Compressive Sensing system for recording of ECoG signals in-vivo

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and interleave these outputs with the others in order to maintain the largest distance betweenthe FFs which are involved, for instance, that means not considered as successive outputs bit 3in 4FF-PRBS and bit 1 in 5FF-PRBS for the output i, and bit 4 in 4FF-PRBS and bit 2 in 5FF-PRBS for the output i + 1, because this choice introduced correlation in that fragment of randomsequence.Figure 4.1.3.2. Serial Implementation with two PRBS (4-FF and 5-FF) to obtain 16 outputs.In 4.1.3 it is studied the randomness of this model, because, as the XORing crossing has beenexploited as much as possible to maximize the number of outputs per pair of PRBScombination, the model shows fragments in some of the states are shifted versions of previousstates. In spite of the partial correlation which exist between successive outputs of the mixedrandom generator, regarding how the random values are provided to the measurement matrixand by considering that each of the outputs of this matrix generator block supplies a column ofthe measurement matrix at each integration period (see Fig. 4.1.3.3), the correlation betweenthe generated sequences in this design does not affect the performance of the reconstructionbecause the similarity periods do not occur simultaneously and they are shifted in time. ThisPRBS has been implemented for different dimensions of the measurement matrix in Cadenceand it is considered in the CS operation along the next chapters.44Figure 4.2.3.3. Random states propagation by columns to the measurement matrix.
4.1.4. Randomness CheckingIn order to ensure that random sequences generation which has been achieved with the newserial-parallel model explain in 4.1.3 is truly random, some simple test have been have beensettled up. The first of them has been to calculate the cross-correlation between the rows of themeasurement matrix in order to evaluate if the outcome is similar to the one which results bychecking the cross-correlation between two random binary sequences create by the availablefunction randint of Matlab.In the same way, if the complete matrix is taken into consideration in an unique sequence, andit is researched by applying a Power Spectra Density (PSD) analysis, if there are binary patternswhich are regularly repeated in the complete sequence.Lastly, the Matlab random benchmark based on the function runstest has been exploited andcompares with the results which are acquired for the case of random sequences created by thepreciously exposed randint function of Matlab. The function runstest performs a runs test on thesequence of observations in the vector x. This is a test of the null hypothesis that the values in xcome in random order, against the alternative that they do not. The test is based on the numberof runs of consecutive values above or below the mean of x. Too few runs indicate a tendencyfor high and low values to cluster. Too many runs indicate a tendency for high and low values toalternate. The test returns the logical value h = 1 if it rejects the null hypothesis at the 5%significance level, and h = 0 if it cannot. The test treats NaN values in x as missing values, andignores them. Thereby if most of h coefficients zero, that state that the vector shows a randomorder.Nonetheless, the three previous common analyses could not to shed light in all cases. Lookingfor randomness is a awkward task because of the fact that as random sequences areconsidered, it is possible that some patterns could be recognised as determinist even when ithas derived from a true random generation, and so the test has to be intended in order to avoidas much as possible fake non-randomness. At this point, the most clarifying test to check if therandom matrix that has been modelled fulfils the required randomness is to introduce it in a CSsystem and observe the reconstruction which is accomplished as it has been done in [31].45
Page 1: August, 31 th , 2012Compressive Sen
Page 5: The present project has been submit
Page 9: AbstractThe project “Compressive
Page 13: RiassuntoIl progetto “Compressive
Page 17 and 18: IndexAcknowledgments 7Abstract 9Gan
Page 19 and 20: E.2. Signal Digital Conversion 84Gl
Page 21 and 22: Figure 6.2.1.2. Input signal Spectr
Page 23: Index of TablesTable 2.1.1. Summary
Page 26 and 27: Figure 1.1. Energy a power costs fo
Page 29 and 30: 2. State of the art2.1 Neural Signa
Page 31 and 32: patterns in response to visual targ
Page 33 and 34: 2.4. Compressive Sensing2.4.1. Comp
Page 35 and 36: 2.4.2. Sparsifying basesSparsifying
Page 37 and 38: It is worth mentioning that compres
Page 39 and 40: y specially considering the integra
Page 41 and 42: Figure 4.1.1.1. LSFR parallel (top)
Page 43: 4.1.3. Serial Implementation with t
Page 48 and 49: een designed independently as it is
Page 50 and 51: time, which has been approximated a
Page 52 and 53: Figure 5.2.2. Original and reconstr
Page 54 and 55: 6. Analog Path Design6.1. Design Di
Page 56 and 57: The spectra of the input signal hav
Page 58 and 59: Figure 6.2.1.4. LASSO reconstructio
Page 60 and 61: Figure 6.2.2.3. Compressed signals
Page 62 and 63: In this way, the pole frequency is
Page 64 and 65: A can be floating when the mixing s
Page 66 and 67: Figure 6.2.4.4. BPDN method reconst
Page 68 and 69: Figure 6.2.5.3. BPDN method reconst
Page 71 and 72: 7. Conclusions7.1. RemarksAs it is
Page 73: AppendixAppendix AConvexOptimizatio
Page 76 and 77: The total power cost for the digita
Page 78 and 79: Figure B.2.2.1. Block diagram for a
Page 80 and 81: 80Figure B.2.3.2. Binary-weighted S
Page 82 and 83: The main model is shown in Fig.C.1.
Page 84 and 85: Appendix EE.1. AmplificationThe sma
Page 87 and 88: GlossaryADC: Analog-to-Digital Conv
Page 89 and 90: References[1] D. Gangopadhyay et al
Page 91: [35] M.F. Duarte et. al., Recovery

Compressive Sensing system for recording of ECoG signals in-vivo

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