Constrained least squares filtering algorithm for ultrasound image deconvolution

A new medical ultrasound tissue model is considered in this paper, which incorporates random fluctuations of the tissue response and provides more realistic interpretation of the received pulse-echo ultrasound signal. Using this new model, we propose an algorithm for restoration of the degraded ultrasound image. The proposed deconvolution is a modification of the classical regularization technique which combines Wiener filter and the constrained least squares (LS) algorithm for restoration of the ultrasound image. The performance of the algorithm is evaluated based on both the simulated phantom images and real ultrasound radio frequency (RF) data. The results show that the algorithm can provide improved ultrasound imaging performance in terms of the resolution gain. The deconvolved images visually show better resolved tissue structures and reduce speckle, which are confirmed by a medical expert.     

Constrained least squares design of 2-D FIR filters

We consider the design of 2-D linear phase finite impulse response (FIR) filters according to the least squares (LS) error criterion subject to equality and/or inequality constraints. Since we use a frequency domain formulation, these constraints can be used to explicitly prescribe (frequency-dependent) error tolerances, the maximum, minimum, or fixed values of the frequency response at certain points and/or regions. Our method combines Lagrange multiplier and Kuhn-Tucker theory to solve a much wider class of problems than do standard methods. It allows arbitrary compromises between the LS and the equiripple design     

Constrained least squares detector for OFDM/SDMA-based wireless networks

The two major obstacles toward high-capacity indoor wireless networks are distortion due to the indoor channel and the limited bandwidth which necessitates a high spectral efficiency. A combined orthogonal frequency division multiplexing (OFDM)/spatial division multiple access (SDMA) approach can efficiently tackle both obstacles and paves the way for cheap, high-capacity wireless indoor networks. The channel distortion due to multipath propagation is efficiently mitigated with OFDM while the bandwidth efficiency can be increased with the use of SDMA. However, to keep the cost of an indoor wireless network comparable to its wired counterpart's cost, low-complexity SDMA processors with good performance are of special interest. In this paper, we propose a new multiuser SDMA detector which is designed for constant modulus signals. This constrained least squares (CLS) receiver, which deterministically exploits the constant modulus nature of the subcarrier modulation to achieve better separation, is compared in terms of performance and complexity with the zero forcing (ZF) and the minimum mean square error (MMSE) receiver. Additionally, since the CLS detector relies on reliable channel knowledge at the receiver, we propose a strategy for estimating the multiple input multiple output (MIMO) channels. Simulations for a Hiperlan II-based case-study show that the CLS detector significantly outperforms the ZF detector and comes close to the performance of the MMSE detector for QPSK. For higher order M-PSK, the CLS detector outperforms the MMSF detector. Furthermore, the estimation complexity for the CLS detector is substantially lower than that for the MMSE detector which additionally requires estimation of the noise power.     

New fast QR decomposition least squares adaptive algorithms

This paper presents two new, closely related adaptive algorithms for LS system identification. The starting point for the derivation of the algorithms is the inverse Cholesky factor of the data correlation matrix, obtained via a QR decomposition (QRD). Both algorithms are of O(p) computational complexity, with p being the order of the system. The first algorithm is a fixed order QRD scheme with enhanced parallelism. The second is an order recursive lattice type algorithm based exclusively on orthogonal Givens rotations, with lower complexity compared to previously derived ones. Both algorithms are derived following a new approach, which exploits efficient the and order updates of a specific state vector quantity     

Efficient least squares adaptive algorithms for FIR transversalfiltering

A unified view of algorithms for adaptive transversal FIR filtering and system identification has been presented. Wiener filtering and stochastic approximation are the origins from which all the algorithms have been derived, via a suitable choice of iterative optimization schemes and appropriate design parameters. Following this philosophy, the LMS algorithm and its offspring have been presented and interpreted as stochastic approximations of iterative deterministic steepest descent optimization schemes. On the other hand, the RLS and the quasi-RLS algorithms, like the quasi-Newton, the FNTN, and the affine projection algorithm, have been derived as stochastic approximations of iterative deterministic Newton and quasi-Newton methods. Fast implementations of these methods have been discussed. Block-adaptive, and block-exact adaptive filtering have also been considered. The performance of the adaptive algorithms has been demonstrated by computer simulations     

Maximum likelihood, least squares, and penalized least squares for PET

The EM algorithm is the basic approach used to maximize the log likelihood objective function for the reconstruction problem in positron emission tomography (PET). The EM algorithm is a scaled steepest ascent algorithm that elegantly handles the nonnegativity constraints of the problem. It is shown that the same scaled steepest descent algorithm can be applied to the least squares merit function, and that it can be accelerated using the conjugate gradient approach. The experiments suggest that one can cut the computation by about a factor of 3 by using this technique. The results are applied to various penalized least squares functions which might be used to produce a smoother image.     

