Most studies of adaptive algorithm behavior consider performance measures based on mean values such as the mean value of the squared error. Behavior models based on average measures models are useful for understanding the algorithm behavior under different environments and can be used for design. Nevertheless, from a practical point of view, the adaptive filter user has only one realization of the algorithm to obtain the desired result. This article derives a model for the variance of the squared-error sample curve of the least-mean-square (LMS) adaptive algorithm, so that the achievable cancellation level can be predicted based on the properties of the steady-state squared error. The derived results provide the user with useful design guidelines.

In hyperspectral sparse unmixing, a successful approach employs spectral bundles to address the variability of the endmembers in the spatial domain. However, the regularization penalties usually employed aggregate substantial computational complexity, and the solutions are very noise-sensitive. We generalize a multiscale spatial regularization approach to solve the unmixing problem by incorporating group sparsity-inducing mixed norms. Then, we propose a noise-robust method that can take advantage of the bundle structure to deal with endmember variability while ensuring inter- and intra-class sparsity in abundance estimation with reasonable computational cost. We also present a general heuristic to select themost representativeabundance estimation over multiple runs of the unmixing process, yielding a solution that is robust and highly reproducible. Experiments illustrate the robustness and consistency of the results when compared to related methods.

This paper proposes ReAdapt–a reconfigurable datapath architecture for scaling the energy-quality trade-off of adaptive filtering at runtime. The ReAdapt can dynamically select four adaptive filtering algorithms for gradating complexity levels during runtime by reconfiguring the processing flow in its datapath and by blocking the switching activity (e.g., reducing the CMOS dynamic power) of unused modules with data-gating. The ReAdapt proposal can scale the energy-quality trade-off by choosing the following four different levels of filter algorithms complexity: 1) least mean square (LMS); 2) partial update normalized LMS (PU-NLMS); 3) set-membership normalized LMS (SM-NLMS); 4) normalized LMS (NLMS). The ReAdapt architecture reuses common modules of each adaptive filter, resulting in a compact VLSI hardware implementation. The ReAdapt architecture operation is implemented in a case-study for interference mitigation for electroencephalogram (EEG) signal processing. The hardware synthesis results show an increase of 6.80 times in throughput and at least a reduction of 2.84 times in energy per operation compared with the state-of-the-art adaptive filters. This paper also investigates the benefits of dynamically reconfiguring the four ReAdapt operating modes at runtime for different levels of signal-to-noise ratio (SNR) for the processed signals. We also demonstrate that dynamically reconfiguring the ReAdapt operating modes during runtime results in an optimal energy-quality trade-off which is advantageous over the conventional single static mode.

Several approaches have been proposed to solve the spectral unmixing problem in hyperspectral image analysis. Among them the use of sparse regression techniques aims to characterize the abundances in pixels based on a large library of spectral signatures known a priori. Recently, the integration of image spatial-contextual information significantly enhanced the performance of sparse unmixing. In this work, we propose a computationally efficient multiscale representation method for hyperspectral data adapted to the unmixing problem. The proposed method is based on a hierarchical extension of the SLIC oversegmentation algorithm constructed using a robust homogeneity testing. The image is subdivided into a set of spectrally homogeneous regions formed by pixels with similar characteristics (superpixels). This representation is then used to provide prior spatial regularity information for the abundances of materials present in the scene, improving the conditioning of the unmixing problem. Simulation results illustrate that the method is capable of estimating abundances with high quality and low computational cost, especially in noisy scenarios.

The approximate computing paradigm emerged as a key alternative for trading off accuracy and energy efficiency. Error-tolerant applications, such as multimedia and signal processing, can process the information with lower-than-standard accuracy at the circuit level while still fulfilling a good and acceptable service quality at the application level. The automatic detection of R-peaks in an electrocardiogram (ECG) signal is the essential step preceding ECG processing and analysis. The Haar discrete wavelet transform (HDWT) is a low-complexity pre-processing filter suitable to detect ECG R-peaks in embedded systems like wearable devices, which are incredibly energy-constrained. This work presents an approximate HDWT hardware architecture for ECG processing at very high energy efficiency. Our best-proposal employing pruning within the approximate HDWT hardware architecture requires just seven additions. The use of a truncation technique to improve energy efficiency is also investigated herein by observing the evolution of the signal-to-noise ratio and the ultimate impact in the ECG peak-detection application. This research finds that our HDWT approximate hardware architecture proposal accepts higher truncation levels than the original HDWT. In summary: Our results show about 9 times energy reduction when combining our HDWT matrix approximation proposal with the pruning and the highest acceptable level of truncation while still maintaining the R-peak detection performance accuracy of 99.68% on average.

Efficient Kalman filter (KF) designs for real-time mobile applications, such as nano-drones navigation, robots localization, spacecraft orbit control, GPS positioning, image recognition, and multisensor data fusion for wearable systems, are key technology goals. The KF is a compute-intensive kernel composed of consecutive complex matrix operations, like multiplications and matrix inversions. The most complex block in the KF is the Kalman gain (KG) function, which involves matrices inversion at each iteration, applying the determinant matrix calculation and division operations. In this article, we combine architectural solutions of different types, for which balancing conflicting low-power and high-performance requirements aiming at real-time KF processing is a key design issue. The key finding in our architectural exploration herein presented is that the KF architectures in semiparallel and sequential forms offer the best balance of circuit area size, power dissipation, and processing speed. Compared to the state-of-the-art solutions, our KF architecture is more efficient, with 2.8 times fewer arithmetic operators, requiring 3.3 times fewer clock cycles. The usefulness of the developed KF in digital signal processing (DSP) is shown herein by simulations of system identification, noise elimination, and state estimation applications. These figures highlight the results of the KF architecture: the speed of adaptation for the system identification applications with root mean square error (RMSE) of 0.01 after 12 samples, precision level in noise elimination applications with RMSE of 0.13, and reliability in state estimation processes with RMSE less than 10% of system peak response.

This paper proposes a new kernel Kalman filter formulation for system identification and time series estimation in nonlinear time-varying environments. The unknown nonlinear time-varying function is approximated by a finite-order linear model in a reproducing kernel Hilbert space. The model coefficients define the state of the Kalman filter. Simulation results illustrate the improvement in estimation performance provided by the new algorithm when compared to the classical kernel LMS filter.

The paper presents an analytical model for predicting the stochastic behavior of the affine projection (AP) algorithm operating in a nonstationary environment. The model is derived for autoregressive (AR) Gaussian inputs and for unity step size (fastest convergence). Deterministic recursive equations are presented for the mean weight and mean square error for a large number of adaptive taps, N, as compared to the algorithm order, P. The model predictions show excellent agreement with Monte Carlo simulations in transient and steady-state. The learning behavior of the AP algorithm in nonstationary environments is of great interest in applications such as acoustic echo cancellation.

The paper presents an analytical model for predicting the stochastic behavior of the affine projection (AP) algorithm. The model is derived for autoregressive (AR) Gaussian inputs and for unity step size (fastest convergence). Deterministic recursive equations are presented for the mean weight and mean square error for a large number of adaptive taps, N, as compared to the algorithm order, P. The model predictions show better agreement between theory and simulations in transient and steady-state than previous models described in the literature. The learning behavior of the AP algorithm is of great interest in applications such as acoustic echo cancellation.