SCAN-MUSIC: An efficient super-resolution algorithm for large-scale single snapshot line spectral estimation

Block motion estimation using full search is computationally intensive. Previously proposed fast algorithms reduce the computation by limiting the number of searching locations. This is accomplished at the expense of less accuracy of motion estimation and gives rise to an appreciably higher mean squared error (MSE) for motion compensated images. We present a new fast and efficient search algorithm for block motion estimation that produces better quality performance and less computational time compared with a three-step search (TSS) algorithm. The proposed algorithms are based on the ideas of the dithering pattern for pixel decimation, multiple-candidate for pixel-decimation-based full search, and center-based distribution of the motion vector. From the experimental results, the proposed algorithm is superior to the TSS in both quality performance (about 0.2 dB) and computational complexity (about half).

This paper presents an efficient joint disparity-motion estimation algorithm and a fast motion estimation algorithm in an MPEG-4 compatible stereoscopic sequence codec for 3D broadcasting. In stereoscopic sequence coding, the critical problems to be solved are double bandwidth and computational complexity. However, the previous trials to reduce coding bits have increased computational complexity. In this paper, we try to implement fast algorithms for stereoscopic sequences while maintaining high coding efficiency. Joint disparity-motion estimation can increase coding efficiency and reduce the computational complexity of the stereoscopic codec by using the relationship between the disparity and motion fields. The disparity vectors are estimated by using the left and right motion vectors and the previous disparity vectors in each time frame. In order to obtain more accurate disparity vectors, we employ the spatial prediction process after joint estimation. From joint estimation and spatial prediction, we can obtain the accurately predicted disparity vectors and then increase the coding efficiency from those predicted vectors. Moreover, we propose a fast motion estimation algorithm which utilizes correlation between the motion vectors of the neighboring blocks. We confirmed that the PSNR of the proposed method is 1.0-2.0 dB higher than ones of conventional methods. In addition, the processing time is reduced by almost 1/10.

We present an efficient computation constrained block-based motion vector estimation algorithm for low bit rate video coding that offers good tradeoffs between motion estimation distortion and number of computations. A reliable predictor determines the search origin. An efficient search pattern exploits structural constraints within the motion field. A flexible cost measure used to terminate the search allows simultaneous control of the motion estimation distortion and the computational cost. Experimental results demonstrate the viability of the proposed algorithm in low bit rate video coding applications, achieving essentially the same levels of rate-distortion performance and subjective quality as that of the full search algorithm when used by the UBC H.263+ video coding reference software. However the proposed motion estimation algorithm provides substantially higher encoding speed as well as graceful computational degradation capabilities.

The ultimate resolution limit of an imaging system is a long-standing puzzle that originated from the 18th century. Although many heuristic resolution criteria have been proposed after the discovery of Abbe's diffraction limit, the exact characterization of the resolution limit is still unknown. In this thesis, we aim to provide a rigorous mathematical theory for the resolution limits in various setups. Specifically, we define and quantitatively characterize the computational resolution limits for number detection and location recovery in the deconvolution problem, the one-dimensional and multi-dimensional line spectral estimation problems, and the imaging problem with multi-illumination. The results explicitly elucidate the dependence of each computational resolution limit on the cutoff frequency, signal-to-noise ratio, sparsity of the source, and illumination pattern. In contrast to the classical resolution limits that are only related to the cutoff frequency, our characterizations highlight the importance of all the aforementioned factors to the super-resolution problem and thus are more applicable to modern super-resolution algorithms whose performances are highly related to the signal-to-noise ratio. Moreover, our results indicate that there are phase transitions in these reconstruction problems. We derive number detection and location recovery algorithms and numerically confirm the predicted phase transition phenomenons. Finally, we propose a fast algorithm for super-resolving point sources with a cluster structure.

Spectrally efficient channel impulse response (CIR) estimation in the sense of minimal training overhead is a key issue for the successful deployment of Filter Bank Multicarrier (FBMC) with Offset Quadrature Amplitude Modulation (OQAM). In this contribution we perform a comparison between channel estimation algorithms considering two different models for the received subcarrier signals: a per-subcarrier narrowband and a broadband channel model. We also consider three cases of spectrally efficient channel estimation by employing different training sequence occupation of the subcarriers.

