Optimal nonnegative color scanning filters

In this correspondence, the problem of designing color scanning filters for multi-illuminant color recording is considered. The filter transmittances are determined from a minimum-mean-squared orthogonal tristimulus error criterion that minimizes the color error in estimates obtained from noisy recorded data. Nonnegativity constraints essential for physical realizability are imposed on the filter transmittances. In order to demonstrate the significant improvements obtained, the resulting filters are compared with suboptimal filters reported in earlier literature.     

Mathematical methods for the analysis of color scanning filters

The problem of the sensitivity analysis of color scanning filters is addressed in this paper. The second differential of the mean square DeltaE(ab) error provides a means of calculating the sensitivity of the mean square DeltaE(ab) error to filter fabrication errors. Tolerances on the allowable change in the mean square DeltaE(ab) error are used to define bounds on the filter fabrication errors at all wavelengths and at single wavelengths.     

Figures of merit for color scanners

In the design and evaluation of color scanners and cameras, it is useful to have a single figure of merit that closely agrees with perceived color accuracy. In the past, several measures of goodness for color scanning filters have been proposed to fulfil such a requirement. Most of the proposed measures have had shortcomings in that they are either based on error metrics in color spaces that are not perceptually uniform, or in that they do not take into account the effects of measurement noise. An extension of the most promising measure, based on linearized CIELAB space, is proposed to obtain a new figure of merit that has a high degree of perceptual relevance and also accounts for the varying noise performance of different filters. The paper also provides a common framework for the different figures of merit and a comprehensive comparison of their computational complexity and reliability.     

Optimization of sensor response functions for colorimetry ofreflective and emissive objects

This paper describes the design of color filters for a surface color measurement device. The function of the device is to return the XYZ tristimulus vector characterizing the color of the surface. The device is designed to measure emissive as well as reflective surfaces. It uses an internal set of LEDs to illuminate reflective surfaces while characterizing their color under assumed standard illuminants. In the design of the filters, we formulate a nonlinear optimization problem with the goal of minimizing error in the uniform color space CIE L*a*b*. Our optimization criteria employs a technique to retain a linear structure while approximating the true L*a*b* error. In addition, our solution is regularized to account for system noise, filter roughness, and filter implementation errors. Experimental results indicate average and worst-case device accuracy of 0.27 L*a*b* DeltaE units and 1.56 L*a*b* DeltaE units for a "system tolerance" of 0.0005.     

Minimax design of two-channel low-delay perfect-reconstruction FIRfilter banks

The authors deal with the design problem of low-delay perfect-reconstruction filter banks for which the FIR analysis and synthesis filters have equiripple magnitude response. Based on the minimax error criterion, the design problem is formulated in such a manner that the coefficients for the FIR analysis filters can be found by minimising the weighted peak error of the designed analysis filters, subject to the perfect-reconstruction constraints. A design technique based on a modified dual-affine scaling variant of Karmarkar's (1989) algorithm, in conjunction with approximation schemes, is then developed for solving the resulting nonlinear optimisation problem. The effectiveness of the proposed design technique is demonstrated by several simulation examples     

Optimal design of complex FIR filters with arbitrary magnitude and group delay responses

This paper presents a method for the frequency-domain design of digital finite impulse response filters with arbitrary magnitude and group delay responses. The method can deal with both the equiripple design problem and the peak constrained least squares (PCLS) design problem. Consequently, the method can also be applied to the equiripple passbands and PCLS stopbands design problem as a special case of the PCLS design. Both the equiripple and the PCLS design problems are converted into weighted least squares optimization problems. They are then solved iteratively with appropriately updated error weighting functions. A novel scheme for updating the error weighting function is developed to incorporate the design requirements. Design examples are included in order to compare the performance of the filters designed using the proposed scheme and several other existing methods.     

Iterative reweighted least-squares design of FIR filters

Develops a new iterative reweighted least squares algorithm for the design of optimal L_p approximation FIR filters. The algorithm combines a variable p technique with a Newton's method to give excellent robust initial convergence and quadratic final convergence. Details of the convergence properties when applied to the L_p optimization problem are given. The primary purpose of L_p approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained L₂ approximation filters. The new method can also be applied to the complex Chebyshev approximation problem and to the design of 2D FIR filters     

Optimal Design of All-Pass Variable Fractional-Delay Digital Filters

This paper presents a computational method for the optimal design of all-pass variable fractional-delay (VFD) filters aiming to minimize the squared error of the fractional group delay subject to a low level of squared error in the phase response. The constrained optimization problem thus formulated is converted to an unconstrained least-squares (LS) optimization problem which is highly nonlinear. However, it can be approximated by a linear LS optimization problem which in turn simply requires the solution of a linear system. The proposed method can efficiently minimize the total error energy of the fractional group delay while maintaining constraints on the level of the error energy of the phase response. To make the error distribution as flat as possible, a weighted LS (WLS) design method is also developed. An error weighting function is obtained according to the solution of the previous constrained LS design. The maximum peak error is then further reduced by an iterative updating of the error weighting function. Numerical examples are included in order to compare the performance of the filters designed using the proposed methods with those designed by several existing methods.     

