scholarly journals On temporal codes and the spatiotemporal response of neurons in the lateral geniculate nucleus

1994 ◽  
Vol 72 (6) ◽  
pp. 2990-3003 ◽  
Author(s):  
D. Golomb ◽  
D. Kleinfeld ◽  
R. C. Reid ◽  
R. M. Shapley ◽  
B. I. Shraiman
Keyword(s):  
Singular Value Decomposition ◽  
Firing Rate ◽  
Impulse Response ◽  
Linear Response ◽  
Impulse Response Function ◽  
Singular Value ◽  
Temporal Coding ◽  
Temporal Mode ◽  
Temporal Modes ◽  
Value Decomposition

1. The present work relates recent experimental studies of the temporal coding of visual stimuli (McClurkin, Optican, Richmond, and Gawne, Science 253: 675, 1991) to the measurements of the spatiotemporal receptive fields of neurons within the lateral geniculate of primate. 2. We analyze both new and previously described magnocellular and parvocellular single units. The spatiotemporal impulse response function of the unit, defined as the time-resolved average firing rate in response to a weak stimulus flashed at a given location and time, is characterized by the singular value decomposition. This analysis allows one to represent the impulse response by a small number, two to three, of spatial and temporal modes. Both magnocellular and parvocellular units are weakly nonseparable, with major and minor modes that account, respectively, for approximately 78 and 22% of the response. The major temporal mode for both types is essentially identical for the first 100 ms. At later times the response of magnocellular units changes sign and decays slowly, whereas the response of parvocellular units decays relatively rapidly. 3. The spatiotemporal impulse response function completely determines the response of a unit to an arbitrary stimulus when linear response theory is valid. Using the measured impulse response, combined with a rectifying neuronal input-output relation, we calculate the responses to a complete set of spatial luminance patterns constructed of "Walsh" functions. Our predicted temporal responses are in qualitative agreement with those reported for parvocellular units (McClurkin, Optican, Richmond, and Gawne, J. Neurophysiol. 66: 794, 1991). Under the additional assumptions of Poisson statistics for the probability of spiking and a plausible background firing rate, we predict the performance of a unit in the Walsh pattern discrimination task as quantified by mutual information. Our prediction is again consistent with the reported results. 4. Last, we consider the issue of temporal coding within linear response. For stimuli presented for fixed time intervals, the singular value decomposition provides a natural relation between the temporal modes of the neuronal response and the spatial pattern of the stimulus. Although it is tempting to interpret each temporal mode as an independent channel that encodes orthogonal features of the stimulus, successively higher order modes are increasingly unreliable and do not significantly increase the discrimination capabilities of the unit.

Multicomponent wave separation using HOSVD/unimodal-ICA subspace method

Geophysics ◽  
2006 ◽  
Vol 71 (5) ◽  
pp. V133-V143 ◽  
Author(s):  
Valeriu D. Vrabie ◽  
Nicolas Le Bihan ◽  
Jérôme I. Mars
Keyword(s):  
Singular Value Decomposition ◽  
Singular Value ◽  
Geophysical Data ◽  
Subspace Method ◽  
Orthogonality Constraints ◽  
Wave Separation ◽  
Polarized Waves ◽  
Temporal Mode ◽  
Value Decomposition ◽  
Mean Square Errors

Multicomponent sensor arrays now are commonly used in seismic acquisition to record polarized waves. In this article, we use a three-mode model (polarization mode, distance mode, and temporal mode) to take into account the specific structure of signals that are recorded with these arrays, providing a data-structure-preserving processing. With the suggested model, we propose a multilinear decomposition named higher-order singular value decomposition and unimodal independent component analysis (HOSVD/unimodal ICA) to split the recorded three-mode data into two orthogonal subspaces: the signal and noise subspaces. This decomposition allows the separation and identification of polarized waves with infinite apparent horizontal propagation velocity. The HOSVD leads to a definition of a subspace method that is the counterpart of the well-known subspace method for matrices that is driven by singular value decomposition (SVD), a classic tool in monocomponent array processing. The proposed three-mode subspace decomposition provides a multicomponent wave-separation algorithm. To enhance the separation result, when the signal-to-noise ratio is low or when orthogonality constraints are not well adapted to the recorded waves, a unimodal-ICA step is included on the temporal mode. Doing this replaces the classic orthogonality constraints between estimated waves with independence constraints that might allow better recovery of recorded seismic waves. A simulation on realistic two-component (2C) geophysical data shows qualitative and quantitative improvements for the wavefield-separation results. The relative-mean-square errors between the original and estimated signal subspaces are, respectively, 52% for SVD applied on each component separately, 27.4% for HOSVD-based technique applied to the whole three-mode dataset, and 7.3% for HOSVD/unimodal-ICA technique. The efficiency of the three-mode subspace decompositions also is shown on real three-component (3C) geophysical data. These results emphasize the potential of the HOSVD/unimodal-ICA subspace method for multicomponent seismic-wave separation.

