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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

Matrix operations in Compressed Sensing. Figure illustrates the encoding equation of CS y = Ax and the corresponding dimensionality. It is actually a combination of the equationis f = Ψ x (sparse representation of signal f) and y = Φ f (sampling of signal f).
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Figure 2: Matrix operations in Compressed Sensing. Figure illustrates the encoding equation of CS y = Ax and the corresponding dimensionality. It is actually a combination of the equationis f = Ψ x (sparse representation of signal f) and y = Φ f (sampling of signal f).

Mentions: Furthermore, assume that the given signal can be represented by a basis set according to the equation f = Ψ x, where Ψ is a N × N matrix whose columns are the components of the basis set, and x is the N × 1 vector which contains the coefficients that analyze the signal f in basis Ψ. Note that x is sparse, i.e., it has K « N nonzero values. For instance, in the case of a gray scale natural image, Ψ could be a wavelet basis set. For the neural network example, the basis set can be represented by the activity of cells that exhibit certain properties, regarding, e.g., their receptive fields, such as mammalian visual cortex cells (Olshausen and Field, 1996), or their spatial firing patterns, such as grid cells (Hafting et al., 2005). Cells with such activity properties can form a basis set if their (appropriate) combination can generate any signal f (activity pattern of neurons) in the cortex. Figure 1A intuitively illustrates the meaning of each one of the above entities in accordance with the wire frame paradigm whereas Figure 2 graphically illustrates the mathematical formalization of the CS framework in a matrix-like operation. In the following section we elaborate more on the measurement/encoding (projection to a low dimensional space) and decoding (high dimensional space data reconstruction) phases according to the CS theory. Figure 1B graphically depicts the aforementioned processes.


A compressed sensing perspective of hippocampal function.

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

Matrix operations in Compressed Sensing. Figure illustrates the encoding equation of CS y = Ax and the corresponding dimensionality. It is actually a combination of the equationis f = Ψ x (sparse representation of signal f) and y = Φ f (sampling of signal f).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Matrix operations in Compressed Sensing. Figure illustrates the encoding equation of CS y = Ax and the corresponding dimensionality. It is actually a combination of the equationis f = Ψ x (sparse representation of signal f) and y = Φ f (sampling of signal f).
Mentions: Furthermore, assume that the given signal can be represented by a basis set according to the equation f = Ψ x, where Ψ is a N × N matrix whose columns are the components of the basis set, and x is the N × 1 vector which contains the coefficients that analyze the signal f in basis Ψ. Note that x is sparse, i.e., it has K « N nonzero values. For instance, in the case of a gray scale natural image, Ψ could be a wavelet basis set. For the neural network example, the basis set can be represented by the activity of cells that exhibit certain properties, regarding, e.g., their receptive fields, such as mammalian visual cortex cells (Olshausen and Field, 1996), or their spatial firing patterns, such as grid cells (Hafting et al., 2005). Cells with such activity properties can form a basis set if their (appropriate) combination can generate any signal f (activity pattern of neurons) in the cortex. Figure 1A intuitively illustrates the meaning of each one of the above entities in accordance with the wire frame paradigm whereas Figure 2 graphically illustrates the mathematical formalization of the CS framework in a matrix-like operation. In the following section we elaborate more on the measurement/encoding (projection to a low dimensional space) and decoding (high dimensional space data reconstruction) phases according to the CS theory. Figure 1B graphically depicts the aforementioned processes.

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