Multichannel recursive least squares adaptive filtering without adesired signal

The author presents a pair of adaptive QR decomposition-based algorithms for the adaptive mixed filter in which no desired signal is available, but the signal-to-data cross-correlation vector is known. The algorithms are derived by formulating the recursive mixed filter as a least-squares problem and then applying orthogonal QR-based techniques in its solution. This leads to algorithms with the performance, numerical, and structural advantages of the RLS/ QR algorithm, but without the requirement of a desired signal. Both Givens and square-root-free Givens rotations are used in implementing the recursive QR decomposition. Because of their structural regularity, the algorithms are easily implemented by triangular systolic array structures. Simulations show that these algorithms require fewer computations and less precision than recursive sample matrix inversion approaches     

Large system transient analysis of adaptive least squares filtering

The performance of adaptive least squares (LS) filtering is analyzed for the suppression of multiple-access interference. Both full-rank LS filters and reduced-rank LS filters, which reside in a lower dimensional Krylov space, are considered with training, and without training but with known signature for the desired user. We compute the large system limit of output signal-to-interference-plus-noise ratio (SINR) as a function of normalized observations, load, and noise level. Specifically, the number of users K, the degrees of freedom N, and the number of training symbols or observations i all tend to infinity with fixed ratios K/N and i/N. Our results account for an arbitrary power distribution over the users, data windowing (e.g., recursive LS (RLS) with exponential windowing), and initial diagonal loading of the covariance matrix to prevent ill-conditioning. Numerical results show that the large system analysis accurately predicts the simulated convergence performance of the algorithms considered with moderate degrees of freedom (typically N=32). Given a fixed, short training length, the relative performance of full- and reduced-rank filters depends on the selected rank and diagonal loading. With an optimized diagonal loading factor, the performance of full- and reduced-rank filters are similar. However, full-rank performance is generally much more sensitive to the choice of diagonal loading factor than reduced-rank performance.     

Systolic architectures for adaptive multichannel least squares lattice filters

A family of systolic array architectures for adaptive multichannel least squares lattice (MLSL) filters is presented. These architectures are based on a recently developed algorithm that provides an efficient, numerically sound, and well-structured set of recursions for realizing MLSL filters. The algorithm is based on the recursive QR decomposition of the forward and backward error correlation matrices. Form input channels andp filter taps,O(pm ²) computations are required per time step. Numerous space-time tradeoffs are available in mapping the algorithm's recursions to systolic architectures, leading to the architectural family presented here.Los Alamos National Laboratory is operated by the University of California for the United States Department of Energy under contract W-7405-ENG-36.     

On the least squares tap adjustment algorithm in adaptive digitalecho cancellers

Fast recursive algorithms for updating coefficients in digital echo cancellers can be derived from the well-known method of least squares. Unless zero initial conditions are assumed, the exact initialization of these algorithms is yet unknown. For random data of more than twice the order of the filter, the existence of a unique least squares solution is proven. A constructive recursive procedure in time and order for computing the pseudoinverse solution for the initial steps is derived. Since the data matrix is composed of integers, this technique facilitates the implementation of stable tap-update algorithms     

Pattern characteristics of linear arrays using the constrained least squares distribution

The constrained least squares (CLS) distribution is a method for obtaining distribution functions that yield low sidelobe patterns with specified constraints on the aperture efficiency, and are especially useful for the transmit patterns of active array antennas. The widely used Taylor distribution optimizes only pattern performance while the CLS distribution optimizes pattern performance while taking into account the constraints on both the peak element amplitude and the total effective radiated voltage (ERV) of the aperture distribution. The paper compares the pattern characteristics of linear arrays with CLS and Taylor distributions. The results help to establish guidelines on when a CLS distribution would be preferable over a Taylor distribution when a specified aperture efficiency is important.     

A fast recursive total least squares algorithm for adaptive IIR filtering

This work develops a new fast recursive total least squares (N-RTLS) algorithm to recursively compute the total least squares (TLS) solution for adaptive infinite-impulse-response (IIR) filtering. The new algorithm is based on the minimization of the constraint Rayleigh quotient in which the first entry of the parameter vector is fixed to the negative one. The highly computational efficiency of the proposed algorithm depends on the efficient computation of the gain vector and the adaptation of the Rayleigh quotient. Using the shift structure of the input data vectors, a fast algorithm for computing the gain vector is established, which is referred to as the fast gain vector (FGV) algorithm. The computational load of the FGV algorithm is smaller than that of the fast Kalman algorithm. Moreover, the new algorithm is numerically stable since it does not use the well-known matrix inversion lemma. The computational complexity of the new algorithm per iteration is also O(L). The global convergence of the new algorithm is studied. The performances of the relevant algorithms are compared via simulations.     

