Compressive Sampling Method For Nuclear Signals

In modern high-energy physics experiments, the collision energy, experimental scale, and physical event rate increase dramatically. The trandional methods in signal acquisition, like amplifying and shaping, are unable to adapt to this development direction. In this way, a waveform digitizer method is developed. It follows Shannon sampling theorem:the sampling rate must be at least twice the maximum of signal frequency. In order to reconstruct the fast detector output signals, the sampling rate is required faster, resulting in a series of problems, such as power consumption, cost, size, cooling, transmission, storage, processing, etc.Compressive sensing/sampling (CS) is a novel theory in signal processing since2004. CS theory asserts that one can stably and accurately reconstruct the original signals from far fewer samples or measurements than traditional Shannon sampling methods use, if certain conditions are met. In this compressive sampling method, the sampling rate will be much lower than the Nyquist rate, and the amount of data generated during the sampling process also will be greatly reduced. In recent years, theories and practical techniques of CS have made considerable progresses. For example, there has been designed a compressed sensing hardware device, the random modulation pre-integrator (RMPI). Furthermore, CS is also carried out extensive applied research in many fields. However, CS has not been researched in signal acquisition in nuclear physics and high-energy physics experiments.Accordingly, a compressive sampling method applicable to the nuclear signals is researched in this paper, which provides a new idea for nuclear signal acquisition of modern high-energy physics and nuclear physics experiments. In order to achieve this goal, this needs to solve at least the following key questions:1. the sparse representation of nuclear signals;2. the feasibility to resolve the compressive sampling of nuclear signals in the existing theoretical framework of CS;3. the suitable sparse recovery algorithm;4. the hardware architecture which can implement the compressive sampling of nuclear signals.The mathematical model of CS represents an underdetermined system of linear equations, which means that the number of equations is less than the number of unknowns. To solve this underdetermined system accurately, one needs to exploit prior knowledge that the signal is sparsely represented in a transform domain. Then the underdetermined system can be transformed to a l0minimization problem with constraint, which is a NP-hard problem. Under certain conditions, the non-convex l0minimization problem can be transformed to a convex l1minimization problem to be solved. According to the characteristics of CS theory, to solve four key scientific questions mentioned before, the research has been carried out in this paper as followers:First, we have made an investigation of the basic generation mechanism of the radiation detector output signals, and then make a simple analysis of the sparsity of nuclear signals. The nuclear signals are sparsely represented as short pulse signals by using the Gabor frame. Second, for comparison, we have made an analysis of the general data acquisition architecture based on Shannon sampling theorem. Third, we use the sparse recovery algorithm to reconstruct the original signals by solving the l1minimization problem of the underdetermined system. Fourth, we use the random demodulator which is one of hardware architectures based on CS to implement the compressive sampling of nuclear signals.