Mixed matrix factorization: a novel algorithm for the extraction of kinematic-muscular synergies

Synergistic models have been employed to investigate motor coordination separately in the muscular and kinematic domains. However, the relationship between muscle synergies, constrained to be non-negative, and kinematic synergies, whose elements can be positive and negative, has received limited attention. Existing algorithms for extracting synergies from combined kinematic and muscular data either do not enforce non-negativity constraints or separate non-negative variables into positive and negative components. We propose a mixed matrix factorization (MMF) algorithm based on a gradient descent update rule which overcomes these limitations. It allows to directly assess the relationship between kinematic and muscle activity variables, by enforcing the non-negativity constrain on a subset of variables. We validated the algorithm on simulated kinematic-muscular data generated from known spatial synergies and temporal coefficients, by evaluating the similarity between extracted and ground truth synergies and temporal coefficients when the data are corrupted by different noise levels. We also compared the performance of MMF to that of non-negative matrix factorization applied to separate positive and negative components (NMFpn). Finally, we factorized kinematic and EMG data collected during upper-limb movements to demonstrate the potential of the algorithm. MMF achieved almost perfect reconstruction on noiseless simulated data. It performed better than NMFpn in recovering the correct spatial synergies and temporal coefficients with noisy simulated data. It also allowed to correctly select the original number of ground truth synergies. We showed meaningful applicability to real data; MMF can also be applied to any multivariate data that contains both non-negative and unconstrained variables.

Matrix methods for perfect signal recovery underlying range space of operators

The purpose of this work is to investigate perfect reconstruction underlying range space of operators in finite dimensional Hilbert spaces by a new matrix method. To this end, first we obtain more structures of the canonical $K$-dual. % and survey optimal $K$-dual problem under probabilistic erasures. Then, we survey the problem of recovering and robustness of signals when the erasure set satisfies the minimal redundancy condition or the $K$-frame is maximal robust. Furthermore, we show that the error rate is reduced under erasures if the $K$-frame is of uniform excess. Toward the protection of encoding frame (K-dual) against erasures, we introduce a new concept so called $(r,k)$-matrix to recover lost data and solve the perfect recovery problem via matrix equations. Moreover, we discuss the existence of such matrices by using minimal redundancy condition on decoding frames for operators. We exhibit several examples that illustrate the advantage of using the new matrix method with respect to the previous approaches in existence construction. And finally, we provide the numerical results to confirm the main results in the case noise-free and test sensitivity of the method with respect to noise.

High-concentration time–frequency analysis for multi-component nonstationary signals based on combined multi-window Gabor transform

PurposeThis study aims to reveal the essential characteristics of nonstationary signals and explore the high-concentration representation in the joint time–frequency (TF) plane.Design/methodology/approachIn this paper, the authors consider the effective TF analysis for nonstationary signals consisting of multiple components.FindingsTo make it, the authors propose the combined multi-window Gabor transform (CMGT) under the scheme of multi-window Gabor transform by introducing the combination operator. The authors establish the completeness utilizing the discrete piecewise Zak transform and provide the perfect-reconstruction conditions with respect to combined TF coefficients. The high-concentration is achieved by optimization. The authors establish the optimization function with considerations of TF concentration and computational complexity. Based on Bergman formulation, the iteration process is further analyzed to obtain the optimal solution.Originality/valueWith numerical experiments, it is verified that the proposed CMGT performs better in TF analysis for multi-component nonstationary signals.

Mixed matrix factorization: a novel algorithm for the extraction of kinematic-muscular synergies

Synergistic models have been employed to investigate motor coordination separately in the muscular and kinematic domains. However, the relationship between muscle synergies, constrained to be non-negative, and kinematic synergies, whose elements can be positive and negative, has received limited attention. Existing algorithms for extracting synergies from combined kinematic and muscular data either do not enforce non-negativity constraints or separate non-negative variables into positive and negative components. We propose a mixed matrix factorization (MMF) algorithm based on a gradient descent update rule which overcomes these limitations. It directly assesses the relationship between kinematic and muscle activity variables, by enforcing the non-negativity constrain on a subset of variables. We validated the algorithm on simulated kinematic-muscular data generated from known spatial synergies and temporal coefficients, by assessing the similarity between extracted and ground truth synergies and temporal coefficients when the data are corrupted by different noise levels. We also compared the performance of MMF to that of non-negative matrix factorization applied to separate positive and negative components (NMFpn). Finally, we factorized kinematic and EMG data collected during upper-limb movements to demonstrate the potential of the algorithm. MMF achieved almost perfect reconstruction on noiseless simulated data. It performed better than NMFpn in recovering the correct spatial synergies and temporal coefficients with noisy simulated data. It allowed to correctly select the original number of ground truth synergies. We showed meaningful applicability to real data. MMF can also be applied to any multivariate data that contains both non-negative and unconstrained variables.

