Kasi Rajgopal

Vector-extrapolated fast maximum likelihood estimation algorithms for emission tomography

A new class of fast maximum-likelihood estimation (MLE) algorithms for emission computed tomography (ECT) is developed. In these cyclic iterative algorithms, vector extrapolation techniques are integrated with the iterations in gradient-based MLE algorithms, with the objective of accelerating the convergence of the base iterations. This results in a substantial reduction in the effective number of base iterations required for obtaining an emission density estimate of specified quality. The mathematical theory behind the minimal polynomial and reduced rank vector extrapolation techniques, in the context of emission tomography, is presented. These extrapolation techniques are implemented in a positron emission tomography system. The new algorithms are evaluated using computer experiments, with measurements taken from simulated phantoms. It is shown that, with minimal additional computations, the proposed approach results in substantial improvement in reconstruction.

Detection of edges from projections

In a number of applications of computerized tomography, the ultimate goal is to detect and characterize objects within a cross section. Detection of edges of different contrast regions yields the required information. The problem of detecting edges from projection data is addressed. It is shown that the class of linear edge detection operators used on images can be used for detection of edges directly from projection data. This not only reduces the computational burden but also avoids the difficulties of postprocessing a reconstructed image. This is accomplished by a convolution backprojection operation. For example, with the Marr-Hildreth edge detection operator, the filtering function that is to be used on the projection data is the Radon transform of the Laplacian of the 2-D Gaussian function which is combined with the reconstruction filter. Simulation results showing the efficacy of the proposed method and a comparison with edges detected from the reconstructed image are presented.

On two-dimensional maximum entropy spectral estimation

A novel method of two-dimensional spectral estimation, which the authors introduced recently (1987) using the Radon transform and a one-dimensional autoregressive model (AR), led them to investigate the maximization of entropy subject to the correlation matching constraints in the Radon space. Instead of solving the 2D maximum entropy (ME) spectral estimation problem, the authors convert it into a problem which is easier to solve. It is shown that a radial slice of the 2D ME spectrum can be obtained by 1D AR modeling of the projections (Radon transform) of a stationary random field (SRF). The advantages and limitations of using this new duality relation to estimate the complete 2D ME spectra on a polar raster are discussed. >

Generalized adaptive IFIR filter bank structures

Adaptive filters based on filter bank (FB) techniques have attracted attention recently due to their ability to improve convergence rate and reduce the computational complexity. This paper investigates a generalized adaptive interpolated finite impulse response (IFIR) FB structure. The IFIR model is a set of cascade of an interpolator and a sparse filter connected in parallel. The IFIR FB models the system impulse response as a linear combination of double indexed set of functions. The modeling capabilities and delay properties of the structure are investigated. Realizations of adaptive IFIR FB structures with delaying and delayless properties are presented. The delaying structure is obtained by employing orthogonal set of the basis functions for the interpolating FB. It is shown that delayless adaptive IFIR FB structure, as a special case of general adaptive IFIR FB, can be obtained by relaxing the orthogonality condition on the basis functions. This allows flexibility to choose the interpolators. The interpolators could be chosen to improve convergence rate of the adaptive algorithm. In general, optimal design of interpolator FB requires a priori knowledge of the input process and the system. One method of choosing the interpolators is by a non-linear optimization procedure based only on a priori knowledge of input process. We present a new method to adapt the interpolators themselves based on a common cost function and hence require no a priori knowledge of the input statistics. The convergence rate and steady state error performance of these structures are compared with the classical fullband filter in system identification scenario. Its application in acoustic echo cancellation (AEC) is presented.

Helical FDK algorithms with no backprojection weight

In this paper, we present two new filtered back-projection (FBP) type algorithms for cylindrical detector helical cone-beam geometry with no position dependent backprojection weight. The algorithms are extension of the recent exact Hilbert filtering based 2D divergent beam reconstruction with no back-projection weight to the FDK type algorithm for reconstruction in 3D helical trajectory cone-beam tomography. The two algorithms named HFDK-W1 and HFDK-W2 result in better image quality, noise uniformity, lower noise and reduced cone-beam artifacts.

