Row Dimension Research Articles

Memory-Efficient and High-Speed VLSI Implementation of Two-Dimensional Discrete Wavelet Transform Using Decomposed Lifting Scheme

Novel decomposed lifting scheme (DLS) is presented to perform one-dimensional (1D) discrete wavelet transform (DWT) with consistent data flow in both row and column dimension. Based on the proposed DLS, intermediate data can be transferred seamlessly between the column processor and the row processor in the hardware implementation of two-dimensional (2D) DWT, resulting in the reduction of on-chip memory, output latency and control complexity. Moreover, the implementation of 2D DWT can be easily extended to achieve higher processing speed with controlled increase of hardware cost. Memory-efficient and high-speed architectures are proposed to implement 2D DWT for JPEG2000, which are called fast architecture (FA) and high-speed architecture (HA). FA and HA can perform 2D DWT in N 2 /2 and N 2 /4 clock cycles for an N×N image, respectively, but the required internal memory is only 4N for 9/7 DWT and 2N for 5/3 DWT. Compared with the works reported in previous literature, the proposed designs provide excellent performance in hardware cost, control complexity, output latency and computing time. The proposed designs were implemented to process 2D 9/7 DWT in SMIC 0.18 μm CMOS logic fabrication with 4 KB internal memory for the image size 512?×?512. The areas are only 999137 um 2 and 1333054 um 2 for FA and HA, respectively, but the operation frequency can be up to 150 MHz.

Identification of Bilinear Systems With White Noise Inputs: An Iterative Deterministic-Stochastic Subspace Approach

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this technical brief, a new subspace state space system identification algorithm for multi-input multi-output bilinear systems driven by white noise inputs is introduced. The new algorithm is based on a uniformly convergent Picard sequence of linear deterministic-stochastic state space subsystems which are easily identifiable by any linear deterministic-stochastic subspace algorithm such as MOESP, N4SID, CVA, or CCA. The key to the proposed algorithm is the fact that the bilinear term is a second-order white noise process. Using a standard linear Kalman filter model, the bilinear term can be estimated and combined with the system inputs at each iteration, thus leading to a linear system with extended inputs of dimension <formula formulatype="inline"><tex Notation="TeX">$m(n+1)$</tex></formula>, where <formula formulatype="inline"> <tex Notation="TeX">$n$</tex></formula> is the system order and <formula formulatype="inline"> <tex Notation="TeX">$m$</tex></formula> is the dimension of the inputs. It is also shown that the model parameters obtained with the new algorithm converge to those of the true bilinear model. Moreover, the proposed algorithm has the same consistency conditions as the linear subspace identification algorithms when <formula formulatype="inline"><tex Notation="TeX">$i\rightarrow\infty$</tex> </formula>, where <formula formulatype="inline"><tex Notation="TeX">$i$</tex> </formula> is the number of block rows in the past/future block Hankel data matrices. Typical bilinear subspace identification algorithms available in the literature cannot handle large values of <formula formulatype="inline"> <tex Notation="TeX">$i$</tex></formula>, thus leading to biased parameter estimates. Unlike existing bilinear subspace identification algorithms whose row dimensions in the data matrices grow exponentially, and hence suffer from the “curse of dimensionality,” in the proposed algorithm the dimensions of the data matrices are comparable to those of a linear subspace identification algorithm. A case study is presented with data from a heat exchanger experiment. </para>

Non-homogeneous spatial configuration of vibrissae cortical representation in layer IV of the barrel somatosensory cortex

In the present experiments we studied exclusive and overlapping cortical representational areas of the vibrissae in layer IV cells, across the entire barrel subfield of the rat somatosensory cortex, looking for evidences that would challenge the present assumptions of homogeneity and symmetry among cortical columns in this sensorial system. Our main findings were that in layer IV of the rat barrel cortex: A) Size of vibrissae cortical representational areas (X=0.4174mm(2); SD=0.025) was not homogeneous, vibrissae in dorsal rows (A-B) had significantly smaller areas than those in ventral rows (D-E), a pattern that repeated itself in ares 1-4. B) This difference arises from vibrissal representational overlap, and not from variations in exclusive zones, which are surprisingly homogeneous in size across the barrel cortex (X=0.079mm(2); SD=0.0075); C) The extent of overlapping cortical areas varied systematically, with intra-row overlapping areas having a predominant bias (71.4% of total overlapping) independent of area sizes. Accordingly, vibrissae shared receptive fields with an average of 1.15 vibrissae in the same row and 0.38 in the same are. Barrel cortex has been viewed operationally as a conglomerate of essentially homogenous cortical columns that interact equivalently in the are and row dimensions. Our simple but global cortical reconstructions show that this predominant view should be revised. We postulate that the vibrissae/barrels spatial disposition in rows and ares has a relevant functional meaning, related to different sensory capabilities.

