Small Number Of Coefficients Research Articles

TH‐EF‐BRD‐01: Fluence Map Optimization Using a Voxel‐Based Reduced‐Order Constrained Optimization Model

Purpose:To develop a method for adaptively imposing dose constraints on individual voxels and structures in IMRT planning, such that a sequence of computationally tractable, low‐dimensional constrained optimization problems is solved that leads to plans satisfying dose‐volume and other clinical constraints.Methods:The previously proposed Reduced Order Constrained Optimization (ROCO) algorithm is applied to parameterize an IMRT problem by a small number of coefficients on learned principal components, instead of a large number of independent beamlet fluences. A sequence of constrained optimization problems is solved over the set of coefficients in which the importance of each voxel and structure is adaptively changed in the objective function. Instead of manually investigating good settings for these parameters, an adaptive gain scheduling rule based on control theory automatically adjusts the weights, quickly converging to a plan satisfying the clinical constraints. In particular, we apply a decentralized proportional‐integral controller that adjusts structure weights using dose‐volume constraint (DVC) violation feedback. We compare our method against a previous approach in which subsets of voxels were iteratively selected and hard‐constrained in an attempt to satisfy DVCs.Results:The technique was tested on five different non‐nodal prostate cases, each resulting in clinically acceptable plans in less than 2.5 minutes on average. The quality of plans is far superior to the alternate method, significantly reducing OARs doses while meeting PTV V95 goals.Conclusion:Compared to alternative optimization schemes in the full intensity space, the propose scheme offers fast convergence rate, demands significantly less memory resources and computational effort, which allows larger IMRT problems to be addressed.

Robust Estimation of Non-Stationary Noise Power Spectrum for Speech Enhancement

We propose a novel method for noise power spectrum estimation in speech enhancement. This method called extended-DATE (E-DATE) extends the $d$ -dimensional amplitude trimmed estimator (DATE), originally introduced for additive white gaussian noise power spectrum estimation in “Robust estimation of noise standard deviation in presence of signals with unknown distributions and occurrences” (D. Pastor and F. Socheleau, IEEE Trans. Signal Processing, vol. 60, no. 4, pp. 1545–1555, Apr. 2012) to the more challenging scenario of non-stationary noise. The key idea is that, in each frequency bin and within a sufficiently short time period, the noise instantaneous power spectrum can be considered as approximately constant and estimated as the variance of a complex gaussian noise process possibly observed in the presence of the signal of interest. The proposed method relies on the fact that the Short-Time Fourier Transform (STFT) of noisy speech signals is sparse in the sense that transformed speech signals can be represented by a relatively small number of coefficients with large amplitudes in the time-frequency domain. The E-DATE estimator is robust in that it does not require prior information about the signal probability distribution except for the weak-sparseness property. In comparison to other state-of-the-art methods, the E-DATE is found to require the smallest number of parameters (only two). The performance of the proposed estimator has been evaluated in combination with noise reduction and compared to alternative methods. This evaluation involves objective as well as pseudo-subjective criteria.

Decomposed Vector Rotation-Based Behavioral Modeling for Digital Predistortion <newline/>of RF Power Amplifiers

A new behavioral model for digital predistortion of radio frequency (RF) power amplifiers (PAs) is proposed in this paper. It is derived from a modified form of the canonical piecewise-linear (CPWL) functions using a decomposed vector rotation (DVR) technique. In this model, the nonlinear basis function is constructed from piecewise vector decomposition, which is completely different from that used in the conventional Volterra series. Theoretical analysis has shown that this model is much more flexible in modeling RF PAs with non-Volterra-like behavior, and experimental results confirmed that the new model can produce excellent performance with a relatively small number of coefficients when compared to conventional models.

