Instrumentation & Measurement Magazine 26-5 - 12

Five Guidelines for Practical
Compressive Sensing with a
Case Study in Antenna Pattern
Measurement
Michael Don and Gonzalo Arce
C
ompressive sensing (CS) is a signal processing technique
that has found applications in numerous
fields, providing benefits such as lower power consumption,
reduced memory usage, higher resolution, and
faster measurement speed. Despite the vast theoretical advancements
in CS, its commercial applications have been
slow to develop. Moreover, alternative sensing strategies may
outperform CS in many real-world scenarios. In a previous
publication [1], five guidelines were proposed to facilitate the
use of CS in practical applications. In this follow-on article,
we delve into each of these guidelines in detail, using compressive
antenna pattern measurement as a case study. By
understanding the limitations of CS and choosing appropriate
applications, the test and measurement community will
be able to successfully utilize its benefits in practical systems.
Introduction
Over the last two decades, CS has emerged as a powerful signal
processing technique that has been applied to diverse areas
ranging from radio astronomy and hyperspectral imaging to
X-ray tomography and electron microscopy. It can be applied
to system design in numerous ways to improve resolution,
memory usage, power consumption, and measurement speed.
Despite substantial theoretical progress, practical hardware implementations
of CS have encountered significant challenges
[2]. Frequently, alternative sensing strategies can outperform
CS in many real-world applications. CS has been particularly
successful with measurement applications in controlled, lownoise
environments, such as magnetic resonance imaging [3],
X-ray computed tomography [4], and spectral imaging [5].
There are many CS review articles [6], [7]. Most are too
detailed for the layman and do not focus on practical implementation.
Others are too general to provide guidance on how
to successfully apply CS to measurement systems. A previous
publication sought to fill this gap, giving an intuitive explanation
of CS, and presenting five guidelines for practical CS,
using compressive antenna pattern measurement as a case
study [1].
The five guidelines are:
1. Critical Need: There must be sufficient motivation to
apply CS to the measurement process. For example, there
must be a pressing need to improve measurement speed,
resolution, or power consumption.
2. Simple Implementation: The CS measurements should be
easily obtainable. Either current measurement hardware
should be easily adaptable to accommodate compressed
measurements, or new hardware should be low-cost and
easy to integrate into the measurement system.
3. Sparse Data: The data must be sparse in some basis. For
example, images are usually sparse in wavelet or Fourier
bases. Typically, higher dimensional 3D or 4D data is very
sparse, making it ideal for CS.
4. Computing Resources: There must be sufficient time and
computational power available for signal reconstruction.
5. Low-Noise Environment: The signal should be measured
in a controlled, low-noise environment.
In this follow-on article, each of the five guidelines is
explained in greater depth, once again using compressive antenna
pattern measurement for illustration. By understanding
these guidelines, the test and measurement community will
be able to find appropriate applications to fully realize the
benefits of CS.
Critical Need
In this age of inexpensive digital computing, many measurement
systems sample continuous analog signals, transforming
them into discrete values for processing, analysis, and storage.
The sampling rate of time varying signals, or the resolution of
spatially varying signals, is a critical system parameter. If it is
too high, it can increase expense, power consumption, processing
resources, and measurement time. If it is too low, important
information can be lost, severely degrading performance.
This paper contains extended research originally presented at IEEE AUTOTESTCON 2022 and recognized as Best Technical Paper
(© IEEE 2022, used with permission, [1]).
12
IEEE Instrumentation & Measurement Magazine
1094-6969/23/$25.00©2023IEEE
August 2023

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