scholarly journals Time Coding OTDM MIMO System Based on Singular Value Decomposition for 5G Applications

2019 ◽  
Vol 9 (13) ◽  
pp. 2691 ◽  
Author(s):  
Rana M. Aly ◽  
Amira Zaki ◽  
Waleed K. Badawi ◽  
Moustafa H. Aly
Keyword(s):  
Singular Value Decomposition ◽  
Impulse Response ◽  
Space Time ◽  
Data Rate ◽  
Singular Value ◽  
Basis Functions ◽  
Channel Impulse Response ◽  
Modulation Techniques ◽  
Time Coding ◽  
Value Decomposition

For 5G and beyond cellular communication systems, new coding and modulation techniques are suggested to reach the requirements of high data rate and quality of service. In this paper, a new space-time coded orthogonal transform division multiplexing (STC OTDM) technique is proposed for 5G applications. The proposed system is used to enhance the data rate and performance of the orthogonal transform division multiplexing (OTDM) technique. The proposed system is based on using space-time coding (STC) with OTDM to increase the system diversity and consequently the system performance. The OTDM technique is based on transmitting data on orthogonal basis functions obtained from the Singular Value Decomposition (SVD) of the channel impulse response of the desired user. Various modulation techniques like QPSK, 64-QAM, and 256-QAM are investigated using different subcarriers and channel models. The simulation results show that the proposed system achieved a better performance when compared to classical and recent multicarrier techniques. The proposed technique increases the diversity gain resulting in a decrease in the fading effect of the multipath channel and an enhancement in the bit error rate (BER) performance. The proposed technique also provides a secure data transmission to the desired user as his data is sent on the basis functions extracted from his own channel impulse response that cannot be decoded by other users.

Implementation of 2D explicit depth extrapolation FIR digital filters for 3D seismic volumes using singular value decomposition

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. V1-V12 ◽  
Author(s):  
Wail A. Mousa ◽  
Said Boussakta ◽  
Desmond C. McLernon ◽  
Mirko Van der Baan
Keyword(s):  
Singular Value Decomposition ◽  
Impulse Response ◽  
Digital Filters ◽  
Finite Impulse Response ◽  
Fir Filter ◽  
Singular Value ◽  
3D Seismic ◽  
Fir Digital Filters ◽  
Value Decomposition ◽  
Seismic Volumes

We propose a new scheme for implementing predesigned 2D complex-valued wavefield extrapolation finite impulse response (FIR) digital filters, which are used for extrapolating 3D seismic wavefields. The implementation is based on singular value decomposition (SVD) of quadrantally symmetric 2D FIR filters (extrapolators). To simplify the SVD computations for such a filter impulse response structure, we apply a special matrix transformation on the extrapolation FIR filter impulse responses where we guarantee the retention of their wavenumber phase response. Unlike the existing 2D FIR filter implementation methods that are used for this geophysical application such as the McClellan transformation or its improved version, this implementation via SVD results in perfect circularly symmetrical magnitude and phase wavenumber responses. In this paper, we also demonstrate that the SVD method can save (depending on the filter size) more than 23% of the number of multiplications per output sample and approximately 62% of the number of additions per output sample when compared to direct implementation with quadrantal symmetry via true 2D convolution. Finally, an application to extrapolation of a seismic impulse is shown to prove our theoretical conclusions.

Sign in / Sign up

Export Citation Format

Share Document