In this paper, we analyze the existing results to derive the cross-correlation distributions of p-ary m-sequences and their decimated sequences for an odd prime p and various decimations d. Based on the previously known results, a methodology to obtain the distribution of their cross-correlation values is also formulated.

Bipolar complementary sequence pairs of Types II and III are defined, enumerated for n ≤ 28, and classified. Type-II pairs are shown to exist only at lengths 2^m, and necessary conditions for Type-III pairs lead to a non-existence conjecture regarding their length.

Variable-weight optical orthogonal codes (OOCs) were introduced by Yang for multi-media optical CDMA systems with multiple quality of service (QoS) requirements. Some works had been done on the existence of optimal (υ,W,1,Q)-OOCs for W ∈ {{3,4}, {3,5}, {4,5}}. In this paper, by using quadratic residues, seven new infinite classes of optimal (υ,{k,6},1,Q)-OOCs for k ∈ {3,4} are constructed.

In this paper, new design of optimal frequency hopping sequences (FHSs) with low hit zone (LHZ) with respect to the Peng-Fan-Lee bound is presented based on interleaving techniques. By the new design, new classes of optimal LHZ FHS sets with large family size are obtained. It is shown that all the sequences in the proposed FHS sets are shift distinct. The proposed FHS sets are suitable for quasi-synchronous time/frequency hopping code division multiple access systems to eliminate multiple-access interference.

Variable-weight optical orthogonal codes (OOCs) have application in multimedia optical code division multiple access (OCDMA) systems supporting multiple quality of services (QoS). In this paper, several combinatorial constructions for optimal variable-weight OOCs are presented explicitly. A useful recursive construction for optimal variable-weight OOCs is proposed as well. Based on these results, two new infinite classes of optimal variable-weight OOCs with Hamming weights 3 and 4 are obtained.

Linear complexity profile and correlation measure of order k are important pseudorandomness measures for sequences used in cryptography. We study both measures for a class of binary sequences called Legendre-Sidelnikov sequences. The proofs involve character sums.

Let PA(n, d) be a permutation array (PA) of order n and the minimum distance d. We propose a new construction of the permutation array PA(p^m, p^m-1k) for a given prime number p, a positive integer k < p and a positive integer m. The resulted array has (|PA(p,k)|p^(m-1)(p-k))^m rows. Compared to the other constructions, the new construction gives a permutation array of far bigger size with a large minimum distance, for example, when k ≥ 2p/3. Moreover the proposed construction provides an algorithm to find the i-th row of PA (p^m, p^m-1k) for a given index i very simply.

We apply the Hadamard equivalence to all the binary matrices of the size mn and study various properties of this equivalence relation and its classes. We propose to use HR-minimal as a representative of each equivalence class, and count and/or estimate the number of HR-minimals of size mn. Some properties and constructions of HR-minimals are investigated. Especially, we figure that the weight on an HR-minimal's second row plays an important role, and introduce the concept of Quasi-Hadamard matrices (QH matrices). We show that the row vectors of mn QH matrices form a set of m binary vectors of length n whose maximum pairwise absolute correlation is minimized over all such sets. Some properties, existence, and constructions of Quasi-orthogonal sequences are also discussed. We also give a relation of these with cyclic difference sets. We report lots of exhaustive search results and open problems, one of which is equivalent to the Hadamard conjecture.

In this paper, a method is proposed for reconstruction of the parameters of a non-binary block encoder using an intercepted sequence of noisy coded data. The proposed method is a generalization of the Barbier's method for the reconstruction of binary block codes to the more problematic case of non-binary codes. It has been shown mathematically that considering some revisions in definitions, such a generalization is possible. The proposed method is able to estimate the code parameters such as the code length, the code dimension, number of bits per symbol, and the dual-code subspace, and also to synchronize the sequence. Since the Reed-Solomon code is the most important type of non-binary block codes, an additional method is proposed to reconstruct the generator polynomial in the case of Reed-Solomon codes. The proposed method is evaluated via computer simulations which verify its strength and effectiveness.