Multi-Rate Filter Banks

This chapter presents the theoretical description and the principle of the operation of analysis and synthesis filter banks. This is essential material for understanding the modern design of transceivers that are based on discrete-time signal processing. The structure of a quadrature mirror filter bank is presented and the operation of the analysis and synthesis component filters is explained. The condition for a perfect reconstruction of a two-channel filter bank is derived. Based on a two-channel quadrature mirror filter bank, the procedure of making a multichannel quadrature mirror filter bank is presented. A brief description of multilevel filter banks with equal or unequal passband widths is given.

Frame multiresolution analysis of continuous piecewise linear functions

The Franklin wavelet is constructed using the multiresolution analysis (MRA) generated from a scaling function [Formula: see text] that is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text] for every [Formula: see text]. For [Formula: see text] and [Formula: see text], it is shown that if a function [Formula: see text] is continuous on [Formula: see text], linear on [Formula: see text] and [Formula: see text], for [Formula: see text], and generates MRA with dilation factor [Formula: see text], then [Formula: see text]. Conversely, for [Formula: see text], it is shown that there exists a [Formula: see text], as satisfying the above conditions, that generates MRA with dilation factor [Formula: see text]. The frame MRA (FMRA) is useful in signal processing, since the perfect reconstruction filter banks associated with FMRA can be narrow-band. So it is natural to ask, whether the above results can be extended for the case of FMRA. In this paper, for [Formula: see text], we prove that if [Formula: see text] generates FMRA with dilation factor [Formula: see text], then [Formula: see text]. For [Formula: see text], we prove similar results when [Formula: see text]. In addition, for [Formula: see text] we prove that there exists a function [Formula: see text] as satisfying the above conditions, that generates FMRA. Also, we construct tight wavelet frame and wavelet frame for such scaling functions.

A proposal of a 3D segmentation tool for HBIM management

There are several studies related to the cultural heritage digitization through HBIM (Heritage Building Information Modelling) techniques. Today, BIM (Building Information Modelling) software cannot represent old buildings with complex prominent and particularly detailed architecture perfectly, and multiple software are combined to obtain the buildings’ representation. In this paper, in order to find an alternative way of replicating the complex details present in antique buildings, a new methodology is presented. The methodology is based on a process of direct insertion of various 3D model parts (.obj), into a BIM environment. These 3D model elements, coming from the points cloud segmentation (from UAV and Laser Scanner), are transformed in intelligent objects and interconnected to form the smart model. The methodology allows to represent detail of the objects that make up an element of cultural heritage, although not standardizable in shape. Although this methodology allows to ensure a perfect reconstruction and digital preservation and to represent the different “defects” that represent and make unique a particular object of cultural heritage, it is not however fast compared with the traditional phases of point cloud tracing and more software are necessary for data processing. The proposed methodology was tested on two specific structures’ reconstruction in Reggio Calabria (South Italy): the Sant’Antonio Abate church and the Vitrioli’s portal.

Uncertainty of hourly-average concentration values derived from non-continuous measurements

Continental greenhouse gas monitoring networks extensively use tall towers for higher spatial representativeness. In most cases, several intakes are built along the tower to give information also on the vertical concentration profile of the components considered. Typically, a single gas analyzer is used, and the intake points are sequentially connected to the instrument. It involves that the continuous concentration signal is only sampled for discrete short periods at each intake point, which does not allow for a perfect reconstruction of the original concentration variation. It increases the uncertainty of the calculated hourly averages usually used by the atmospheric transport and budget models. The purpose of the study is to give the data users an impression of the potential magnitude of this kind of uncertainty, as well as how it depends on the number of intakes sampled, on the length of the sampling period at each intake, on the season, and on the time of the day. It presents how much improvement can be achieved using linear or spline interpolation between the measurement periods instead of the simple arithmetic averaging of the available measurements. Although the results presented here may be site-specific, the study calls attention to the potentially rather heterogeneous spatial and temporal distribution of the uncertainty of the hourly-average concentration values derived from tall-tower measurements applying sequential sampling.

Progressive Secret Sharing with Adaptive Priority and Perfect Reconstruction

A new technique for progressive visual secret sharing (PVSS) with adaptive priority weight is proposed in this paper. This approach employs the bitwise and eXclusive-OR (XOR) based approaches for generating a set of shared images from a single secret image. It effectively overcomes the former scheme limitation on dealing with an odd number of stacked or collected shared images in the recovery process. The presented technique works well when the number of stacked shared images is odd or even. As documented in experimental results, the proposed method offers good results over binary, grayscale, and color images with a perfectly reconstructed secret image. In addition, the performance of the proposed method is also supported with theoretical analysis showing its lossless ability to recover the secret image. However, it can be considered as a strong substitutive candidate for implementing a PVSS system.