Clutter suppression for airborne phased radar with conformal arrays by least squares estimation

The radar clutter statistics for airborne conformal arrays varies by range, i.e., the clutter distributions are nonstationary, which causes performance degradation for the conventional space-time adaptive processing (STAP), which estimates the clutter covariance matrix (CCM) from data at adjacent range cells. In this paper, a novel clutter suppression method for airborne phased radar with conformal arrays is proposed that takes a form of corrected sample matrix inversion (SMI) through the CCM estimated by the least squares (LS) estimation. The estimated CCM can provide partial information about the real CCM in the novel method, which results in improved detection performance for targets in conformal array applications. Simulation results relative to several typical conformal arrays verify the effectivity of the presented method.     

Finite word-length effects in recursive least squares algorithms with application to adaptive equalization

In this paper we provide a summary of recent and new results on finite word length effects in recursive least squares adaptive algorithms. We define the numerical accuracy and numerical stability of adaptive recursive least squares algorithms and show that these two properties are related to each other, but are not equivalent. The numerical stability of adaptive recursive least squares algorithms is analyzed theoretically and the numerical accuracy with finite word length is investigated by computer simulation. It is shown that the conventional recursive least squares algorithm gives poor numerical accuracy when a short word length is used. A new form of a recursive least squares lattice algorithm is presented which is more robust to round-off errors compared to the conventional form. Optimum scaling of recursive least squares algorithms for fixedpoint implementation is also considered.     

Comparison of the linear least squares and nonlinear least squares spheres

Two important, to scientists and engineers, sphere fitting procedures, namely the linear least squares (LLS) and the non-linear least squares (NLLS) methods and their general random-error analysis are described. The first-order random errors of the center coordinates and the radius of the fitted sphere using the above mentioned procedures are derived in detail under the assumption that the variance-covariance matrix exists for the random error vector. With the additional trivariate normal error distribution assumption, the Maximum Likelihood (ML) estimators and their standard deviations are also derived. The effectiveness of these procedures are studied through computer stimulation.     

Application of a least squares predictive-transform modelingmethodology to space-time adaptive array processing

In a companion paper, an efficient least squares (LS) predictive transform (PT) multichannel modeling framework was presented that arose as an inherent byproduct of the optimization of a PT signal source “encoder.” In this correspondence, the LS PT approach is applied to the space-time adaptive array processing problem arising in airborne moving target indicator (MTI) radar. Simulation results are presented that demonstrate the utility of the LS PT approach     

On the block least squares adaptive digital filters realized usingthe fast Fourier transform

The authors formulate a block-based least-squares problem in the frequency domain. They then develop computationally efficient block least-squares algorithms that can be realized using the fast Fourier transform. They also present computer simulation results demonstrating the convergence characteristics of the proposed algorithms     

A fast recursive least squares adaptive second order Volterrafilter and its performance analysis

A fast, recursive least squares (RLS) adaptive nonlinear filter modeled using a second-order Volterra series expansion is presented. The structure uses the ideas of fast RLS multichannel filters, and has a computational complexity of O(N³) multiplications, where N-1 represents the memory span in number of samples of the nonlinear system model. A theoretical performance analysis of its steady-state behaviour in both stationary and nonstationary environments is presented. The analysis shows that, when the input is zero mean and Gaussian distributed, and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error due to the coefficient noise vector is independent of the statistics of the input signal. The results of several simulation experiments show that the filter performs well in a variety of situations. The steady-state behaviour predicted by the analysis is in very good agreement with the experimental results     

A numerically stable fast Newton-type adaptive filter based on order recursive least squares algorithm

This paper presents a numerically stable fast Newton-type adaptive filter algorithm. Two problems are dealt with in the paper. First, we derive the proposed algorithm from an order-recursive least squares algorithm. The result of the proposed algorithm is equivalent to that of the fast Newton transversal filter (FNTF) algorithm. However, the derivation process is different. Instead of extending a covariance matrix of the input based on the min-max and the max-min criteria, the derivation shown in this paper is to solve an optimum extension problem of the gain vector based on the information of the Mth-order forward or backward predictor. The derivation provides an intuitive explanation of the FNTF algorithm, which may be easier to understand. Second, we present stability analysis of the proposed algorithm using a linear time-variant state-space method. We show that the proposed algorithm has a well-analyzable stability structure, which is indicated by a transition matrix. The eigenvalues of the ensemble average of the transition matrix are proved all to be asymptotically less than unity. This results in a much-improved numerical performance of the proposed algorithm compared with the combination of the stabilized fast recursive least squares (SFRLS) and the FNTF algorithms. Computer simulations implemented by using a finite-precision arithmetic have confirmed the validity of our analysis.     

Total least mean squares algorithm

Widrow (1971) proposed the least mean squares (LMS) algorithm, which has been extensively applied in adaptive signal processing and adaptive control. The LMS algorithm is based on the minimum mean squares error. On the basis of the total least mean squares error or the minimum Raleigh quotient, we propose the total least mean squares (TLMS) algorithm. The paper gives the statistical analysis for this algorithm, studies the global asymptotic convergence of this algorithm by an equivalent energy function, and evaluates the performances of this algorithm via computer simulations