This letter proposes a Perfect-Reconstruction (PR) encryption scheme based on a PR QMF bank. Using the proposed scheme, signals can be encrypted and reconstructed perfectly by using two Periodically Time-Varying (PTV) digital filters respectively. Also we find that the proposed scheme has a "good" encryption effect and compares favorably with frequency scramble in the aspects of computation complexity, PR property, and degree of security.

This paper proposes a statistical expression of the output error variance due to coefficient quantization in separable denominator M-D digital filters. Using this expression, this paper shows that minimization of overall quantization errors can be performed by minimizing the roundoff noise.

This paper proposes statistical analysis of phase-only correlation functions with phase-spectrum differences following wrapped distributions. We first assume phase-spectrum differences between two signals to be random variables following a linear distribution. Next, based on directional statistics, we convert the linear distribution into a wrapped distribution by wrapping the linear distribution around the circumference of the unit circle. Finally, we derive general expressions of the expectation and variance of the POC functions with phase-spectrum differences following wrapped distributions. We obtain exactly the same expressions between a linear distribution and its corresponding wrapped distribution.

In this paper, we propose an enlargement method for images with Gaussian noise based on the Laplacian pyramid (LP) representation. Unlike lowpass pre-processing approaches to the LP enlargement method, an embedded approach is used in this paper. Since the amplitude of Gaussian noise signals is smaller than the amplitude of image edge signals in the predicted LP stage, we adopt a modified ε-filter in the proposed LP enlargement algorithm to reduce the Gaussian noise. Experimental results show that the proposed method can obtain high accuracy denoise enlarged images.

The aim of this study is to improve the accuracy of flicker parameters estimation in old film sequences in which moving objects are present. Conventional methods tend to fail in flicker parameters estimation due to the effects of moving objects. Our proposed method firstly utilizes an adaptive Gaussian mixture model (GMM)-based method to detect the moving objects in the film sequences, and combines the detected results with the histogram-matched frames to generate reference frames for flicker parameters estimation. Then, on the basis of a linear flicker model, the proposed method uses an M-estimator with the reference frames to estimate the flicker parameters. Experimental results show that the proposed method can effectively improve the accuracy of flicker parameters estimation when the moving objects are present in the film sequences.

In this paper, we propose a novel bicubic method for digital image interpolation. Since the conventional bicubic method does not consider image local features, the interpolated images obtained by the conventional bicubic method often have a blurring problem. In this paper, the proposed bicubic method adopts both the local asymmetry features and the local gradient features of an image in the interpolation processing. Experimental results show that the proposed method can obtain high accuracy interpolated images.

On the basis of the controllability gramians, the observability gramians and the second order modes, this paper shows that optimal realizations (filter structures having minimum roundoff noises) of quarter-plane-causal, recursive and separable in denominator 2-D digital filters (CRSD filters for short) are scaled and rotated balanced realizations. Two applications of this relation are given. The first one gives a simple proof of the absence of overflow oscillations in optimal realizations. The second one, which is the main result of this paper, gives a direct design method of CRSD filters in the spatial domain. This method simplifies traditional two-step design (approximation and synthesis) into a one-step design with much less computational complexity. Resulting filters of this direct design method can approximate given 2-D impulse responses closely. In addition, they are always guaranteed to be stable, nearly optimal with respect to roundoff noise and free of overflow oscillations. The efficiency of the direct design method is shown by numerical examples.

This paper studies the design problem of causal, recursive and separable denominator (CRSD) 3-D state-space digital filters. First, a balanced approximation method and a synthesis method of optimal realizations of CRSD 3-D digital filters are proposed by introducing the concept of characteristic filters. Then, a simple equivalent relation between balanced realizations and optimal realizations of CRSD 3-D digital filters is revealed. Using this relation and the balanced approximation method proposed, this paper proposes a spatial-domain direct design method of CRSD 3-D digital filters. This direct design method can perform approximation and synthesis of CRSD 3-D digital filters simultaneously. Further, it can result in stable state-space digital filters which are nealy optimal with respect to roundoff noise, and free of overflow oscillations. Effciency of direct design method is shown by a numerical example.

The average coefficient sensitivity is defined for 2-D systems described by Roesser's local state space model. The sensitivity can be computed by using the 2-D observability Gramian and the 2-D controllability Gramian, which are also called the 2-D noise matrix and the 2-D covariance matrix if the 2-D systems are considered to be 2-D digital filters. Minimization of sensitivity via 2-D equivalent transforms is studied in cases of having no constraint and having a scaling constraint on the state vector. In the first case, the minimum sensitivity realizations are equivalent to the 2-D balanced realizations modulo a block orthogonal transform. In the second case, the 2-D systems are considered to be 2-D digital filters and the minimization of sensitivity is equivalent to the minimization of roundoff noise under l2-norm scaling constraint. An example is given to show method of analysing and minimizing the sensitivity of 2-D systems.

This paper designs and evaluates highly parallel VLSI processors for real time 2-D state-space digital filters using hierarchical behavioral description language and synthesizer. The architecture of the 2-D state-space digital filtering system is a linear systolic array of homogeneous VLSI processors, each of which consists of eight processing elements (PEs) executing 1-D state-space digital filtering with multi-input and multi-output. Hierarchical behavioral description language and synthesizer are adopted to design and evaluate PE's and the VLSI processors. One 16 bit fixed-point PE executing a (4, 4)-th order 2-D state-space digital filtering is described on the basis of distributed arithmetic in about 1,200 steps by the description language and is composed of 15 K gates in terms of 2 input NAND gate. One VLSI processor which is a cascade connection of eight PEs is composed of 129 K gates and can be integrated into one 1515 [mm2] VLSI chip using 1 µm CMOS standard cell. The 2-D state-space digital filtering system composed of 128 VLSI processors at 25 MHz clock can execute a 1,0241,024 image in 1.47 [msec] and thus can be applied to real-time conventional video signal processing.