Multicarrier communications including orthogonal frequency-division multiplexing (OFDM) is a technique which has been adopted for various wireless applications. However, a major drawback to the widespread acceptance of OFDM is the high peak-to-mean envelope power ratio (PMEPR) of uncoded OFDM signals. Finding methods for construction of sequences with low PMEPR is an active research area. In this paper, by employing some new shortened and extended Golay complementary pairs as the seeds, we enlarge the family size of near-complementary sequences given by Yu and Gong. We also show that the new set of sequences we obtained is just a reversal of the original set. Numerical results show that the enlarged family size is almost twice of the original one. Besides, the Hamming distances of the binary near-complementary sequences are also analyzed.

In this paper, we propose a decentralized strategy to find out the linear precoding matrices for a two-hop multiuser relay communication system. From a game-theoretic perspective, we model the source allocation process as a strategic noncooperative game for fixing relay precoding matrix and the multiuser interference treating as additive colored noise. Alternately, from the global optimization perspective, we prove that the optimum relay precoding matrix follows the transceiver Winner filter structure for giving a set of source transmit matrices. Closed-form solutions are finally obtained by using our proposed joint iterative SMSE algorithm and numerical results are provided to give insights on the proposed algorithms.

In this paper, we focus on the cancellation of interference among Destination Users (DU's) and the improvement of achievable sum rate of the nonregenerative multiuser Multiple-Input Multiple-Output (MIMO) relay downlink system. A novel design method of transmit weight is proposed to successively eliminate the interference among DU's, each of which is equipped with multiple receive antennas. We firstly investigate the transmit weight design for the Amplify-and-Forward (AF) relay scheme where the Relay Station (RS) just retransmits the received signals from Base Station (BS), then extend it to the joint design scheme of transmit weights at the both BS and RS. In the proposed joint design scheme, through the comparison of lower bound of achievable rate, an effective DU selection algorithm is proposed to generate the transmit weight at the RS and obtain the multiuser diversity. Dirty Paper Coding (DPC) technique is employed to remove the interference among DU's and ensures the achievable rate of downlink. Theoretical derivation and simulation results demonstrate the effectiveness of the proposed scheme in obtaining the achievable rate performance and BER characteristics.

This paper proposes a downlink multi-user transmission scheme for the amplify-and-forward(AF)-based multi-relay cellular network, in which Tomlinson-Harashima precoding(TH precoding) and interference alignment(IA) are jointly applied. The whole process of transmission is divided into two phases: TH precoding is first performed at base-station(BS) to support the multiplexing of data streams transmitted to both mobile-stations(MS) and relay-stations(RS), and then IA is performed at both BS and RSs to achieve the interference-free communication. During the whole process, neither data exchange nor strict synchronization is required among BS and RSs thus reducing the cooperative complexity as well as improving the system performance. Theoretical analysis is provided with respect to the channel capacity of different types of users, resulting the upper-bounds of channel capacity. Our analysis and simulation results show that the joint applications of TH precoding and IA outperforms other schemes in the presented multi-relay cellular network.

In time-varying frequency selective channels, to obtain high-rate joint time-frequency diversity, linear dispersion coded orthogonal frequency division multiplexing (LDC-OFDM), has recently been proposed. Compared with OFDM systems, single-carrier systems may retain the advantages of lower PAPR and lower sensitivity to carrier frequency offset (CFO) effects, which motivates this paper to investigate how to achieve joint frequency and time diversity for high-rate single-carrier block transmission systems. Two systems are proposed: linear dispersion coded cyclic-prefix single-carrier modulation (LDC-CP-SCM) and linear dispersion coded zero-padded single-carrier modulation (LDC-ZP-SCM) across either multiple CP-SCM or ZP-SCM blocks, respectively. LDC-SCM may use a layered two-stage LDC decoding with lower complexity. This paper analyzes the diversity properties of LDC-CP-SCM, and provides a sufficient condition for LDC-CP-SCM to maximize all available joint frequency and time diversity gain and coding gain. This paper shows that LDC-ZP-SCM may be effectively equipped with low-complexity minimum mean-squared error (MMSE) equalizers. A lower complexity scheme, linear transformation coded SCM (LTC-SCM), is also proposed with good diversity performance.

Optical orthogonal codes (OOCs) were introduced by Salehi, as signature sequences to facilitate multiple access in optical fibre networks. The existence of optimal (υ,3,1)-OOCs had been solved completely. Although there are some partial results, the existence of optimal (υ, 4, 1)-OOCs is far from settled. In this letter, three general constructions for (υ, 4, 1)-OOCs via perfect difference families are presented, new infinite classes of (υ, 4, 1)-OOCs are then obtained.

