered around a given pair of frequencies is also obtained Finally, a FIR ID Gaussian filter is designed, from which we derive a multi-band 2D FIR filter, with given peak frequencies.

In this paper the state space model for 2D filters originally proposed by Attasi (1976) is re-examined. A necessary and sufficient condition for the Attasi state space model to be minimal is shown. A canonic form is developed for this state space model. The canonic form is then used to provide a computationally beneficial technique for realizing the Attasi state space model from 2D filter pulse response data.

The extension of Luenberger's observer theory to 2D systems is considered. Equations are developed for the design of 2D observers Conditions are given for the use of these observers in the stabilization of 2D systems through state feedback.