Table 2: Complexity Comparison.
W
t
FANQEX
t
FANQMS−3
t
FANEX
t
FANQMS−3
t
FANQMS−3
t
t
FANQEX
t
FANQMS−2
t
FANEX
t
FANQMS−2
t
FANQMS−2
t
500 29.18 4.50 4.18 47.75 7.35 2.80
1000 29.06 4.49 4.21 46.07 7.12 2.64
across more windows (updating model infrequently),
this overhead can also be signiﬁcantly reduced. This
is also indicated by the comparing the rowsof Table 2,
as the complexity gains for FANQMS-2 increase as
W increases from 500 to 1000 (the ratio
t
FANQMS−2
t
de-
creases from 2.80 to 2.64).
7 CONCLUSIONS
We present a low-complexity joint non-uniform sam-
pling and quantization based strategy for signal com-
pression. Speciﬁcally, we combine the FAN algo-
rithm with a minimum mean-squared error quantiza-
tion strategy to compress ECG signals. We ﬁrst for-
mulate the joint design of non-uniform sampling and
quantization for compression, as a constrained opti-
mization problem in terms of maximizing the relevant
distortion metric given the desired compression rate.
The solution of this optimization yields the optimal
sampling sensitivity, and the number of levels to be
used by the quantizer. In general, and for arbitrary
signals, it may not be possible to solve this optimiza-
tion efﬁciently. However, for ECG signals, we show
that we can develop simple parametric models to cap-
ture the impact of the FAN algorithm and quantiza-
tion on the resulting distortion (PRD) and rate, es-
pecially in very low bit-rate operating regions. Us-
ing these models we can efﬁciently determine the op-
timal FAN selectivity parameter ε and quantization
levels L to minimize the PRD for a given rate con-
straint. We design two model based algorithms, one
that re-estimates model parameters for every window
(W samples), and another that updates model parame-
ters every alternate window. We show that with these
strategies, we can achieve up to 2 times the compres-
sion rate of FAN (for the same PRD) with a com-
plexity less than 3 times that of FAN alone. We also
show that the performance of these algorithms ap-
proaches (within 10% in rate when ε < 1.8) an ex-
haustive search based strategy for different signals,
and window sizes. Given the low complexity of FAN
our algorithms still remain signiﬁcantly lower com-
plexity than state-of-the-art transform based compres-
sion schemes, while achieving comparable perfor-
mance. Directions for future research include design
of the optimal search strategy to re-estimate model pa-
rameters (how often, optimal window size etc.), the-
oretical analysis of the signal frequency and statis-
tical properties as well as algorithm complexity for
rate-distortion-complexityoptimal joint sampling and
quantization, and application of these ideas for other
multi-dimensional medical signals.
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PROCESSING
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