Recently, asymmetric zero-correlation zone (A-ZCZ) sequence sets that are composed of several sequence subsets have been proposed. In A-ZCZ sequence sets, the zero-cross-correlation zone (ZCCZ) length between different sequence subsets is larger than the zero-correlation zone (ZCZ) length in each sequence subset. However, the ZCCZ length between different sequence subsets was not precisely shown in previous studies. The present letter shows precisely the ZCCZ length between different sequence subsets. This information is useful for estimating the magnitude of inter-cell interference when designing approximately synchronized code-division multiple-access (AS-CDMA) systems.

The present paper introduces a new approach to the construction of a sequence set with a zero-correlation zone (ZCZ), which is referred to as a ZCZ sequence set. The proposed sequence construction generates a ZCZ sequence set from a ZCZ sequence set. The proposed method can generate an almost optimal ZCZ sequence set, the member size of which approaches the theoretical bound, when an almost optimal ZCZ sequence is used for the sequence construction. The proposed sequence set consists of N_O subsets, where a ZCZ sequence set Z(L_O, N_O, Z_O is used in sequence construction. The correlation function of the sequences of a pair of different subsets, referred to as the inter-subset correlation function, has a ZCZ with a width that is about times that of the correlation function of sequences of the same subset (intra-subset correlation function) for integers Λ ≥ 1, T, and m ≥ 0. Wide inter-subset zero-correlation enables improved performance during application of the proposed sequence set.

The even-shift orthogonal sequence whose out-of-phase aperiodic autocorrelation function takes zero at any even shifts is generalized to multi-dimension called even-shift orthogonal array (E-array), and the logic function of E-array of power-of-two length is clarified. It is shown that E-array can be constructed by complementary arrays, which mean pairs of arrays that the sum of each aperiodic autocorrelation function at the same phase shifts takes zero at any shift except zero shift, as well as the one-dimensional case. It is also shown that the number of mates of E-array with which the cross correlation function between E-arrays takes zero at any even shifts is equal to the dimension. Furthermore it is investigated that E-array possesses good aperiodic autocorrelation that the rate of zero correlation values to array length approaches one as the dimension becomes large.

In this letter, a timing-offset estimation scheme is proposed for cooperative networks. The estimation scheme consists of coarse timing-offset estimation and fine timing-offset estimation. The presented scheme relies on periodic training data and linear mean square estimation for efficient estimation. The simulation results indicate that the performance of the proposed approach is better than or comparable to that of the conventional methods with lower computational complexity in the fine estimation.

Scalable video coding with different modulation and coding schemes (MCSs) applied to different video layers is very appropriate for wireless multicast services because it can provide different video quality to different users according to their channel conditions, and a promising solution to handle packet losses induced by fading wireless channels is the use of layered hybrid FEC/ARQ scheme according to light-weight feedback messages from users about how many packets they have received. It is important to choose an appropriate MCS for each layer, decide how many parity packets in one layer should be transmitted, and determine the resources allocated to multiple video sessions to apply scalable video coding to wireless multicast streaming. We prove that such resource allocation problem is NP-hard and propose an approximate optimal algorithm with a polynomial run time. The algorithm can get the optimal transmission configuration to maximize the expected utility for all users where the utility can be a generic non-negative, non-decreasing function of the received rate. The results from simulations revealed that our algorithm offer significant improvements to video quality over a nave algorithm, an optimal algorithm without feedback from users, and an algorithm with feedback from designated users, especially in scenarios with multiple video sessions and limited radio resources.

In block transmissions, inter-block interference (IBI) due to delayed waves exceeding a cyclic prefix severely limits the performance. To suppress IBI in downlink MC-CDMA systems, this paper proposes a novel channel shortening method using a time-domain equalizer. The proposed method minimizes a cost function related to equalizer output autocorrelations without the transmission of training symbols. We prove that the method can shorten a channel and suppress IBI completely. Simulation results show that the proposed method can significantly suppress IBI using relatively less number of received blocks than a conventional method when the number of users is moderate.

In this paper, training symbol designs for estimation of frequency selective channels and compensation of in-phase (I) and quadrature (Q) imbalances on orthogonal frequency division multiplexing (OFDM) transmitters and receivers are studied. We utilize cross entropy (CE) optimization techniques together with convex optimization to design training sequences having low channel estimate mean squared error (MSE) and minimum effects of I/Q mismatch, while lowering the peak power of the training signals. The proposed design provides better channel estimate MSE and bit error rate (BER) performances and is applicable to OFDM systems with and without null subcarriers. The efficacies of the proposed designs are corroborated by analysis and simulation results.

