On robust detection of brain stimuli with Ramanujan Periodicity Transforms

Saidi, Pouria; Atia, George K.; Vosoughi, Azadeh

doi:10.1109/acssc.2017.8335440

Cited by 8 publications

(4 citation statements)

References 11 publications

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“…denotes the Q-function, which is the tail of the standard Normal distribution. Figure 3(b) illustrates the ROC curves, where P D and P F corresponding to the exact pdfs are obtained using numerical integration of the exact pdfs in (17), and P D and P F corresponding to the approximate Gaussian pdfs in (21) are found using (22). Clearly, the ROC curves are in close agreement.…”

Section: Theorem 2 (Distribution Of Test Statistic For Orthogonal Cas...mentioning

confidence: 74%

“…However, only few works have investigated their application with biomedical signals, such as in the analysis of T-wave alternans [19] and the detection of tandem repeats in DNA [20]. We leveraged an RPT-based model to detect SSVEPs for the first time in [21][22][23] providing preliminary results for the current work, and demonstrated its ability to capture the underlying periodicity in SSVEPs and its robustness to latencies naturally present in the brain's response to external stimuli.…”

Section: Introductionmentioning

confidence: 95%

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Detection of brain stimuli using Ramanujan periodicity transforms

Saidi

Vosoughi²,

Atia³

2019

J. Neural Eng.

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Objective: The ability to efficiently match the frequency of the brain's response to repetitive visual stimuli in real time is the basis for reliable SSVEP-based Brain-Computer-Interfacing (BCI). Approach: The detection of different stimuli is posed as a composite hypothesis test, where SSVEPs are assumed to admit a sparse representation in a Ramanujan Periodicity Transform (RPT) dictionary. For the binary case, we develop and analyze the performance of an RPT detector based on a derived generalized likelihood ratio test. Our approach is extended to multi-hypothesis multi-electrode settings, where we capture the spatial correlation between the electrodes using prestimulus data. We also introduce a new metric for evaluating SSVEP detection schemes based on their achievable efficiency and discrimination rate tradeoff for given system resources. Results:We obtain exact distributions of the test statistic in terms of confluent hypergeometric functions. Results based on extensive simulations with both synthesized and real data indicate that the RPT detector substantially outperforms spectral-based methods. Its performance also surpasses the state-of-the-art Canonical Correlation Analysis (CCA) methods with respect to accuracy and sample complexity in short data lengths regimes crucial for real-time applications. The proposed approach is asymptotically optimal as it closes the gap to a perfect measurement bound as the data length increases. In contrast to existing supervised methods which are highly data-dependent, the RPT detector only uses pre-stimulus data to estimate the per-subject spatial correlation, thereby dispensing with considerable overhead associated with data collection for a large number of subjects and stimuli. Significance: Our work advances the theory and practice of emerging real-time BCI and affords a new framework for comparing SSVEP detection schemes across a wider spectrum of operating regimes.Index Terms-Ramanujan periodicity transform, Nested periodic matrices, Steady-state visual evoked potentials, Brain computer interface, error exponent-discrimination rate tradeoff.

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Section: Theorem 2 (Distribution Of Test Statistic For Orthogonal Cas...mentioning

confidence: 74%

Section: Introductionmentioning

confidence: 95%

Detection of brain stimuli using Ramanujan periodicity transforms

Saidi

Vosoughi²,

Atia³

2019

J. Neural Eng.

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“…Ramanujan filter banks have also been shown to be applicable in the identification of epileptic seizures in patients, which are characterized by sudden appearance of periodic waveforms in the measured EEG records [38]. Other interesting applications have recently been reported by a number of authors such as, for example in source-separation [39], RF communications [40], ECG signal processing [41] and brain-computer interfacing [42,43]. For details, the reader is requested to consult the above papers and references therein.…”

Section: Discussionmentioning

confidence: 99%

Srinivasa Ramanujan and signal-processing problems

Vaidyanathan

Tenneti

2019

Phil. Trans. R. Soc. A.

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The Ramanujan sum c q ( n ) has been used by mathematicians to derive many important infinite series expansions for arithmetic-functions in number theory. Interestingly, this sum has many properties which are attractive from the point of view of digital signal processing. One of these is that c q ( n ) is periodic with period q , and another is that it is always integer-valued in spite of the presence of complex roots of unity in the definition. Engineers and physicists have in the past used the Ramanujan-sum to extract periodicity information from signals. In recent years, this idea has been developed further by introducing the concept of Ramanujan-subspaces. Based on this, Ramanujan dictionaries and filter banks have been developed, which are very useful to identify integer-valued periods in possibly complex-valued signals. This paper gives an overview of these developments from the view point of signal processing. This article is part of a discussion meeting issue ‘Srinivasa Ramanujan: in celebration of the centenary of his election as FRS’.

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“…The infinite sum in (7) converges to RHS only when |z| ą 1, whereas no such assumption is required in the derivation (6). Now from (6), we can see that either of the two factors in (6) can contribute to zeros of p C q pzq.…”

Section: Locations Of Zeros Of C Q Pzqmentioning

confidence: 98%

On the Zeros of Ramanujan Filters

Kulkarni

Vaidyanathan

2020

IEEE Signal Process. Lett.

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Ramanujan filter banks have been used for identifying periodicity structure in streaming data. This paper studies the locations of zeros of Ramanujan filters. All the zeros of Ramanujan filters are shown to lie on or inside the unit circle in the z-plane. A convenient factorization appears as a corollary of this result, which is useful to identify common factors between different Ramanujan filters in a filter bank. For certain families of Ramanujan filters, further structure is identified in the locations of zeros of those filters. It is shown that increasing the number of periods of Ramanujan sums in the filter definition only increases zeros on the unit circle in z-plane. A potential application of these results is that by identifying common factors between Ramanujan filters, one can obtain efficient implementations of Ramanujan filter banks (RFB) as demonstrated here.

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On robust detection of brain stimuli with Ramanujan Periodicity Transforms

Cited by 8 publications

References 11 publications

Detection of brain stimuli using Ramanujan periodicity transforms

Detection of brain stimuli using Ramanujan periodicity transforms

Srinivasa Ramanujan and signal-processing problems

On the Zeros of Ramanujan Filters

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