A novel single-trial event-related potential estimation method based on compressed sensing

National Basic Research Development Program (973 program) of China [2012CB825500, 2011CB707800]; National Natural Science Foundation of China [31271168]; Natural Science Foundation of Fujian Province, China [2011J01344]Cognitive functions are often studied using event-related potentials (ERPs) that are usually estimated by an averaging algorithm. Clearly, estimation of single-trial ERPs can provide researchers with many more details of cognitive activity than the averaging algorithm. A novel method to estimate single-trial ERPs is proposed in this paper. This method includes two key ideas. First, singular value decomposition was used to construct a matrix, which mapped single-trial electroencephalographic recordings (EEG) into a low-dimensional vector that contained little information from the spontaneous EEG. Second, we used the theory of compressed sensing to build a procedure to restore single-trial ERPs from this low-dimensional vector. ERPs are sparse or approximately sparse in the frequency domain. This fact allowed us to use the theory of compressed sensing. We verified this method in simulated and real data. Our method and dVCA (differentially variable component analysis), another method of single-trial ERPs estimation, were both used to estimate single-trial ERPs from the same simulated data. Results demonstrated that our method significantly outperforms dVCA under various conditions of signal-to-noise ratio. Moreover, the single-trial ERPs estimated from the real data by our method are statistically consistent with the theories of cognitive science

Behavioral scores of tremor, imbalance, bradykinesia and defensive reaction in the two groups before and after the administration of morphine or L-Dopa.

<p>Behavioral measurements were taken before and immediately after the administration of drug. (A) Behavioral scores after an acute dose of morphine. Tremor and loss of balance were significantly attenuated, while bradykinesia became much more prominent in group II monkeys. (B) Behavioral scores after the first dose of L-Dopa. Monkeys in group I displayed short-term amelioration of bradykinesia and defensive reaction on the first day of L-Dopa therapy. Tremor did not statistically change. (C) Behavioral scores after the last dose of L-Dopa. Monkeys in group I received L-Dopa treatments for 31 days and displayed amelioration of bradykinesia and defensive reaction on the last day (day 31) of L-Dopa therapy. No significant differences were found for tremor. Group I, n = 2; group II, n = 3. ^**P<0.001. Data are presented as mean ± SEM.</p

Chronic effects of L-Dopa treatments on total motor scores.

<p>(A) Evolution of daily motor scores during L-Dopa treatment. Timelines are aligned such that day 0 corresponds to the day on which the MPTP intoxication was stopped for each animal. Monkeys in group I received L-Dopa from day 1 and scores were taken from recordings prior to the daily L-Dopa administration. Significant differences between the two groups appeared at day 15 and continued into the later days (day 16–30). (B) Total Kurlan scores on day 31 of the two groups. Monkeys in group I received L-Dopa and displayed improvement in their total PD scores compared with the control group. Group I, n = 2; group II, n = 3. ^*P< 0.05, ^**P<0.001. Data are presented as mean ± SEM.</p

The appearance of individual PD symptoms in monkeys given MPTP intoxication.

<p>This graph presents the average day of appearance for each symptom. Error bars indicate the SEM for appearance of each symptom (n = 5).</p