Combining Gradient-Based and Thresholding Methods for Improved Signal Reconstruction Performance

Analysis of sparse signals has been attracting the attention of the research community in recent years. Several approaches for sparse signal recovery have been developed to provide accurate recovery from a small portion of available data. This paper proposes an improved combined approach for both accurate and computationally efficient signal recovery. Particularly, the proposed approach uses the benefits of the gradient-based steepest descent method (that belongs to the convex optimization group of algorithms) in combination with a specially designed thresholding method. This approach includes solutions for several commonly used sparse bases – the discrete Fourier, discrete cosine transform, and discrete Hermite transform, but can be adapted for other transformations as well. The presented theory is experimentally evaluated and supported by empirical data. Various analytic and real-world signals are used to assess the performance of the proposed algorithm. The analyses are performed for different percentages of available samples. The complexity of the presented algorithm can be seen through the analog hardware implementation presented in this paper. Additionally, the user-friendly graphical interface is developed with a belonging signal database to ease usage and testing. The interface allows users to choose various parameters and to examine the performance of the proposed tool in different scenarios and transformation bases.