A non-stationary time-series modeling approach for CT image reconstruction from truncated data

Truncated data problems are encountered in computed tomographic (CT) scanning scenarios where it is desirable to restrict the radiation dosage to a region-of-interest (ROI) of the object cross-section being imaged. In this paper, we propose a new image reconstruction technique for handling truncated data based on projection data extrapolation using a non-stationary time-series modeling approach. A special case of the autoregressive integrated moving average (ARIMA) modeling is investigated and a new algorithmic approach for completing truncated data is proposed. The proposed scheme allows easy incorporation of parallel-beam data consistency conditions to improve the reconstructed image quality. We evaluate the performance of the proposed schemes against existing data completion techniques and also illustrate the validity of the approaches for clinically relevant images.

A wavelet based Teager energy operator for spike detection in microelectrode array recordings

Spike detection in neural recordings is the initial step in the creation of brain machine interfaces. The Teager energy operator (TEO) treats a spike as an increase in the ‘local’ energy and detects this increase. The performance of TEO in detecting action potential spikes suffers due to its sensitivity to the frequency of spikes in the presence of noise which is present in microelectrode array (MEA) recordings. The multiresolution TEO (mTEO) method overcomes this shortcoming of the TEO by tuning the parameter k to an optimal value m so as to match to frequency of the spike. In this paper, we present an algorithm for the mTEO using the multiresolution structure of wavelets along with inbuilt lowpass filtering of the subband signals. The algorithm is efficient and can be implemented for real-time processing of neural signals for spike detection. The performance of the algorithm is tested on a simulated neural signal with 10 spike templates obtained from [14]. The background noise is modeled as a colored Gaussian random process. Using the noise standard deviation and autocorrelation functions obtained from recorded data, background noise was simulated by an autoregressive (AR(5)) filter. The simulations show a spike detection accuracy of 90% and above with less than 5% false positives at an SNR of 2.35 dB as compared to 80% accuracy and 10% false positives reported [6] on simulated neural signals.

FDK-Type Algorithms with No Backprojection Weight for Circular and Helical Scan CT

We develop two Feldkamp-type reconstruction algorithms with no backprojection weight for circular and helical trajectory with planar detector geometry. Advances in solid-state electronic detector technologies lend importance to CT systems with the equispaced linear array, the planar (flat panel) detectors, and the corresponding algorithms. We derive two exact Hilbert filtered backprojection (FBP) reconstruction algorithms with no backprojection weight for 2D fan-beam equispace linear array detector geometry (complement of the equi-angular curved array detector). Based on these algorithms, the Feldkamp-type algorithms with no backprojection weight for 3D reconstruction are developed using the standard heuristic extension of the divergent beam FBP algorithm. The simulation results show that the axial intensity drop in the reconstructed image using the FDK algorithms with no backprojection weight with circular trajectory is similar to that obtained by using Hus and T-FDK, algorithms. Further, we present efficient algorithms to reduce the axial intensity drop encountered in the standard FDK reconstructions in circular cone-beam CT. The proposed algorithms consist of mainly two steps: reconstruction of the object using FDK algorithm with no backprojection weight and estimation of the missing term. The efficient algorithms are compared with the FDK algorithm, Hus algorithm, T-FDK, and Zhu et al.s algorithm in terms of axial intensity drop and noise. Simulation shows that the efficient algorithms give similar performance in axial intensity drop as that of Zhu et al.s algorithm while one of the efficient algorithms outperforms Zhu et al.s algorithm in terms of computational complexity.

Image reconstruction with laterally truncated projections in helical cone-beam CT: Linear prediction based projection completion techniques

Lateral or transaxial truncation of cone-beam data can occur either due to the field of view limitation of the scanning apparatus or in region-of-interest tomography. In this paper, we suggest two new methods to handle lateral truncation in helical scan CT. It is seen that reconstruction with laterally truncated projection data, assuming it to be complete, gives severe artifacts which even penetrates into the field of view. A row-by-row data completion approach using linear prediction is introduced for helical scan truncated data. An extension of this technique known as windowed linear prediction approach is introduced. Efficacy of the two techniques are shown using simulation with standard phantoms. A quantitative image quality measure of the resulting reconstructed images are used to evaluate the performance of the proposed methods against an extension of a standard existing technique.

Shape from shading: analysis of implicit surfaces by synthesis

In this paper, we present a general framework for solving the shape from shading problem for a class of surfaces called implicit surfaces by applying image synthesis techniques from computer graphics. The method relies on iterative synthesis of images from object descriptions in order to minimize an error function. The technique is illustrated in detail for quadric surfaces, with the ellipsoid as the specific example. The advantage of this approach is that reconstructing the shape of objects from shading is possible even under very general imaging conditions.