Use Of Nonlinear Algorithms Research Articles

Enhancing Signal Recognition Accuracy in Delay-Based Optical Reservoir Computing: A Comparative Analysis of Training Algorithms

To improve the accuracy of signal recognition in delay-based optical reservoir computing (RC) systems, this paper proposes the use of nonlinear algorithms at the output layer to replace traditional linear algorithms for training and testing datasets and apply them to the identification of frequency-modulated continuous wave (FMCW) LiDAR signals. This marks the inaugural use of the system for the identification of FMCW LiDAR signals. We elaborate on the fundamental principles of a delay-based optical RC system using an optical-injected distributed feedback laser (DFB) laser and discriminate four FMCW LiDAR signals through this setup. In the output layer, three distinct training algorithms—namely linear regression, support vector machine (SVM), and random forest—were employed to train the optical reservoir. Upon analyzing the experimental results, it was found that regardless of the size of the dataset, the recognition accuracy of the two nonlinear training algorithms was superior to that of the linear regression algorithm. Among the two nonlinear algorithms, the Random Forest algorithm had a higher recognition accuracy than SVM when the sample size was relatively small.

Tractability of sampling recovery on unweighted function classes

It is well-known that the problem of sampling recovery in the L 2 L_2 -norm on unweighted Korobov spaces (Sobolev spaces with mixed smoothness) as well as classical smoothness classes such as Hölder classes suffers from the curse of dimensionality. We show that the problem is tractable for those classes if they are intersected with the Wiener algebra of functions with summable Fourier coefficients. In fact, this is a relatively simple implication of powerful results from the theory of compressed sensing. Tractability is achieved by the use of non-linear algorithms, while linear algorithms cannot do the job.

New-generation maximum entropy method: a Lagrangian-based algorithm for dynamic reconstruction of interferometric data

ABSTRACT Imaging interferometric data in radio astronomy requires the use of non-linear algorithms that rely on different assumptions on the source structure and may produce non-unique results. This is especially true for very long baseline interferometry (VLBI) observations, where the sampling of Fourier space is very sparse. A basic tenet in standard VLBI imaging techniques is to assume that the observed source structure does not evolve during the observation. However, the recent VLBI results of the supermassive black hole at our Galactic Centre (Sagittarius A*), recently reported by the Event Horizon Telescope Collaboration, require the development of dynamic imaging algorithms, since it exhibits variability at minute time-scales. In this paper, we introduce a new non-convex optimization problem that extends the standard maximum entropy method (MEM), for reconstructing intra-observation dynamical images from interferometric data that evolve in every integration time. We present a rigorous mathematical formalism to solve the problem via the primal–dual approach. We build a Newton strategy and we give its numerical complexity. We also give a strategy to iteratively improve the obtained solution and, finally, we define a novel figure of merit to evaluate the quality of the recovered solution. Then, we test the algorithm, called the new-generation MEM (ngMEM), in different synthetic data sets, with increasing difficulty. Finally, we compare it with another well-established dynamical imaging method. Within this comparison, we have identified a significant improvement of the ngMEM reconstructions. Moreover, the evaluation of the integration time evolution scheme and the time contribution showed that this method can play a crucial role in obtaining good dynamic reconstructions.

Discrete-time complementary filter for attitude estimation based on MARG sensor

The MARG sensor, which stands for the combination of a magnetometer, an accelerometer, and a gyroscope, is widely used for 3D attitude measurement. Among the mainstream solutions for MARG-based attitude estimation, the complementary filter (CF) is normally regarded as a simplified alternative to the Kalman filter (KF), mainly because CF can reduce the amount of calculations. A dual-vector discrete-time CF (DV-DTCF) and its tuning methods are introduced in this paper. Different from the quaternion-based attitude estimation algorithms, DV-DTCF has a linear measurement model, since it utilizes the gravity and geomagnetic vectors as its state variables instead of quaternions. This feature of DV-DTCF can avoid linearization error or the use of nonlinear algorithms, and can also greatly reduce its computational complexity. More interestingly, it is analytically revealed, and experimentally proven, that the proposed DV-DTCF is fully equivalent to a fixed-gain KF. This fascinating fact leads straightforwardly to the tuning methods of DV-DTCF via the corresponding fixed-gain KF and Riccati equation. These tuning methods of DV-DTCF are based on the statistic characteristics of MARG sensor noise, and that makes them solid and feasible. According to experimental results, DV-DTCF can achieve the same accuracy as that of commonly-used KF algorithms in MARG-based attitude estimation, but with much lower time consumption. Hence, the proposed DV-DTCF is especially suitable for applications that have strict limitations on computational costs.

Non-Linear Reconstruction of Delta-Sigma Modulated Signals: Randomized Surrogate Constraint Decoding Algorithm

Delta-sigma (ΔΣ) A/D conversion is a popular technique used to achieve high resolution data conversion for low to moderate bandwidth applications. It is commonly accepted that the digital circuitry of the ΔΣ A/D converters should perform a linear time-invariant (LTI) filtering on the output of the ΔΣ modulator in order to reconstruct the input signal. However, it has been shown that, when higher order ΔΣ A/D converters are operated at higher oversampling ratios (OSRs), non-linear reconstruction algorithms extract more information about the input signal than LTI methods. Still, use of non-linear algorithms has been limited due to their complexity and stability issues. Two practical non-linear methods presented in the literature are fast projection onto convex sets (POCS) and direct projection (DP). In this work, we show that the non-linear reconstruction process for ΔΣ modulated sequences can be treated as a linear feasibility problem (LFP). We then show that if the reconstruction process is defined as an LFP, its implementation is less complex than in the case of the DP method. We further describe how the LFP can be well-conditioned and demonstrate the reconstruction process by using the surrogate constraint algorithm with random constraint selection. The described algorithm considers a small number of constraints at a time, which makes it suitable for serial implementation.

Superiority of nonlinear mapping in decoding multiple single-unit neuronal spike trains: A simulation study

One of the most important building blocks of the brain–machine interface (BMI) based on neuronal spike trains is the decoding algorithm, a computational method for the reconstruction of desired information from spike trains. Previous studies have reported that a simple linear filter is effective for this purpose and that no noteworthy gain is achieved from the use of nonlinear algorithms. In order to test this premise, we designed several decoding algorithms based on the linear filter, and two nonlinear mapping algorithms using multilayer perceptron (MLP) and support vector machine regression (SVR). Their performances were assessed using multiple neuronal spike trains generated by a biophysical neuron model and by a directional tuning model of the primary motor cortex. The performances of the nonlinear algorithms, in general, were superior. The advantages of using nonlinear algorithms were more profound for cases where false-positive/negative errors occurred in spike trains. When the MLPs were trained using trial-and-error, they often showed disappointing performance comparable to that of the linear filter. The nonlinear SVR showed the highest performance, and this may be due to the superiority of SVR in training and generalization.