Robust minimum variance filtering

This paper deals with the robust minimum variance filtering problem for linear systems subject to norm-bounded parameter uncertainty in both the state and the output matrices of the state-space model. The problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty. Two methods for designing robust filters are investigated. The first one deals with constant parameter uncertainty and focuses on the design of steady-state filters that yield an upper bound to the worst-case asymptotic error variance. This bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system, and it can be made tighter if a tight bound on the latter power spectrum can be obtained. The second method allows for time-varying parameter uncertainty and for general time-varying systems and is more systematic. We develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems     

A mixed norm performance measure for the design of multiratefilterbanks

A mixed norm performance measure is presented to design the synthesis filters of a multirate filterbank. The mixed norm performance measure is based on the energy as well as the peak value of the error signal. Mathematically, the performance measure minimizes the l₂ -norm of the error signal subject to the l_∞-norm of the error being bounded by some positive value v (this imposes a bound on the peak value of the error signal). The design problem is shown to be that of a mixed ℋ₂/ℋ_∞ optimization problem. The theory of linear matrix inequalities (LMIs) offers a tractable solution to such multiobjective synthesis problems. The synthesis filters designed with the new performance measure are compared with those obtained by similar induced norm minimization techniques in terms of degree of reconstruction, order of the synthesis filters, SNR, and aliasing distortion     

L(p) norm design of stack filters.

Addresses the problem of designing optimal stack filters by employing an L(p) norm of the error between the desired signal and the estimated one. It is shown that the L(p) norm can be expressed as a linear function of the decision errors at the binary levels of the filter. Thus, an L(p)-optimal stack filter can be determined as the solution of a linear program. The conventional design of using the mean absolute error (MAE), therefore, becomes a special ease of the general L(p) norm-based design developed here. Other special cases of the proposed approach, of particular interest in signal processing, are the problems of optimal mean square error (p=2) and minimax (p-->infinity) stack filtering. Since an Linfinity optimization is a combinatorial problem, with its complexity increasing faster than exponentially with the filter size, the proposed L(p ) norm approach to stack filter design offers an additional benefit of a sound mathematical framework to obtain a practical engineering approximation to the solution of the minimax optimization problem. The conventional MAE design of an important subclass of stack filters, the weighted order statistic filters, is also extended to the L(p) norm-based design. By considering a typical application of restoring images corrupted with impulsive noise, several design examples are presented, to illustrate the performance of the L(p)-optimal stack filters with different values of p. Simulation results show that the L(p)-optimal stack filters with p=/>2 provide a better performance in terms of their capability in removing impulsive noise, compared to that achieved by using the conventional minimum MAE stack filters.     

Variable Digital Filter With Group Delay Flatness Specification or Phase Constraints

In this paper, we consider the design of finite-impulse response variable digital filters (VDFs) with variable cutoff frequency or variable fractional delay. We propose the design of VDFs with minimum integral squared error and constraints on the maximum error deviation in conjunction with flatness group delay specification or phase constraints. These specifications allow the VDFs to have approximately linear phase, especially in the passband. As these specifications are required to be satisfied for all the filters generated by the VDF with controllable spectral characteristics, the linear constraints resulting from the flatness specification are relaxed to inequality constraints. To make the optimization problem tractable for the phase constrained problem, suitable approximations are employed in the paper. The design problem is formulated as an optimization problem with a quadratic cost function and infinite number of constraints. A numerical scheme with adaptive grid step size is proposed for solving the optimization problem.     

Design of tone-dependent color-error diffusion halftoning systems.

Grayscale error diffusion introduces nonlinear distortion (directional artifacts and false textures), linear distortion (sharpening), and additive noise. Tone-dependent error diffusion (TDED) reduces these artifacts by controlling the diffusion of quantization errors based on the input graylevel. We present an extension of TDED to color. In color-error diffusion, which color to render becomes a major concern in addition to finding optimal dot patterns. We propose a visually meaningful scheme to train input-level (or tone-) dependent color-error filters. Our design approach employs a Neugebauer printer model and a color human visual system model that takes into account spatial considerations in color reproduction. The resulting halftones overcome several traditional error-diffusion artifacts and achieve significantly greater accuracy in color rendition.     