In this paper, an imaging components transmission scheme for the improvement of multipath delay resolution in a Fractional Sampling (FS) OFDM receiver is proposed. FS has been proposed as a diversity scheme and achieves path diversity by enlarging the bandwidth of the baseband filters in order to transmit the imaging components of the desired signal. However, FS is not able to achieve diversity with very short delay multipaths because of its low multipath delay resolution. Wider bandwidth of the transmission signal is required to improve the resolution of the delay. On the other hand, cognitive radio is an emerging technology to utilize frequency spectrum flexibly through dynamic spectrum access (DSA). To resolve the small delay multipaths and to use the spectrum flexibly with DSA, this paper investigates the FS path diversity with the imaging components on the separated frequency channel. The correlation between the 2 FS branches is analyzed theoretically on the 2 path channel under the conditions of sampling interval, delay spread, and frequency separation. Numerical results through computer simulation show that the proposed scheme improves the multipath resolution and the bit error rate (BER) performance under the existence of small delay multipaths.

In this study, we propose a cooperative sensing with distributed pre-detection for gathering sensing information on shared primary system. We have proposed a system that gathers multiple sensing information by using the orthogonal narrowband signal; the system is called the orthogonal frequency-based sensing information gathering (OF-SIG) method. By using this method, sensing information from multiple secondary nodes can be gathered from the surrounding secondary nodes simultaneously by using the orthogonal narrowband signals. The advantage of this method is that the interference from each node is small because a narrowband tone signal is transmitted from each node. Therefore, if appropriate power and transmission control are applied at the surrounding nodes, the sensing information can be gathered in the same spectrum as the primary system. To avoid interference with the primary receiver, we propose a cooperative sensing with distributed pre-detection for gathering sensing information in each node by limiting sensing node power. In the proposed method, the number of sensing information transmitting nodes depends on the pre-detection ability of the individual sensing at each node. Then the secondary node can increase the transmit power by improving the sensing detection ability, and the secondary node can gather the sensing information from the surrounding secondary nodes which are located more far by redesign the transmit power of the secondary nodes. Here, we design the secondary transmit power based on OF-SIG while considering the aggregated interference from multiple sensing nodes and individual sensing ability. Finally we confirm the performance of the cooperative sensing of the proposed method through computer simulation.

In this paper, we propose a hardware architecture of high-speed sorted QR decomposition for 44 MIMO wireless communication systems. QR decomposition (QRD) is commonly used in many MIMO detection algorithms. In particular, sorted QR decomposition (SQRD) is the advanced algorithm to improve MIMO detection performance. We design an SQRD hardware architecture by using a modified Gram-Schmidt algorithm with pipelining and recursive processing. In addition, we propose an extended architecture which can decompose an augmented channel matrix for MMSE MIMO detection. These architecture can be applied in high-throughput MIMO-OFDM system such as IEEE802.11n which supports data throughput of up to 600 Mbps. We implement the proposed SQRD architecture and the proposed MMSE-SQRD architecture with 179k and 334k gates in 90 nm CMOS technology. These proposed design can achieve a high performance of up to 40.8 and 50.0 million 44 SQRD operations per second with the maximum operating frequency of 245 and 300 MHz.

Limited Random Sequence (LRS) is quite important for Analog-to-Information Converter (AIC) because it determines the random sampling scheme and the resultant performance. LRS is established with the elements of “0” and “1”. The “1” appears randomly in the segment of the sequence, so that the production of the original signal and LRS can be considered as the approximation of the random sampling of the original signal. The random sampling result can perfectly recover the signal with Compressive Sensing (CS) algorithm. In this paper, a high order LRS is proposed for the AIC design in Distributed Compressive Sensing (DCS), which has the following three typical features: 1) The high order LRS has the elements of integer which can indicate the index number of the sensor in DCS. 2) High order LRS can adapt to the sparsity variation of the original signal detected by each sensor. 3) Employing the AIC with high order LRS, the DCS algorithm can recover the signal with very low sampling rate, usually above 2 orders less than the traditional distributed sensors. In the paper, the scheme and the construction algorithm of high order LRS are proposed. The performance is evaluated with the application studies of the distributed sensor network and the camera picture correspondingly.