Exact and Approximate Algorithms for the Filter Design Optimization Problem

The filter design optimization (FDO) problem is defined as finding a set of filter coefficients that yields a filter design with minimum complexity, satisfying the filter constraints. It has received a tremendous interest due to the widespread application of filters. Assuming that the coefficient multiplications in the filter design are realized under a shift-adds architecture, the complexity is generally defined in terms of the total number of adders and subtractors. In this paper, we present an exact FDO algorithm that can guarantee the minimum design complexity under the minimum quantization value, but can only be applied to filters with a small number of coefficients. We also introduce an approximate algorithm that can handle filters with a large number of coefficients using less computational resources than the exact FDO algorithm and find better solutions than existing FDO heuristics. We describe how these algorithms can be modified to handle a delay constraint in the shift-adds designs of the multiplier blocks and to target different filter constraints and filter forms. Experimental results show the effectiveness of the proposed algorithms with respect to prominent FDO algorithms and explore the impact of design parameters, such as the filter length, quantization value, and filter form, on the complexity and performance of filter designs.

A novel algorithm for radar classification based on doppler characteristics exploiting orthogonal Pseudo-Zernike polynomials

Phase modulation induced by target micromotions introduces sidebands in the radar spectral signature returns. Time-frequency distributions facilitate the representation of such modulations in a micro-Doppler signature that is useful in the characterization and classification of targets. Reliable micro-Doppler signature classification requires the use of robust features that are capable of uniquely describing the micromotion. Moreover, future applications of micro-Doppler classification will require meaningful representation of the observed target by using a limited set of values. In this paper, the application of the pseudo-Zernike moments for micro-Doppler classification is introduced. Specifically, the proposed algorithm consists of the extraction of the pseudo-Zernike moments from the cadence velocity diagram (CVD). The use of pseudo-Zernike moments allows invariant features to be obtained that are able to discriminate the content of two-dimensional matrices with a small number of coefficients. The analysis has been conducted both on simulated and on real radar data, demonstrating the effectiveness of the proposed approach for classification purposes.

Optimization of Wind Power Dispatch to Minimize Energy Storage System Capacity

By combining a wind turbine with an energy storage system (ESS), we are able to attenuate the intermittent wind power characteristic making the power derived from a wind farm dispatchable. This paper evaluates the influence of the phase delay of the low-pass filter in the conventional smoothing power control on the ESS capacity; longer phase delays require a larger ESS capacity. In order to eliminate the effect of the phase delay, we optimize the power dispatch using a zero-phase low-pass filter that results in a non-delayed response in the power dispatch. The proposed power dispatching method significantly minimizes the ESS capacity. In addition, the zero-phase low- pass filter, which is a symmetrical forward-reverse finite impulse response type, is designed simply with a small number of coefficients. Therefore, the proposed dispatching method is not only optimal, but can also be feasibly applied to real wind farms. The efficacy of the proposed dispatching method is verified by integrating a 3 MW wind turbine into the grid using wind data measured on Jeju Island.

Compressed convolution

We introduce the concept of compressed convolution, a technique to convolve a given data set with a large number of non-orthogonal kernels. In typical applications our technique drastically reduces the effective number of computations. The new method is applicable to convolutions with symmetric and asymmetric kernels and can be easily controlled for an optimal trade-off between speed and accuracy. It is based on linear compression of the collection of kernels into a small number of coefficients in an optimal eigenbasis. The final result can then be decompressed in constant time for each desired convolved output. The method is fully general and suitable for a wide variety of problems. We give explicit examples in the context of simulation challenges for upcoming multi-kilo-detector cosmic microwave background (CMB) missions. For a CMB experiment with detectors with similar beam properties, we demonstrate that the algorithm can decrease the costs of beam convolution by two to three orders of magnitude with negligible loss of accuracy. Likewise, it has the potential to allow the reduction of disk space required to store signal simulations by a similar amount. Applications in other areas of astrophysics and beyond are optimal searches for a large number of templates in noisy data, e.g. from a parametrized family of gravitational wave templates; or calculating convolutions with highly overcomplete wavelet dictionaries, e.g. in methods designed to uncover sparse signal representations.

Wavelet based denoising technique for liquid level system

The purpose of this paper is to employ wavelet based noise removal technique to remove measurement noise from differential pressure transmitter (DPT) output indicating the level of a process tank. The liquid level system (LLS) is approximated as a first order plant with time delay. When connected in closed loop, the LLS is ideally associated with a PI controller, an actuator, a final control element and a level sensor (DP transmitter in present system). There are enough chances of contaminating the output of LLS by the high frequency measurement noise. In this work, an attempt has been made to judge the performance of discrete wavelet transform (DWT) and discrete wavelet packet transform (DWPT) based noise removal technique when applied to LLS. The available denoised response using wavelet based filtering is compared with that of conventional Butterworth filtering method. Applying hard thresholding that typically retains a very small number of coefficients, the results are often smoothed at the cost of loosing information. By retaining larger number of coefficients and shrinking them, the soft thresholding methods usually give more useful results to denoise the signal. Threshold value has been calculated by Visu Shrink method and Minimax method in different cases.