Minimax Design of IIR Digital Filters Using SDP Relaxation Technique

This paper presents a new algorithm using semidefinite programming (SDP) relaxation to design infinite impulse response digital filters in the minimax sense. Unlike traditional design algorithms that try to directly minimize the error limit, the proposed algorithm employs a bisection searching procedure to locate the minimum error limit of the approximation error. Given a fixed error limit at each iteration, the SDP relaxation technique is adopted to formulate the design problem in a convex form. In practice, the true minimax design cannot be always obtained. Thus, a regularized feasibility problem is adopted in the bisection searching procedure. The stability of the designed filters can also be guaranteed by adjusting the regularization coefficient. Unlike other sequential design methods, the proposed algorithm tries to find a feasible solution at each iteration of the sequential design procedure within a feasible set defined by the relaxed constraints. This feasible set is not restricted within the neighborhood of a given point obtained from the previous iteration. Thus, the proposed method can avoid being trapped in the locally minimum point. Four examples are presented in this paper to demonstrate the effectiveness of the proposed method.      

Design of Nonuniform Transmultiplexers with Block Samplers and Single-Input Single-Output Linear Time-Invariant Filters Based on Perfect Reconstruction Condition

This paper proposes a design of a nonuniform transmultiplexer with block samplers and single-input single-output linear time-invariant filters. First, the perfect reconstruction condition of the nonuniform transmultiplexer is derived. Then, the design problem is formulated as an optimization problem. In particular, the perfect reconstruction error is minimized in the \(L_{1}\) norm sense subject to the frequency selectivities of the filters. Computer numerical simulation results show that the designed nonuniform transmultiplexer with block samplers is robust to the channel noise and achieves a small reconstruction error.     

Decision-feedback equalization via separating hyperplanes

The design of finite-length decision-feedback equalization (DFE) forward and feedback filters under the assumption of genie-aided feedback and independent and equally likely transmitted symbols is considered. It is shown that the problem of determining DFE filters that minimize the probability of symbol error at high signal-to-noise ratio (SNR) is equivalent to finding the hyperplane that maximally separates two given finite groups of points in a finite-dimensional Euclidean space. The latter task can be formulated as a quadratic program which is readily solved numerically. It is also shown that the problem of finding finite-length DFE filters that minimize the probability of symbol error at any SNR subject to a certain separation condition is a convex optimization problem. The case where the transmitted data is coded using a runlength-limited code is also investigated. Examples show that this criterion yields a performance that is better than zero-forcing DFE on severely distorted channels at high SNR     

Optimal 100% Excess Bandwidth Signaling in Cochannel Interference

The problem of transmitter-receiver (T-R) filter design for detection of a binary phase-shift keying signal in asynchronous cochannel interference and Gaussian noise is considered. It is shown that maximum signal-to-interference-plus-noise ratio (SINR) can be achieved only if the T-R filters have a flat spectrum with 100% excess bandwidth. The bit error probability (BEP) performance of a system with the proposed filters is compared to that of a system with conventional root raised-cosine filters both for perfect and imperfect timing recovery cases. It is shown that the proposed filter design is superior to the conventional root raised-cosine filters both in having larger SINR and smaller BEP     

Design and analysis of vector color error diffusion halftoningsystems

Traditional error diffusion halftoning is a high quality method for producing binary images from digital grayscale images. Error diffusion shapes the quantization noise power into the high frequency regions where the human eye is the least sensitive. Error diffusion may be extended to color images by using error filters with matrix-valued coefficients to take into account the correlation among color planes. For vector color error diffusion, we propose three contributions. First, we analyze vector color error diffusion based on a new matrix gain model for the quantizer, which linearizes vector error diffusion. The model predicts the key characteristics of color error diffusion, esp. image sharpening and noise shaping. The proposed model includes linear gain models for the quantizer by Ardalan and Paulos (1987) and by Kite et al. (1997) as special cases. Second, based on our model, we optimize the noise shaping behavior of color error diffusion by designing error filters that are optimum with respect to any given linear spatially-invariant model of the human visual system. Our approach allows the error filter to have matrix-valued coefficients and diffuse quantization error across color channels in an opponent color representation. Thus, the noise is shaped into frequency regions of reduced human color sensitivity. To obtain the optimal filter, we derive a matrix version of the Yule-Walker equations which we solve by using a gradient descent algorithm. Finally, we show that the vector error filter has a parallel implementation as a polyphase filterbank.     

Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.