Optimization theory and discrete invariant imbedding is used in order to derive computationally efficient sequential algorithms for the maximum likelihood estimation of bias errors in linear discrete recursive filtering with noise corrupted input observations and correlated plant and measurement noise. Error analysis algorithms are derived for adaptive and nonadaptive systems with bias and modeling errors. Examples demonstrate the efficiency of the adaptive estimation algorithms and the error analysis algorithms for estimation with bias uncertainty.

This paper presents a new pel subsampling-based search algorithm for motion estimation. The proposed quartet-pel motion estimation (QME) search algorithm reduces the number of pels taken into account for the cost function of the matching criteria at every search position, therefore reduces the computational complexity and the required memory bandwidth. Furthermore, the proposed algorithm has a regular data flow, which in turn leads to hardware-efficient implementations. Simulation results show that QME achieves almost the same coding performance as full-search block matching algorithm (FBMA) in terms of PSNR and the size of the coded bitstream. A flexible and efficient architecture design using QME is also proposed. The flexibility is based on the configurations of processing units, such that the processing time and memory access of QME architecture can be reduced with facility. On the other hand, the efficiency of proposed hardware design, characterized by normalized processing capability per gate, also surpasses other designs.

An adaptive and computationally efficient algorithm for parameters estimation of superimposed exponential signals with observations missing randomly

: The objective of this study was to conduct applied research directed toward understanding the relationship between the complexity or efficiency of algorithms and the overall quality of computer software. The final report is presented in a two volume series consisting of a total of eight parts. This volume, containing Parts 1 and 2, comprises a general introduction to the entire series and a research plan. Part 1 begins with a description of the goals of the overall contract effort. This is followed by a discussion of previous RADC work on software quality metrics, emphasizing measures concerned with the time and storage efficiency of programs. Next, an overview of the field of algorithm analysis and computational complexity is given. A final section contains an introduction to the particular research investigations pursued in the other portions of this study. Part 2 presents a research plan for advancing the state-of-the-art in the area of algorithm performance. An Appendix contains an outline of the major topics and issues addressed in the area of algorithm analysis and computational complexity, together with an annotated select bibliography.

Owing to low cost and relatively accurate range measurement, ultrasonic sensors are widely used in various simultaneous localisation and mapping (SLAM) applications. In spite of the abundance of ultrasonic sensor based SLAM applications, a simple and efficient algorithm for an ultrasonic sensor based positioning system with good accuracy and low computational complexity has not yet emerged. The major difficulty is the trade-off between localisation accuracy and computational complexity in most SLAM algorithms, such as extended Kalman filter (EKF) and particle filter. Typically, they improve localisation accuracy by increasing the density of the landmarks, as a result leading to high computational complexity of algorithms and limiting the utilisation of algorithms into online SLAM systems. This study addresses an improved particle filter algorithm to solve ultrasonic sensor based 2D range-only SLAM problem with relatively good accuracy and low computational complexity. This algorithm uses a simple four fixed features based system model to limit the density of the landmarks. A technique called map adjustment is proposed to increase the accuracy and efficiency of the algorithm. Using map adjustment, the proposed particle filter algorithm can improve localisation accuracy and lower computational complexity. The experiment results demonstrate that this algorithm has a better performance than conventional particle filter localisation algorithm.

The optimal detection for coded system requires the use of a maximum a posteriori (MAP) detection. A list sphere detector (LSD) can be used to approximate the MAP detector. Depending on the used list size, LSD provides a tradeoff between the performance and the computational complexity. The LSD output candidate list is used to calculate the approximation of the probability log-likelihood ratio (LLR) of each transmitted bit. The list should be large enough and it should include at least one candidate for both possible bits for good approximation. The use of a small list size causes inaccurate and, especially, very large LLRs that prevent the decoder from correcting the falsely detected signals and, thus, degrades performance. We study the effect of the LLR clipping to the performance and complexity of the LSD algorithm. We show that by limiting the dynamic range of the LLR the required LSD list size can be decreased, and, thus, the complexity of the algorithms is decreased. The optimal dynamic range values for LLR clipping are determined and the effect of the clipping to the complexity of the LSD algorithms is analyzed.