This paper proposes a video-quality estimation method based on a no-reference model for realtime quality monitoring in video-streaming services. The proposed method analyzes both bitstream information and decoded pixel information to estimate video-quality degradation by transmission errors. Video quality in terms of a mean squared error (MSE) between degraded video frames and error-free video frames is estimated on the basis of the number of impairment macroblocks in which the quality degradation has not been possible to be concealed. Error-concealment effectiveness is evaluated using motion information and luminance discontinuity at the boundaries of impairment regions. Simulation results show a high correlation (correlation coefficients of 0.93) between the actual MSE and the number of macroblocks in which error concealment has not been effective. These results show that the proposed method works well in reatime quality monitoring for video-streaming services.

A new spatial and temporal error concealment method for three-dimensional discrete wavelet transform (3D DWT) video coding is analyzed. 3D DWT video coding employing dispersive grouping (DG) and two-step error concealment is an efficient method in a packet loss channel [20],[21]. In the two-step error concealment method, the interpolations are only spatially applied however, higher efficiency of the interpolation can be expected by utilizing spatial and temporal similarities. In this paper, we propose an enhanced spatial and temporal error concealment method in order to achieve higher error concealment (EC) performance in packet loss networks. In the temporal error concealment method, structural similarity (SSIM) index is employed for inter group of pictures (GOP) EC and minimum mean square error (MMSE) is used for intra GOP EC. Experimental results show that the proposed method can obtain remarkable performance compared with the conventional methods.

In this paper, impulse noise removal for digital images is handled. It is well-known that switching-type processing is effective for the impulse noise removal. In the process, noise-corrupted pixels are first detected, and then, filtering is applied to the detected pixels. This switching process prevents distorting original signals. A noise detector is of course important in the process, a filter for pixel value restoration is also important to obtain excellent results. The authors have proposed a local similarity-based filter (LSF). It utilizes local similarity in a digital image and its capability against restoration of orderly regions has shown in the previous paper. In this paper, first, further experiments are carried out and properties of the LSF are revealed. Although LSF is inferior to an existing filter when disorderly regions are processed and evaluated by the peak signal-to-noise ratio, its outputs are subjectively adequate even in the case. If noise positions are correctly detected, capability of the LSF is guaranteed. On the other hand, some errors may occur in actual noise detection. In that case, LSF sometimes fails to restoration. After properties are examined, we propose two effective extensions to the LSF. First one is for computational cost reduction and another is for color image processing. The original LSF is very time consuming, and in this paper, computational cost reduction is realized introducing a search area. Second proposal is the vector LSF (VLSF) for color images. Although color images can be processed using a filter, which is for monochrome images, to each color component, it sometimes causes color drift. Hence vector processing has been investigated so far. However, existing vector filters do not excel in preservation of orderly pattern although color drift is suppressed. Our proposed VLSF is superior both in orderly pattern preservation and color drift suppression. Effectiveness of the proposed extensions to LSF is verified through experiments.

This paper proposes Burst Error Resilient coding (BRC) technology in mobile broadcasting network. The proposed method utilizes Scalable Video Coding (SVC) and Forward Error Correction (FEC) to overcome service outage due to burst loss in mobile network. The performance evaluation is performed by comparing PSNR of SVC and the proposed method under MBSFN simulation channel. The simulation result shows PSNR of SVC equal error protection (EEP), unequal error protection (UEP) and proposed BRC using Raptor FEC code.

In this paper, we propose an automatic parameter adjustment method for audio equalizers using an interactive genetic algorithm (IGA). It is very difficult for ordinary users who are not familiar with audio devices to appropriately adjust the parameters of audio equalizers. We therefore propose a system that can automatically adjust the parameters of audio equalizers on the basis of user's evaluation of the reproduced sound. The proposed system utilizes an IGA to adjust the gains and Q values of the peaking filters included in audio equalizers. Listening test results demonstrate that the proposed system can appropriately adjust the parameters on the basis of the user's evaluation.

In this paper, we propose a normalization method dividing the gradient vector by the sum of the diagonal and two adjoining elements of the matrix expressing the correlation between the components of the discrete Fourier transform (DFT) of the reference signal used for the identification of unknown system. The proposed method can thereby improve the estimation speed of coefficients of adaptive filter.