Non-homogeneous spatial configuration of vibrissae cortical representation in layer IV of the barrel somatosensory cortex.

In the present experiments we studied exclusive and overlapping cortical representational areas of the vibrissae in layer IV cells, across the entire barrel subfield of the rat somatosensory cortex, looking for evidences that would challenge the present assumptions of homogeneity and symmetry among cortical columns in this sensorial system. Our main findings were that in layer IV of the rat barrel cortex: A) Size of vibrissae cortical representational areas (X=0.4174mm(2); SD=0.025) was not homogeneous, vibrissae in dorsal rows (A-B) had significantly smaller areas than those in ventral rows (D-E), a pattern that repeated itself in ares 1-4. B) This difference arises from vibrissal representational overlap, and not from variations in exclusive zones, which are surprisingly homogeneous in size across the barrel cortex (X=0.079mm(2); SD=0.0075); C) The extent of overlapping cortical areas varied systematically, with intra-row overlapping areas having a predominant bias (71.4% of total overlapping) independent of area sizes. Accordingly, vibrissae shared receptive fields with an average of 1.15 vibrissae in the same row and 0.38 in the same are. Barrel cortex has been viewed operationally as a conglomerate of essentially homogenous cortical columns that interact equivalently in the are and row dimensions. Our simple but global cortical reconstructions show that this predominant view should be revised. We postulate that the vibrissae/barrels spatial disposition in rows and ares has a relevant functional meaning, related to different sensory capabilities.

ADAPTIVE ESTIMATORS OF A MEAN MATRIX: TOTAL LEAST SQUARES VERSUS TOTAL SHRINKAGE

An unknown constant matrix M is observed with additive random error. The basic problem considered is to devise an estimator of M that trades off bias against variance so as to achieve relatively low quadratic risk. This paper develops an adaptive total least squares estimator and an adaptive total shrinkage estimator of M that minimize estimated risk over certain large classes of linear estimators. It is shown that the asymptotic risk of the adaptive total least squares estimator is the smallest attainable among reduced rank total least squares fits to the data matrix. The asymptotic risk of the adaptive total shrinkage estimator is shown to be smaller still. A close link is established between total shrinkage and the Efron-Morris estimator of M. In the asymptotics, the row dimension of M tends to infinity, and the column dimension stays fixed. The risks converge uniformly when the signal to-noise ratio and the measurement error variance are both bounded. A second problem treated is estimation of M under the assumption that a linear relation holds among its columns. In this formulation of the errors-in-variables linear regres sion model, rank constrained adaptive total least squares asymptotically domi nates the usual total least squares estimator of M, and rank constrained adaptive total shrinkage is better still.

Estimating a mean matrix: boosting efficiency by multiple affine shrinkage

The unknown matrix M is the mean of the observed response matrix in a multivariate linear model with independent random errors. This paper constructs regularized estimators of M that dominate, in asymptotic risk, least squares fits to the model and to specified nested submodels. In the first construction, the response matrix is expressed as the sum of orthogonal components determined by the submodels; each component is replaced by an adaptive total least squares fit of possibly lower rank; and these fits are then summed. The second, lower risk, construction differs only in the second step: each orthogonal component is replaced by a modified Efron-Morris fit before summation. Singular value decompositions yield computable formulae for the estimators and their asymptotic and estimated risks. In the asymptotics, the row dimension of M tends to infinity while the column dimension remains fixed. Convergences are uniform when signal-to-noise ratio is bounded.

Square hankel SVD subspace tracking algorithms

In this paper, we describe two sliding window singular-value decomposition (SVD) subspace tracking algorithms for the serialized (time series) data case. In time series analysis, one often uses a Hankel matrix representation of the data. In sliding window low rank adaptive time-series analysis with overmodeling, we can set both column and row dimensions of this Hankel data matrix equal to the window length. This special case is of particular interest because a square Hankel matrix is symmetrtic and has identical left and right singular subspaces. Thus, we can track the square Hankel SVD using a fast variant of sequential orthogonal iteration. We develop two sliding window square Hankel SVD subspace tracking algorithms for the serialized data case on this basis. These algorithms are studied experimentally in an adaptive filtering context. They have proven particularly useful for enhancement of unknown transients in noise. Further potential application areas are sliding window adaptive frequency estimation and detection for time series data.