Designing for Compressive Sensing: Compressive Art, Camouflage, Fonts, and Quick Response Codes

Achieving optimal CS performance requires a balance between object sparsity and distortion.

Compressive sensing (CS) is a relatively new field that has caused a lot of excitement in the signal processing community. It has superseded Shannon's time-honored sampling theorem, which states that the sampling rate of a signal must be at least twice its highest frequency. In CS, the necessary sampling rate depends on the sparsity of signal, not its highest frequency, reducing sampling requirements for many signals that exhibit natural sparsity. This compression happens on the hardware level, allowing systems to be designed with benefits ranging from increased resolution and frame rates to decreased power consumption and memory usage. Despite this enthusiasm for CS and the large quantity of research being performed, the number of commercial systems that use CS is relatively few. The problem of designing a CS strategy that increases functionality while actually reducing overall system cost has not been solved in many areas. This is a developing field where not only are new applications for CS still being developed, but also fundamental aspects of CS theory are still evolving.

Even though CS has not become ubiquitous at this early date, one can look forward to a time in which it plays an important role in many sensing systems. Considering this possible future, it is important not only to properly design the CS sensor, but to also consider how the objects being sensed can be designed to increase overall system performance.

Figure 1. Moire pattern example

This idea is not unique to CS; examples of designing objects to improve the performance of specific technologies can be found in other areas as well. The image on the left of Figure 1 shows a moire pattern caused by interference between the shirt's stripes and the pattern of the imaging array. When television (TV) newscasters are told to avoid clothes that could cause these patterns, the objects being sensed (the newscasters) are effectively being designed to increase the performance of the sensing system (the TV cameras). Another example is the magnetic ink character recognition (MICR) font shown in Figure 2. This font is used on checks and was designed not only to be readable by humans but also to increase the character recognition performance of MICR readers.

Figure 2. MICR font

Before exploring how objects can be designed for CS, a short review of CS theory is presented and simple examples are shown demonstrating the advantage of modifying an object's sparsity to increase or decrease CS performance. In more complex object recognition applications, an object's sparsity must be balanced against other factors. Increasing an object's sparsity improves CS performance, resulting in higher reconstruction quality and improved object recognition. But the very act of increasing sparsity distorts the object, which can impair recognition. Simulation results show that by balancing these competing factors, an optimal design can be achieved.

This work was done by Michael L Don for the Army Research Laboratory. ARL-0209

This Brief includes a Technical Support Package (TSP).
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Designing for Compressive Sensing: Compressive Art, Camouflage, Fonts, and Quick Response Codes

(reference ARL-0209) is currently available for download from the TSP library.

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