Feature SQUARES-©ISTOCKPHOTO.COM/EMCHUK, COMPRESSION- ©ISTOCKPHOTO.COM/BIZOO_N Adapted Compressed Sensing: A Game Worth Playing Mauro Mangia, Fabio Pareschi, Riccardo Rovatti, and Gianluca Setti Abstract Despite the universal nature of the compressed sensing mechanism, additional information on the class of sparse signals to acquire allows adjustments that yield substantial improvements. In facts, proper exploitation of these priors allows to significantly increase compression for a given reconstruction quality. Since one of the most promising scopes of application of compressed sensing is that of IoT devices subject to extremely low resource constraint, adaptation is especially interesting when it can cope with hardware-related constraint allowing low complexity implementations. We here review and compare many algorithmic adaptation policies that focus either on the encoding part or on the recovery part of compressed sensing. We also review other more hardware-oriented adaptation techniques that are actually able Digital Object Identifier 10.1109/MCAS.2019.2961727 Date of current version: 11 February 2020 40 IEEE CIRCUITS AND SYSTEMS MAGAZINE to make the difference when coming to real-world implementations. In all cases, adaptation proves to be a tool that should be mastered in practical applications to unleash the full potential of compressed sensing. I. Introduction ll the magic of Compressed Sensing (CS) [1] is in the possibility of going back and forth between two vectors x ! R n and y ! R m with m 1 n providing the first is l-sparse (l 1 m). This means that an n × d matrix D called dictionary exists such that the instances of x can be expressed as x = Dp with p having not more than l non-zero entries. We go from x to y (the encoding step) with a linear transformation y = Ax for a certain m × n matrix. We go from y to x (the decoding step) by exploiting the sparsity A 1531-636X/20©2020IEEE FIRST QUARTER 2020http://www.ISTOCKPHOTO.COM/BIZOO_N