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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

The Compressed Sensing framework. (A) The essence of the CS framework can be conceived if we consider the example of the wire-frame object (Ganguli and Sompolinsky, 2012). The three-dimensional object (e.g., a wire-frame cube or a wire frame sphere) is projected onto a two dimensional screen when a light beam is applied on it. The wired frame represents the f signal, the light beams the sampling process (Φ) whereas different shadows correspond to different samples of the signal (vector y). CS shows that it is possible to reconstruct the initial wire frame (e.g., the cube or the sphere) from a set of different shadows, as long as the wire frame is sparse enough and the sampling is random. For instance, consider a non-random lighting where the light beams are aligned with a specific wire of the object. The shadows would be biased to that wire and, as a result, not representative of the higher dimensional structure of the object. Moreover, in the case where the wire-frame object has dense wiring (i.e., not sparse), all shadows would be almost the same no matter what the lighting angle was. The basis Ψ (blue box) includes items that can be used to reconstruct signal f (the wired-object) as dictated by vector x, which is produced by the L1 minimization algorithm subject to measurements y (shadows). (B) CS encoding and decoding schemes. The encoding of the signal is a simple, linear sampling/measurement process derived as y = Ax, where A is analyzed as A = Φ Ψ. Thus, the decoding process is performed by knowing A and vector y′, which is a noisy version of y. CS theory provides mathematical proofs that, knowing y′ and A, it is possible to retrieve x or x′ ≈ x by a L1 minimization procedure.
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Figure 1: The Compressed Sensing framework. (A) The essence of the CS framework can be conceived if we consider the example of the wire-frame object (Ganguli and Sompolinsky, 2012). The three-dimensional object (e.g., a wire-frame cube or a wire frame sphere) is projected onto a two dimensional screen when a light beam is applied on it. The wired frame represents the f signal, the light beams the sampling process (Φ) whereas different shadows correspond to different samples of the signal (vector y). CS shows that it is possible to reconstruct the initial wire frame (e.g., the cube or the sphere) from a set of different shadows, as long as the wire frame is sparse enough and the sampling is random. For instance, consider a non-random lighting where the light beams are aligned with a specific wire of the object. The shadows would be biased to that wire and, as a result, not representative of the higher dimensional structure of the object. Moreover, in the case where the wire-frame object has dense wiring (i.e., not sparse), all shadows would be almost the same no matter what the lighting angle was. The basis Ψ (blue box) includes items that can be used to reconstruct signal f (the wired-object) as dictated by vector x, which is produced by the L1 minimization algorithm subject to measurements y (shadows). (B) CS encoding and decoding schemes. The encoding of the signal is a simple, linear sampling/measurement process derived as y = Ax, where A is analyzed as A = Φ Ψ. Thus, the decoding process is performed by knowing A and vector y′, which is a noisy version of y. CS theory provides mathematical proofs that, knowing y′ and A, it is possible to retrieve x or x′ ≈ x by a L1 minimization procedure.

Mentions: The CS theory originates from the field of high-dimensional statistics. Recent advances in this field have led to a powerful, yet extremely simple methodology for dealing with the curse of dimensionality, termed Random Projections (RP). This entails a random projection of data patterns from high dimensional spaces to lower ones (Baraniuk, 2011), which reduces the dimensionality while retaining the valuable content of the original data, allowing for efficient processing in the lower dimensional space. What the CS theory adds to this framework is that, once the data with high dimensionality are represented by sparse components of a suitable basis set, it is possible to reconstruct them by their RPs! Thus, low dimensional RPs are not only suitable for interpreting the original, high dimensional data patterns but also comprise an efficient encoding that can be used as a compressed representation of the original data; high dimensional patterns can then be recovered by appropriate decoding processes. Figure 1A depicts 3D objects and their 2D shadows which can be parallelized with the high dimensional data and lower dimensional RPs, respectively. CS theory implies that it is possible to infer the form of the 3D structure using only a limited set of 2D shadows (random projections) of the wired frames.