Automatic Classification of Ground-Penetrating-Radar Signals for Railway-Ballast Assessment

The ground-penetrating radar (GPR) has been widely used in many applications. However, the processing and interpretation of the acquired signals remain challenging tasks since an experienced user is required to manage the entire operation. In this paper, we present an automatic classification system to assess railway-ballast conditions. It is based on the extraction of magnitude spectra at salient frequencies and their classification using support vector machines. The system is evaluated on real-world railway GPR data. The experimental results show that the proposed method efficiently represents the GPR signal using a small number of coefficients and achieves a high classification rate when distinguishing GPR signals reflected by ballasts of different conditions.

The Elastic Strain Energy of Damaged Solids with Applications to Non-Linear Deformation of Crystalline Rocks

Laboratory and field data indicate that rocks subjected to sufficiently high loads clearly deviate from linear behavior. Non-linear stress–strain relations can be approximated by including third and higher-order terms of the strain tensor in the elastic energy expression (e.g., the Murnaghan model). Such classical non-linear models are successful for calculating deformation of soft materials, for example graphite, but cannot explain with the same elastic moduli small and large non-linear deformation of stiff rocks, such as granite. The values of the third (higher-order) Murnaghan moduli estimated from acoustic experiments are one to two orders of magnitude above the values estimated from stress–strain relations in quasi-static rock-mechanics experiments. The Murnaghan model also fails to reproduce an abrupt change in the elastic moduli upon stress reversal from compression to tension, observed in laboratory experiments with rocks, concrete, and composite brittle material samples, and it predicts macroscopic failure at stress levels lower than observations associated with granite. An alternative energy function based on second-order dependency on the strain tensor, as in the Hookean framework, but with an additional non-analytical term, can account for the abrupt change in the effective elastic moduli upon stress reversal, and extended pre-yielding deformation regime with one set of elastic moduli. We show that the non-analytical second-order model is a generalization of other non-classical non-linear models, for example “bi-linear”, “clapping non-linearity”, and “unilateral damage” models. These models were designed to explain the abrupt changes of elastic moduli and non-linearity of stiff rocks under small strains. The present model produces dilation under shear loading and other non-linear deformation features of the stiff rocks mentioned above, and extends the results to account for gradual closure of an arbitrary distribution of initial cracks. The results provide a quantitative framework that can be used to model simultaneously, with a small number of coefficients, multiple observed aspects of non-linear deformation of stiff rocks. These include, in addition to the features mentioned above, stress-induced anisotropy and non-linear effects in resonance experiments with damaged materials.

Robust focus measure for unsupervised auto-focusing based on optimum discrete cosine transform coefficients

In this paper we present a robust focus measure for unsupervised auto-focusing based on optimum discrete cosine transform (DCT) coefficients. DCT has a low computational complexity due to real-valued coefficients, and a small number of coefficients have to be calculated to achieve a good spectral representation of an image. The focusing region of an input image is divided into nonoverlapping 8 × 8 sub-images, and spectra of sub-images are obtained by 8 × 8 DCT. The focusing measure is computed from the middle frequency components. By appropriately chosen DCT coefficients, the proposed focusing measure is robust to Gaussian and impulsive noises. Experimental results show that the proposed method is more effective than the traditional methods based on the comparison with well-known autofocusing uncertainty measure (AUM).

Approximate Clustering on Data Streams Using Discrete Cosine Transform

In this study, a clustering algorithm that uses DCT transformed data is presented. The algorithm is a grid density-based clustering algorithm that can identify clusters of arbitrary shape. Streaming data are transformed and reconstructed as needed for clustering. Experimental results show that DCT is able to approximate a data distribution efficiently using only a small number of coefficients and preserve the clusters well. The grid based clustering algorithm works well with DCT transformed data, demonstrating the viability of DCT for data stream clustering applications.

