Sanzheng Qiao

Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation

The authors propose a method of direction of arrival (DOA) estimation of signals in the presence of noise whose covariance matrix is unknown and arbitrary, other than being positive definite. They examine the projection of the data onto the noise subspace. The conditional probability density function (PDF) of the projected data given the signal parameters and the unknown projected noise covariance matrix is first formed. The a posteriori PDF of the signal parameters alone is then obtained by assigning a noninformative a priori PDF to the unknown noise covariance matrix and integrating out this quantity. A simple criterion for the maximum a posteriori (MAP) estimate of the DOAs of the signals is established. Some properties of this criterion are discussed, and an efficient numerical algorithm for the implementation of this criterion is developed. The advantage of this method is that the noise covariance matrix does not have to be known, nor must it be estimated. >

Regularization of RIF blind image deconvolution

Blind image restoration is the process of estimating both the true image and the blur from the degraded image, using only partial information about degradation sources and the imaging system. Our main interest concerns optical image enhancement, where the degradation often involves a convolution process. We provide a method to incorporate truncated eigenvalue and total variation regularization into a nonlinear recursive inverse filter (RIF) blind deconvolution scheme first proposed by Kundar, and by Kundur and Hatzinakos. Tests are reported on simulated and optical imaging problems.

The representation and approximation of the Drazin inverse of a linear operator in Hilbert space

We present a unified representation theorem for the Drazin inverse of linear operators in Hilbert space and a general error bound. Five specific expressions, computational procedures, and their error bounds for the Drazin inverse are uniformly derived from the unified representation theorem.

A novel anonymization algorithm: Privacy protection and knowledge preservation

In data mining and knowledge discovery, there are two conflicting goals: privacy protection and knowledge preservation. On the one hand, we anonymize data to protect privacy; on the other hand, we allow miners to discover useful knowledge from anonymized data. In this paper, we present an anonymization method which provides both privacy protection and knowledge preservation. Unlike most anonymization methods, where data are generalized or permuted, our method anonymizes data by randomly breaking links among attribute values in records. By data randomization, our method maintains statistical relations among data to preserve knowledge, whereas in most anonymization methods, knowledge is lost. Thus the data anonymized by our method maintains useful knowledge for statistical study. Furthermore, we propose an enhanced algorithm for extra privacy protection to tackle the situation where the users prior knowledge of original data may cause privacy leakage. The privacy levels and the accuracy of knowledge preservation of our method, along with their relations to the parameters in the method are analyzed. Experiment results demonstrate that our method is effective on both privacy protection and knowledge preservation comparing with existing methods.

HKZ and Minkowski Reduction Algorithms for Lattice-Reduction-Aided MIMO Detection

Recently, lattice reduction has been widely used for signal detection in multiinput multioutput (MIMO) communications. In this paper, we present three novel lattice reduction algorithms. First, using a unimodular transformation, a significant improvement on an existing Hermite-Korkine-Zolotareff-reduction algorithm is proposed. Then, we present two practical algorithms for constructing Minkowski-reduced bases. To assess the output quality, we compare the orthogonality defect of the reduced bases produced by LLL algorithm and our new algorithms, and find that in practice Minkowski-reduced basis vectors are the closest to being orthogonal. An error-rate analysis of suboptimal decoding algorithms aided by different reduction notions is also presented. To this aim, the proximity factor is employed as a measurement. We improve some existing results and derive upper bounds for the proximity factors of Minkowski-reduction-aided decoding (MRAD) to show that MRAD can achieve the same diversity order with infinite lattice decoding (ILD).

A Divide-and-Conquer Method for the Takagi Factorization

This paper presents a divide-and-conquer method for computing the symmetric singular value decomposition, or Takagi factorization, of a complex symmetric and tridiagonal matrix. An analysis of accuracy shows that our method produces accurate Takagi values and orthogonal Takagi vectors. Our preliminary numerical experiments have confirmed our analysis and demonstrated that our divide-and-conquer method is much more efficient than the implicit QR method even for moderately large matrices.

Perturbation analysis and condition numbers of scaled total least squares problems

The standard approaches to solving an overdetermined linear system Ax ≈ b find minimal corrections to the vector b and/or the matrix A such that the corrected system is consistent, such as the least squares (LS), the data least squares (DLS) and the total least squares (TLS). The scaled total least squares (STLS) method unifies the LS, DLS and TLS methods. The classical normwise condition numbers for the LS problem have been widely studied. However, there are no such similar results for the TLS and the STLS problems. In this paper, we first present a perturbation analysis of the STLS problem, which is a generalization of the TLS problem, and give a normwise condition number for the STLS problem. Different from normwise condition numbers, which measure the sizes of both input perturbations and output errors using some norms, componentwise condition numbers take into account the relation of each data component, and possible data sparsity. Then in this paper we give explicit expressions for the estimates of the mixed and componentwise condition numbers for the STLS problem. Since the TLS problem is a special case of the STLS problem, the condition numbers for the TLS problem follow immediately from our STLS results. All the discussions in this paper are under the Golub-Van Loan condition for the existence and uniqueness of the STLS solution.

Integer least squares: sphere decoding and the LLL algorithm

This paper considers the problem of integer least squares, where the least squares solution is an integer vector, whereas the coefficient matrix is real. In particular, we discuss the sphere decoding method in communications. One of the key issues in sphere decoding is the determination of the radius of search sphere. We propose a deterministic method for finding a radius of search sphere. Also, we investigate the impact of the LLL algorithm on the computational complexity of the sphere decoding method.

Fast singular value algorithm for Hankel matrices

We present an O(n2logn) algorithm for finding all the singular values of an n-by-n complex Hankel matrix.

A Diagonal Lattice Reduction Algorithm for MIMO Detection

Recently, an efficient lattice reduction method, called the effective LLL (ELLL) algorithm, was presented for the detection of multiinput multioutput (MIMO) systems. In this letter, a novel lattice reduction criterion, called diagonal reduction, is proposed. The diagonal reduction is weaker than the ELLL reduction, however, like the ELLL reduction, it has identical performance with the LLL reduction when applied for the sphere decoding and successive interference cancelation (SIC) decoding. It improves the efficiency of the ELLL algorithm by significantly reducing the size-reduction operations. Furthermore, we present a greedy column traverse strategy, which reduces the column swap operations in addition to the size-reduction operations.