Compressive sensing is a computational framework for acquisition and processing of sparse signals at sampling rates below the rates mandated by the Nyquist sampling theorem. In this paper, we present seven MATLAB functions for compressive sensing based time-frequency processing of sparse nonstationary signals. These functions are developed to reproduce figures in our companion review paper.

The design of effective transcutaneous systems demands the consideration of inevitable variations in tissue characteristics, which vary across body areas, among individuals, and over time. The purpose of this paper was to design and evaluate several printed antenna topologies for ultrahigh frequency (UHF) transcutaneous power transfer to implantable medical devices, and to investigate the effects of variations in tissue properties on dipole and loop topologies. Here, we show that a loop antenna topology provides the greatest achievable gain with the smallest implanted antenna, while a dipole system provides higher impedance for conjugate matching and the ability to increase gain with a larger external antenna. In comparison to the dipole system, the loop system exhibits greater sensitivity to changes in tissue structure and properties in terms of power gain, but provides higher gain when the separation is on the order of the smaller antenna dimension. The dipole system was shown to provide higher gain than the loop system at greater implant depths for the same implanted antenna area, and was less sensitive to variations in tissue properties and structure in terms of power gain at all investigated implant depths. The results show the potential of easily-fabricated, low-cost printed antenna topologies for UHF transcutaneous power, and the importance of environmental considerations in choosing the antenna topology.

Compressive sensing is a framework for acquiring sparse signals at sub-Nyquist rates. Once compressively acquired, many signals need to be processed using advanced techniques such as time-frequency representations. Hence, we overview recent advances dealing with time-frequency processing of sparse signals acquired using compressive sensing approaches. The paper is geared towards signal processing practitioners and we emphasize practical aspects of these algorithms. First, we briefly review the idea of compressive sensing. Second, we review two major approaches for compressive sensing in the time-frequency domain. Thirdly, compressive sensing based time-frequency representations are reviewed followed by descriptions of compressive sensing approaches based on the polynomial Fourier transform and the short-time Fourier transform. Lastly, we provide brief conclusions along with several future directions for this field.

Deep learning, a relatively new branch of machine learning, has been investigated for use in a variety of biomedical applications. Deep learning algorithms have been used to analyze different physiological signals and gain a better understanding of human physiology for automated diagnosis of abnormal conditions. In this paper, we provide an overview of deep learning approaches with a focus on deep belief networks in electroencephalography applications. We investigate the state-of-the-art algorithms for deep belief networks and then cover the application of these algorithms and their performances in electroencephalographic applications. We covered various applications of electroencephalography in medicine, including emotion recognition, sleep stage classification, and seizure detection, in order to understand how deep learning algorithms could be modified to better suit the tasks desired. This review is intended to provide researchers with a broad overview of the currently existing deep belief network methodology for electroencephalography signals, as well as to highlight potential challenges for future research.