This paper proposes an adaptive comb filter with flexible notch gain. It can appropriately remove a periodic noise from an observed signal. The proposed adaptive comb filter uses a simple LMS algorithm to update the notch gain coefficient for removing the noise and preserving a desired signal, simultaneously. Simulation results show the effectiveness of the proposed comb filter.

In this paper, we present a method to combine lapped transforms with various downsampling factors. The factor is changed depending on a local feature of a given signal, and it can be realized by using time-domain lapped transforms. In image coding application, our method maintains good image coding performance for a wide range of bitrates and fills the gap between undersampled and critically-/oversampled systems.

We introduce an efficient fully simulatable construction of oblivious transfer based on the McEliece assumptions in the common reference string model. This is the first efficient fully simulatable oblivious protocol based on coding assumptions. Moreover, being based on the McEliece assumptions, the proposed protocol is a good candidate for the post-quantum scenario.

This paper precisely characterizes secret sharing schemes based on arbitrary linear codes by using the relative dimension/length profile (RDLP) and the relative generalized Hamming weight (RGHW). We first describe the equivocation Δ_m of the secret vector =[s₁,...,s_l] given m shares in terms of the RDLP of linear codes. We also characterize two thresholds t₁ and t₂ in the secret sharing schemes by the RGHW of linear codes. One shows that any set of at most t₁ shares leaks no information about , and the other shows that any set of at least t₂ shares uniquely determines . It is clarified that both characterizations for t₁ and t₂ are better than Chen et al.'s ones derived by the regular minimum Hamming weight. Moreover, this paper characterizes the strong security in secret sharing schemes based on linear codes, by generalizing the definition of strongly-secure threshold ramp schemes. We define a secret sharing scheme achieving the α-strong security as the one such that the mutual information between any r elements of (s₁,...,s_l) and any α-r+1 shares is always zero. Then, it is clarified that secret sharing schemes based on linear codes can always achieve the α-strong security where the value α is precisely characterized by the RGHW.

In this letter, we consider a control problem of a chain of integrators where there is an uncertain delay in the input and sensor noise. This is an output feedback control result over [10] in which a state feedback control is suggested. The several generalized features are: i) output feedback control is developed instead of full state feedback control, ii) uncertain delay in the input is allowed, iii) all states are derived to be arbitrarily small under uncertain sensor noise.

Constructing APN or 4-differentially uniform permutations achieving all the necessary criteria is an open problem, and the research on it progresses slowly. In ACISP 2011, Carlet put forth an idea for constructing differentially uniform permutations using extension fields, which was illustrated with a construction of a 4-differentially uniform (n,n)-permutation. The permutation has optimum algebraic degree and very good nonlinearity. However, it was proved to be a permutation only for n odd. In this note, we investigate further the construction of differentially uniform permutations using extension fields, and construct a 4-differentially uniform (n,n)-permutation for any n. These permutations also have optimum algebraic degree and very good nonlinearity. Moreover, we consider a more general type of construction, and illustrate it with an example of a 4-differentially uniform (n,n)-permutation with good cryptographic properties.

In contemporary communications, Golay, periodic and Z- complementary sequence sets play a very important role, since such sequence sets possess impulse-like or zero correlation zone (ZCZ) autocorrelation. On the other hand, the advantages of the signals over the quadrature amplitude modulation (QAM) constellation are more and more prominent. Hence, the design of such sequence sets over the QAM constellation has turned into one of the all-important issues in communications. Therefore, the construction methods of such sequence sets over the 16-QAM constellation are investigated, in this letter, and our goals are arrived at by the known quaternary Golay, periodic and Z- complementary sequence sets. Finally, many examples illuminate the validity of the proposed methods.

Histogram modification based image enhancement algorithms have been extensively used in 2-D image applications. In this letter, we apply a histogram modification framework to stereoscopic image enhancement. The proposed algorithm estimates the histogram of a stereo image pair without explicitly computing the pixel-wise disparity. Then, the histogram in the occluded regions is estimated and used to determine the target histogram of the stereo image. Experimental results demonstrate the effectiveness of the proposed algorithm.

A method obtaining a monochrome image which can rebuild colors is proposed. In this method, colors in an input image are quantized under a lightness constraint and a palette, which represents relationship between quantized colors and gray-levels, is generated. Using the palette, an output monochrome image is obtained. Experiments show that the proposed method obtains good monochrome and rebuilt color images.