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A compressed sensing perspective of hippocampal function.

Petrantonakis PC, Poirazi P - Front Syst Neurosci (2014)

Bottom Line: Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex.In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes.This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology Lab, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas Heraklion, Greece.

ABSTRACT
Hippocampus is one of the most important information processing units in the brain. Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex. Here, we review evidence of the hypothesis that information flow and processing in the hippocampus complies with the principles of Compressed Sensing (CS). The CS theory comprises a mathematical framework that describes how and under which conditions, restricted sampling of information (data set) can lead to condensed, yet concise, forms of the initial, subsampled information entity (i.e., of the original data set). In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes. This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

No MeSH data available.


Related in: MedlinePlus

Restricted Isometry Property. Illustration of RIP for a K-sparse model of signals, where geometric information is preserved when mapped, via A, from the N-dimensional space to the M-dimensional one, M < N.
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Figure 3: Restricted Isometry Property. Illustration of RIP for a K-sparse model of signals, where geometric information is preserved when mapped, via A, from the N-dimensional space to the M-dimensional one, M < N.

Mentions: According to CS, the matrix A must obey the Restricted Isometry Property (RIP) (Candes and Tao, 2005) as a fundamental condition for efficient encoding and reconstruction/decoding. Specifically, for a predefined integer, K, there must be an isometry constant, δK, of a matrix A such that:(1)(1−δK) ‖x‖L22 ≤ ‖Ax‖L22 ≤ (1 + δK) ‖x‖L22holds for all K-sparse vectors x, i.e., for all vectors x that have exactly K nonzero elements. The L2 norm is the magnitude of a vector. Loosely, a matrix A obeys the RIP of order K if δK is sufficiently smaller than one (Candes and Wakin, 2008). Intuitively, RIP entails that all pairs of vectors, xi, xj, which are K-sparse in Ψ, preserve their between distance even after the projection to the M-dimensional space through matrix A. This preserves the geometric properties of the vectors in the projected/measurement space and ensures an efficient decoding. A representative example of RIP is graphically illustrated in Figure 3.


A compressed sensing perspective of hippocampal function.

Petrantonakis PC, Poirazi P - Front Syst Neurosci (2014)

Restricted Isometry Property. Illustration of RIP for a K-sparse model of signals, where geometric information is preserved when mapped, via A, from the N-dimensional space to the M-dimensional one, M < N.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126371&req=5

Figure 3: Restricted Isometry Property. Illustration of RIP for a K-sparse model of signals, where geometric information is preserved when mapped, via A, from the N-dimensional space to the M-dimensional one, M < N.
Mentions: According to CS, the matrix A must obey the Restricted Isometry Property (RIP) (Candes and Tao, 2005) as a fundamental condition for efficient encoding and reconstruction/decoding. Specifically, for a predefined integer, K, there must be an isometry constant, δK, of a matrix A such that:(1)(1−δK) ‖x‖L22 ≤ ‖Ax‖L22 ≤ (1 + δK) ‖x‖L22holds for all K-sparse vectors x, i.e., for all vectors x that have exactly K nonzero elements. The L2 norm is the magnitude of a vector. Loosely, a matrix A obeys the RIP of order K if δK is sufficiently smaller than one (Candes and Wakin, 2008). Intuitively, RIP entails that all pairs of vectors, xi, xj, which are K-sparse in Ψ, preserve their between distance even after the projection to the M-dimensional space through matrix A. This preserves the geometric properties of the vectors in the projected/measurement space and ensures an efficient decoding. A representative example of RIP is graphically illustrated in Figure 3.

Bottom Line: Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex.In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes.This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

View Article: PubMed Central - PubMed

Affiliation: Computational Biology Lab, Institute of Molecular Biology and Biotechnology, Foundation for Research and Technology-Hellas Heraklion, Greece.

ABSTRACT
Hippocampus is one of the most important information processing units in the brain. Input from the cortex passes through convergent axon pathways to the downstream hippocampal subregions and, after being appropriately processed, is fanned out back to the cortex. Here, we review evidence of the hypothesis that information flow and processing in the hippocampus complies with the principles of Compressed Sensing (CS). The CS theory comprises a mathematical framework that describes how and under which conditions, restricted sampling of information (data set) can lead to condensed, yet concise, forms of the initial, subsampled information entity (i.e., of the original data set). In this work, hippocampus related regions and their respective circuitry are presented as a CS-based system whose different components collaborate to realize efficient memory encoding and decoding processes. This proposition introduces a unifying mathematical framework for hippocampal function and opens new avenues for exploring coding and decoding strategies in the brain.

No MeSH data available.


Related in: MedlinePlus