In this paper we propose an efficient motion estimation algorithm as well as its supporting FPGA-based, field programmable system-on-chip (FPSoC), for integer and fractional motion estimation. Our results show that the rate-distortion loss of our algorithm is insignificant when compared to full search in H.264/AVC, while our FPSoC is hardware-efficient, even out-performing some state-of-the-art ASIC implementations.

Extreme UltraViolet (EUV) lithography is a new technology for production of integrated circuits. In EUV lithographic machines, optical elements are heated by absorption of exposure energy. Heating induces thermoelastic deformations of optical elements and consequently, it creates wavefront aberrations. These Thermally Induced Wavefront Aberrations (TIWA) can significantly degrade the resolution of EUV lithographic machines. One of the ways to correct TIWA and consequently, to improve the resolution of EUV lithographic machines, is to use the Adaptive Optics (AO) technique and predictive control algorithms. However, the predictive control of TIWA is a challenging problem, mainly because the dynamical behavior of TIWA is described by thermoelastic Partial Differential Equations (PDEs). By discretizing the thermoelastic equations using the finite difference or finite element methods, large-scale state-space models can be obtained. A striking feature of these state-space models is that they have sparse (multi) banded matrices. Consequently, these state-space models can be interpreted as large-scale networks of local subsystems. All this implies that the problem of correcting TIWA can be placed in a much more general context of identifying, estimating and controlling large-scale interconnected (distributed) systems. However, currently used estimation and control algorithms are not computationally feasible for large-scale systems. For this reason, this thesis focuses on the development of computationally efficient identification, estimation and control algorithms for large-scale interconnected systems. In this thesis, we prove that the inverses of (finite-time) Gramians of large-scale interconnected systems, obtained by discretizing PDEs, belong to a class of off-diagonally decaying matrices. Consequently, these inverses can be approximated by sparse (multi) banded matrices with O(N) complexity, where N is the number of local subsystems. To compute the approximate inverses, the Chebyshev approximation method and the Newton iteration are used. On the basis of these theoretical results, we develop novel estimation and identification algorithms for large-scale interconnected systems. The computational and memory complexity of these methods scale with O(N). This is the main advantage over the traditional estimation and identification methods, which complexity is O(N^3). Furthermore, in this thesis we develop and experimentally verify AO control algorithms for predictive correction of TIWA. The experimental results give a good first indication for a possible implementation of the developed predictive control algorithms in EUV lithographic machines. Finally, we develop and experimentally test an iterative learning control algorithm for high performance correction of wavefront aberrations.

We present a novel algorithm for rapid and efficient estimation of the fundamental frequency, phase and amplitude of harmonically distorted signals in balanced three-phase (3PH) power systems. The proposed algorithm exploits the harmonic structure of the signal to enhance the quality of the parameter estimates. It operates in the frequency domain, employing an efficient iterative interpolation procedure on the Fourier coefficients. The estimator has a low computational complexity, being of the same order as the fast Fourier transform (FFT) algorithm. Yet, it outperforms state-of-art high resolution parameter estimators for 3PH power system signals, especially when the available data points are limited and/or the signal to noise ratio is poor.

The presence of an accurate and efficient system state estimator is a precondition for supervision and closed-loop-control of low voltage grids. Such an estimator has to perform in consecutive periods of minutes. Between two periods in most cases, only the measurement values will change, but sometimes also the measurement model. This paper gives suggestions on how to improve the computationally efficiency of state estimation algorithms that have to perform in such an environment. The efficiency improvements are achieved by the application of advanced matrix inversion methods. Further the use of a linear measurement model and the application of the standard augmented matrix approach for solving the state estimation formula is suggested. However, these improvements can also be applied to other measurement models and estimation methods. The efficiency of the improvements is benchmarked against standard methods for different real grid operation cases. In particular, cases when new measurements are added or measurement values get lost are considered. The final result of the paper is an adjustable, robust and efficient algorithm for low voltage state estimation, presented in a way to support manufacturers and operators to implement and maintain it. The paper is a contribution in the field of static state estimation and short-term operation in distribution systems, in particular, low voltage grids.