A compressed sensing perspective of hippocampal function.

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

The Compressed Sensing framework. (A) The essence of the CS framework can be conceived if we consider the example of the wire-frame object (Ganguli and Sompolinsky, 2012). The three-dimensional object (e.g., a wire-frame cube or a wire frame sphere) is projected onto a two dimensional screen when a light beam is applied on it. The wired frame represents the f signal, the light beams the sampling process (Φ) whereas different shadows correspond to different samples of the signal (vector y). CS shows that it is possible to reconstruct the initial wire frame (e.g., the cube or the sphere) from a set of different shadows, as long as the wire frame is sparse enough and the sampling is random. For instance, consider a non-random lighting where the light beams are aligned with a specific wire of the object. The shadows would be biased to that wire and, as a result, not representative of the higher dimensional structure of the object. Moreover, in the case where the wire-frame object has dense wiring (i.e., not sparse), all shadows would be almost the same no matter what the lighting angle was. The basis Ψ (blue box) includes items that can be used to reconstruct signal f (the wired-object) as dictated by vector x, which is produced by the L1 minimization algorithm subject to measurements y (shadows). (B) CS encoding and decoding schemes. The encoding of the signal is a simple, linear sampling/measurement process derived as y = Ax, where A is analyzed as A = Φ Ψ. Thus, the decoding process is performed by knowing A and vector y′, which is a noisy version of y. CS theory provides mathematical proofs that, knowing y′ and A, it is possible to retrieve x or x′ ≈ x by a L1 minimization procedure.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 1: The Compressed Sensing framework. (A) The essence of the CS framework can be conceived if we consider the example of the wire-frame object (Ganguli and Sompolinsky, 2012). The three-dimensional object (e.g., a wire-frame cube or a wire frame sphere) is projected onto a two dimensional screen when a light beam is applied on it. The wired frame represents the f signal, the light beams the sampling process (Φ) whereas different shadows correspond to different samples of the signal (vector y). CS shows that it is possible to reconstruct the initial wire frame (e.g., the cube or the sphere) from a set of different shadows, as long as the wire frame is sparse enough and the sampling is random. For instance, consider a non-random lighting where the light beams are aligned with a specific wire of the object. The shadows would be biased to that wire and, as a result, not representative of the higher dimensional structure of the object. Moreover, in the case where the wire-frame object has dense wiring (i.e., not sparse), all shadows would be almost the same no matter what the lighting angle was. The basis Ψ (blue box) includes items that can be used to reconstruct signal f (the wired-object) as dictated by vector x, which is produced by the L1 minimization algorithm subject to measurements y (shadows). (B) CS encoding and decoding schemes. The encoding of the signal is a simple, linear sampling/measurement process derived as y = Ax, where A is analyzed as A = Φ Ψ. Thus, the decoding process is performed by knowing A and vector y′, which is a noisy version of y. CS theory provides mathematical proofs that, knowing y′ and A, it is possible to retrieve x or x′ ≈ x by a L1 minimization procedure.
Mentions: The CS theory originates from the field of high-dimensional statistics. Recent advances in this field have led to a powerful, yet extremely simple methodology for dealing with the curse of dimensionality, termed Random Projections (RP). This entails a random projection of data patterns from high dimensional spaces to lower ones (Baraniuk, 2011), which reduces the dimensionality while retaining the valuable content of the original data, allowing for efficient processing in the lower dimensional space. What the CS theory adds to this framework is that, once the data with high dimensionality are represented by sparse components of a suitable basis set, it is possible to reconstruct them by their RPs! Thus, low dimensional RPs are not only suitable for interpreting the original, high dimensional data patterns but also comprise an efficient encoding that can be used as a compressed representation of the original data; high dimensional patterns can then be recovered by appropriate decoding processes. Figure 1A depicts 3D objects and their 2D shadows which can be parallelized with the high dimensional data and lower dimensional RPs, respectively. CS theory implies that it is possible to infer the form of the 3D structure using only a limited set of 2D shadows (random projections) of the wired frames.

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