The dogma of signal processing maintains that a signal must be sampled at a rate at least twice its highest frequency in order to be represented without error. However, in practice, we often compress the data soon after sensing, trading off signal representation complexity (bits) for some error (consider JPEG image compression in digital cameras, for example). Clearly, this is wasteful of valuable sensing resources. Over the past few years, a new theory of "compressive sensing" has begun to emerge, in which the signal is sampled (and simultaneously compressed) at a greatly reduced rate. As the compressive sensing research community continues to expand rapidly, it behooves us to heed Shannon's advice.
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Brain computer interfaces (BCI) provide a direct communication link between the brain and a computer or other external devices. They offer an extended degree of freedom either by strengthening or by substituting human peripheral working capacity and have potential applications in various fields such as rehabilitation, affective computing, robotics, gaming, and neuroscience. Significant research efforts on a global scale have delivered common platforms for technology standardization and help tackle highly complex and non-linear brain dynamics and related feature extraction and classification challenges. Time-variant psycho-neurophysiological fluctuations and their impact on brain signals impose another challenge for BCI researchers to transform the technology from laboratory experiments to plug-and-play daily life. This review summarizes state-of-the-art progress in the BCI field over the last decades and highlights critical challenges.
Computing systems are reaching the fundamental limits of the energy required for fully reliable computation [16, 128]. At the same time, many important applications have nondeterministic specifications or are robust to noise in their execution. We dedicate the next section of the review (Section 2) to providing an overview of application domains with quality versus resource usage tradeoffs, and we provide two detailed examples in Section 3. They thus do not necessarily require fully reliable computing systems and their resource consumption can be reduced. For instance, many applications processing physical-world signals often have multiple acceptable outputs for a large part of their input domain. Because all measurements of analog signals have some amount of measurement uncertainty or noise and digital signal representations necessarily introduce quantization noise, it is not always necessary to perform exact computation on data resulting from uncertain measurements of real-world physical signals.
Many computing systems that interact with the physical world or that process data gathered from it, have high computational demands under tightly constrained resources. These systems, which include many embedded and multi-media systems, must often process noisy inputs and must trade fidelity of their outputs for lower resource usage. Because they are designed to process data from noisy inputs, such as from sensors that convert from an analog signal into a digital representation, these applications are often designed to be resilient to errors or noise in their inputs [207].
Several pioneering research efforts investigated trading precision and accuracy for signal processing performance [7] and exploiting the tolerance of signal processing algorithms to noise [79, 186]. When the outputs of such systems are destined for human consumption (e.g., audio and video), common use cases can often tolerate some amount of noise in their I/O interfaces [201--203, 206, 208].
Many applications from the domains of signal processing and machine learning have traditionally had to grapple with tradeoffs between precision, accuracy, application output fidelity, performance, and energy efficiency (see, e.g., Sections 2.2 and 2.6). Many of the techniques applied in these domains have been reimagined in recent years, with a greater willingness of system designers to explicitly trade reduced quality for improved efficiency.
We discuss two applications from the signal processing and machine learning domains: a pedometer and digit recognition. Using these examples, we suggest ways in which resource usage versus correctness tradeoffs can be applied across the layers of the hardware stack, from sensors, over I/O, and to computation. We use these applications to demonstrate how end-to-end resource usage could potentially be improved even more when tradeoffs are exploited at more than one layer of the system stack.
Applications that process data measured from the physical world must often contend with noisy inputs. Signals such as temperature, motion, and so on, which are analyzed by such sensor-driven systems, are usually the result of multiple interacting phenomena that measurement equipment or sensors can rarely isolate. At the same time, the results of these sensor signal processing applications may not have a rigid reference for correctness. This combination of input noise and output flexibility leads to many sensor signal processing applications having tradeoffs between correctness and resource usage.
Digit recognition is the computational task of determining the correct cardinal number corresponding to an image of a single handwritten digit. Neural networks [111] are one popular technique to perform digit recognition. A typical neural network implementation of digit recognition takes an array of pixel values from an image capture device such as a CMOS or CCD camera and outputs, on its final layer, an encoding of the classified digit value. The ultimate input source is a potentially noisy digital representation of an analog signal (an image) and the output is a digital (decimal) interpretation of that input.
The effect of quantization errors can be observed by treating the inputs and outputs of a computing system as real-valued analog signals and comparing these signals to an ideal (error-free) computing system that accepts analog inputs and produces analog outputs. When such ideal outputs are not available, designers often use the output of the highest precision available (e.g., double-precision floating point) as the reference from which to determine the error of a reduced-precision block. Such analyses are common in the design process of digital signal processing algorithms such as filters [154] where the choice of number representation and quantization level enables a tradeoff between the performance and signal-to-noise ratio properties of a system.
Temam et al. empirically show that the conceptual error tolerance of neural networks translates into the defect tolerance of hardware neural networks [213], paving the way for their introduction in heterogeneous processors as intrinsically error-tolerant and energy-efficient accelerators. St. Amant et al. demonstrate a complete system and toolchain, from circuits to a compiler, that features an area- and energy-efficient analog implementation of a neural accelerator that can be configured to approximate general purpose code [198]. The solution of St. Amant et al. comes with a compiler workflow that configures the neural network's topology and weights. A similar solution was demonstrated with digital neural processing units, tightly coupled to the processor pipeline [57], delivering low-power approximate results for small regions of general-purpose code. Neural accelerators have also been developed for GPUs [229], as well as FPGAs [145].
In contrast to channel coding techniques whose objective is to counteract the effect of noise, Chen et al. [36] exploit the presence of noise to improve image processing tasks, demonstrating how adding Gaussian noise to quantized images can improve the output quality of signal processing tasks. This observation that noise can improve a computing system's performance has parallels to randomized algorithms (see, e.g., Section 9). 2ff7e9595c