This paper proposes a closed form solution to L2-sensitivity minimization of second-order state-space digital filters. Restricting ourselves to the second-order case of state-space digital filters, we can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, the L2-sensitivity minimization problem can be converted into a problem to find the solution to a fourth-degree polynomial equation of constant coefficients, which can be algebraically solved in closed form without iterative calculations.

This paper proposes closed form solutions to the L2-sensitivity minimization subject to L2-scaling constraints for second-order state-space digital filters with real poles. We consider two cases of second-order digital filters: distinct real poles and multiple real poles. The proposed approach reduces the constrained optimization problem to an unconstrained optimization problem by appropriate variable transformation. We can express the L2-sensitivity by a simple linear combination of exponential functions and formulate the L2-sensitivity minimization problem by a simple polynomial equation. As a result, L2-sensitivity is expressed in closed form, and its minimization subject to L2-scaling constraints is achieved without iterative calculations.

This paper studies the model reduction of separable denominator multi-dimensional (SD M-D, M is used as an integer) linear, shift-invariant systems (systems for short). First, it shows that the controllability, observability and stability of an SD M-D system are completely determined by M 1-D multi-input multi-output systems, which are referred to as the characteristic systems in this paper. Then the balanced realizations of SD M-D systems are defined, and a synthesis method of such realizations is given. Finally, a model reduction method based on the balanced realizations is proposed. Validity of this method is illustrated by a numerical example of a 3-D system.

In order to suppress constant input limit cycles in 2-D separable denominator digital filters, bias cancel realizations are proposed by modifying 2-D separable denominator digital filters free of zero imput limit cycles.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have odd-symmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions considering the odd-symmetry of the phase-spectrum differences. As a result, the expectation and variance of the POC functions can be expressed by characteristic functions or trigonometric moments of the phase-spectrum differences. Furthermore, it is shown that the peak value of the POC function monotonically decreases and the sidelobe values monotonically increase as the variance of the phase-spectrum differences increases.

A new approach to design variable IIR digital filters by using a cascade of N identical individual filters of any order n is proposed in this paper. First, the approximation method for lowpass filter specifications is outlined, then the general limitations of the new method are investigated and a compact formula is derived. Next, the limitations for the main canonic approximations (Butterworth, Chebyshev and Elliptic) are investigated and compared and convenient expressions for design and evaluation are obtained. New first- and second-order filter sections, permitting very easy tuning of the cutoff frequency by recalculating and reprogramming of a single multiplier coefficient value, are developed and the design and tuning strategies for highpass, bandpass and bandstop filters are proposed. Finally design examples are given and the sound superiority of the new method compared to other known is demonstrated experimentally.

This paper proposes an efficient design method of three-dimensional (3-D) recursive digital filters for video signal processing via decomposition of magnitude specifications. A given magnitude specification of a 3-D digital filter is decomposed into specifications of 1-D digital filters with three different (horizontal, vertical, and temporal) directions. This decomposition can reduce design problems of 3-D digital filters to design problems of 1-D digital filters, which can be designed with ease by conventional methods. Consequently, design of 3-D digital filters can be efficiently performed without complicated tests for stability and large amount of computations. In order to process video signal in real time, the 1-D digital filters with temporal direction must be causal, which is not the case in horizontal and vertical directions. Since the proposed method can approximate negative magnitude specifications obtained by the decomposition with causal 1-D R filters, the 1-D digital filters with temporal direction can be causal. Therefore the 3-D digital filters designed by the proposed method is suitable for real time video signal processing. The designed 3-D digital filters have a parallel separable structure having high parallelism, regularity and modularity, and thus is suitable for high-speed VLSI implementation.

This paper presents FIR digital filters based on stochastic/binary hybrid computation with reduced hardware complexity and high computational accuracy. Recently, some attempts have been made to apply stochastic computation to realization of digital filters. Such realization methods lead to significant reduction of hardware complexity over the conventional filter realizations based on binary computation. However, the stochastic digital filters suffer from lower computational accuracy than the digital filters based on binary computation because of the random error fluctuations that are generated in stochastic bit streams, stochastic multipliers, and stochastic adders. This becomes a serious problem in the case of FIR filter realizations compared with the IIR counterparts because FIR filters usually require larger number of multiplications and additions than IIR filters. To improve the computational accuracy, this paper presents a stochastic/binary hybrid realization, where multipliers are realized using stochastic computation but adders are realized using binary computation. In addition, a coefficient-scaling technique is proposed to further improve the computational accuracy of stochastic FIR filters. Furthermore, the transposed structure is applied to the FIR filter realization, leading to reduction of hardware complexity. Evaluation results demonstrate that our method achieves at most 40dB improvement in minimum stopband attenuation compared with the conventional pure stochastic design.

This paper proposes an analysis method of the roundoff error due to finite-wordlength decoding in fractal image coding. The proposed method can be applied to large images such as 256 256 or 512 512 images because it needs no complex matrix computation. The simplified model used here ignores the effect of decimation ratio on the roundoff error because it is negligible. As an analysis result, the proposed method gives the output error variance which consists of grey-tone scaling coefficients and an iteration number. This method is tested on various types of 12 standard images which have 256 256 size or 512 512 size with 256 grey levels. Comparisons of simulation results with analysis results are given. The results show that our analysis method is valid for the fractal image coding.