IEEE Circuits and Systems Magazine - Q1 2020 - 51

VII. Adaptation for Hardware Implementation
When dealing with implementations of CS-based acquisition systems, the concept of adaptation can be considered also from an "hardware-oriented" perspective.
As an example, CS has been characterized so far by the
set of linear projections expressed by y = Ax. However,
when dealing with a real world input signal, the very
concept of projection and scalar product is heavily dependent on the way in which the input signal information is encoded. In other word, it is fundamental to keep
into account the signal representation.
The aim of this section is to review both standard
and innovative approaches to examine practical problems that can arise in hardware implementations of
CS-based acquisition systems and present an overview
of solutions employed in integrated circuits presented
so far in the literature. Referring to the above example,
a brief survey is enough to identify the many different
FIRST QUARTER 2020

possibilities in which the linear projections y = Ax are
computed according to the different input signal model.
The solution for this and other issues usually requires
the adaptation of the CS framework either at circuital or
even at system level.

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The previous analysis (see Figure 6(b)) suggests that,
since D is an orthonormal basis, it is convenient to us
the pow-R method that yields consistent improvement
across multiple target quality levels. From [12] we get
that LQ reconstruction supporting, for example, heart
rate estimation may feature an ARSNR as low as 7 dB.
Yet, from [46] we get that HQ reconstruction must provide an ARSNR not smaller than 34 dB.
From Figure 7 we get that, when neither the encoder nor the decoder is adapted, an LQ recovery of the
signal requires m LQ = 86 thus yielding a 6.0:1 compression, while HQ recovery requires m HQ = 232 thus yielding a 2.2:1 compression. This second result is a pretty
standard one as it is accepted that straightforward CS
applied to ECGs is a computationally effective way of enjoying a compression in the order of 2:1.
Furthermore, introducing pow-R at the encoder and
dec-P at the decoder, i.e., the case where both encoder
and decoder are designed in according to an adapted
CS method, the number of measurements is reduced to
m LQ = 36 and m HQ = 137 thus increasing the compression ratio from 6.0:1 to 14.2:1 in the LQ case and from
2.2:1 to 3.7:1 in the HQ case. To give an intuitive feeling on the improvement due to adaptation we may consider 5 windows of an ideal ECG profile as reported at
the top of Figure 8. Based on that profile we test both
the non-adapted encoder-decoder pair and the adapted one, using the number of measurements that make
the adapted pair work either at LQ (m LQ = 36) or HQ
(m HQ = 137 ).
In Figure 8, the yellow-background plots refer to the
m LQ = 36, while the green-background plots refer to
m HQ = 137. Independently of the compression, adapted
CS widely outperforms the non-adapted option.

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dec-ZZ
dec-JZ
dec-p
BPDN

100

34 40
ARSNR

Figure 7. Performance of different decoder adaptation policies.

Original Signal

i.i.d. + BPDN

pow-R + dec-P (Compression Ratio 14.2:1)
LQ

i.i.d. + BPDN

pow-R + dec-P (Compression Ratio 3.7:1)
HQ

Time

Figure 8. Example reconstruction of an ECG signal (black
track) by non-adapted (red tracks) and adapted (blue tracks)
CS for different compression ratios.

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