Comparing Measures of Sparsity

Sparsity of representations of signals has been shown to be a key concept of fundamental importance in fields such as blind source separation, compression, sampling and signal analysis. The aim of this paper is to compare several commonly-used sparsity measures based on intuitive attributes. Intuitively, a sparse representation is one in which a small number of coefficients contain a large proportion of the energy. In this paper, six properties are discussed: (Robin Hood, Scaling, Rising Tide, Cloning, Bill Gates, and Babies), each of which a sparsity measure should have. The main contributions of this paper are the proofs and the associated summary table which classify commonly-used sparsity measures based on whether or not they satisfy these six propositions. Only two of these measures satisfy all six: the pq-mean with p les 1, q > 1 and the Gini index.

Optimized Sinusoid Synthesis via Inverse Truncated Fourier Transform

It was shown that sinusoid synthesis can be implemented efficiently by an inverse Fourier transform on consecutive frames where all but a small number of coefficients per oscillator are dropped. This leads to a compromise between computational complexity and approximation accuracy. The method can be improved by two approaches. First, optimal coefficients can be found by minimizing the average approximation error. Second, the optimal window function can be found through an iterative process. The gain in signal-to-noise ratio (SNR) is between 10 and 40 dB and can be used to reduce computational complexity while satisfying required synthesis quality.

Modeling medium-scale TEC structures, observed by Belgian GPS receivers network

GALOCAD project “Development of a Galileo Local Component for the nowcasting and forecasting of atmospheric disturbances affecting the integrity of high precision Galileo applications” aims to perform a detailed study on ionospheric small- and medium-scale structures and to assess the influence of these structures on the reliability of Galileo precise positioning applications. GPS-derived TEC (total electron content) is obtained from the Belgium Dense Network (BDN), consisting of 67 permanent GPS stations. An empirical 3-D model is developed for studying these ionospheric structures. The model, named LLT model, described temporal variations of TEC in latitude/longitude frame (46°, 52°)N and (−1°, 11°)E. The spatial variations of TEC are modeled by Tchebishev base functions, while the temporal variations are described by a trigonometric basis. To fit the model to the data, the observed area is divided into bins with (1° × 1°) geographic scale and 6 min on time axis. LLT model is made flexible, with varying number of coefficients along each axis. This allows different degree of smoothing, which is the key element of the present approach. Model runs with higher number of coefficients, capturing in details medium-scale TEC structures are subtracted from results obtained with smaller number of coefficients; the latter represent the background ionosphere. The residual structures are localized and followed as they travel across the observed area. In this way, the size, velocity, and direction of the irregular structures are obtained.

Applied comparisons between SCHA and R‐SCHA regional modeling techniques

Spherical cap harmonic analysis (SCHA) has become a common tool for the regional modeling of potential fields since its introduction by Haines (1985). The fact that SCHA satisfies Laplace equation and the possibility of representing high‐frequency fields with a small number of coefficients (compared to the global spherical harmonic analysis) made SCHA the preferred choice for the development, for example, of magnetic field models at national scale. However, Thébault et al. (2006a) demonstrated that the traditional SCHA presented some deficiencies, in particular related to the inversion of multilevel data sets. The authors presented the R‐SCHA technique as an alternative method in which the introduction of a new set of basis functions and boundary conditions solved this issue. In this paper we present some numerical comparisons between the SCHA and R‐SCHA techniques applied with different synthetic vector data sets, from near‐surface main field, main difference, and crustal field data simulating a World Digital Magnetic Anomaly Map subset. Other analyses are carried out with synthetic vector data set that mimics the expected data distribution from a multisatellite mission like the forthcoming European Swarm mission. No regularization, weighting, or ad hoc procedures are applied to the synthetic vector data, and a cap of 7° aperture is considered. The numerical analyses show that SCHA is a satisfying approximation in a band‐limited spectral region that depends on the cap's size. It does not work correctly either for main field or for the short‐scale crustal field modeling. These aspects are supported by equations illustrating why SCHA may fail. On the contrary, R‐SCHA converges more slowly than SCHA but is valid in all cases. It gives a consistent set of regional coefficients and fits the radial variation of the field in a realistic way. At last, the special case of data incompatibility shows that R‐SCHA does not fit incompatible data while SCHA assimilates most of them. These results should help the scientific community to evaluate the level of approximation needed for the development of regional magnetic field models in the era of the European Space Agency Swarm mission.

The Standard Reference Method of Beer Color Specification as the Basis for a New Method of Beer Color Reporting

Ensembles of beer optical absorption spectra normalized by the standard reference method (SRM) exhibit small variances, suggesting that Karhunen-Loeve (KL) principal component approximations of these spectra, using only a few coefficients, might facilitate reconstruction of the originals with enough fidelity to permit calculation of accurate tristimulus color. To test this hypothesis, the spectra of 99 beers were measured and grouped into ensembles that were used as bases for computation of KL coefficients. Approximations of spectra were reconstructed from small numbers of these coefficients. CIELAB (tristimulus) colors computed from reconstructed and original spectra were compared using CIELAB ΔE*ab as the metric. The sensitivity of color error to the form of the spectrum (transmission or absorption, normalized or not), number of coefficients, optical path length, illuminant, observer, and ensemble makeup were studied. The data and analysis indicate that accurate (ΔE*ab ≈ 1) tristimulus color can be obtained under various viewing conditions from the SRM value and 2–6 KL coefficients. Thus, SRM plus some small number of KL coefficients constitutes a full reporting of visible beer color.

An efficient face verification method in a transformed domain

In this paper we propose a low-complexity face verification system based on the Walsh–Hadamard transform. This system can be easily implemented on a fixed point processor and offers a good compromise between computational burden and verification rates. We have evaluated that with 36 integer coefficients per face we achieve better Detection Cost Function (6.05%) than the classical eigenfaces approach (minimum value 6.99% with 126 coefficients), with a smaller number of coefficients.

Comparison of compression ratios for ECG signals by using three time-frequency transformations

In this paper are presented compression results of ECG signal by using three time-frequency transformations: Discrete Wavelet Transform, Wavelet Packets and Modified Cosine Transform. By using transforms mentioned, samples of signals are transformed to appropriate groups of transformation coefficients. Almost all coefficients below the determined threshold are rounded to zero values and by inverse transform the similar signal to original one is created. By using run-length coder, consecutive zero value coefficients can be replaced by single value that shows how many consecutive coefficients with zero value exists. In this way small number of coefficients is stored, and compression is obtained. Depending on transform used, different number of coefficients is rounded to zero in different positions, hence the reconstructed signal is more or less similar to the original one. In general there exists measures that show how much reconstructed signal is similar to the original one, and the most used is Percentage Root mean square Difference (PRD). Comparison of compression is performed in obtaining the larger compression ratio for the smaller PRD.

Highly precise estimation scheme for remote video PSNR using spread spectrum and extraction of orthogonal transform coefficients

AbstractWith the widespread use of the digital transmission of TV signals, it is highly desirable to establish a remote monitoring scheme for video transmission quality. As a monitoring scheme for the digital video quality in the actual transmission, the reduced reference (RR) scheme is considered promising: in this scheme the feature parameters of the original picture are extracted and transmitted for comparison with the parameters in the receiver. Consequently, this paper proposes an RR‐type picture quality‐monitoring scheme which can provide highly precise remote estimation of the PSNR of the received picture. In the proposed scheme, the sent and received signals are whitened by spectrum spreading, and orthogonal transformation is applied to the results. The transform coefficients are extracted and transmitted through the monitoring link. Due to the whitening process, highly precise PSNR estimation is realized, even though only a small number of coefficients are extracted. In order to make the whitening effective, the degradation must be distributed as uniformly as possible in the transform block. In order to deal with local picture degradation due to channel error and other factors, multiplication by a PN sequence (spatial spreading) and the inverse orthogonal transform are applied in the transform domain, resulting in effective spreading and helping to improve the precision of PSNR estimation. The Walsh–Hadamard transform, which is easy to implement, is used as the orthogonal transform. By using the proposed scheme, a PSNR estimation error of approximately ±0.1 to 0.3 dB for a monitoring link rate of 40 kbit/s is obtained, which meets practical requirements for highly precise estimation. © 2006 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 89(6): 51–62, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20188