Maximum length sequence encoded Hadamard measurement paradigm for compressed sensing

The development of compressed sensing technology has greatly facilitated its applications in many fields, such as medical imaging, multi-sensor and distributed sensing, coding theory, hyper-spectral imaging, and machine learning. Among these applications, the permuted Walsh-Hadamard matrices are frequently chosen for modeling real-world measurements that are limited to binary entry states by special structure (one typical example is the digital mirror device in singlepixel cameras) because the fast Walsh-Hadamard transform can efficiently calculate its multiplications; however, for a large-scale problem, the Walsh-Hadamard matrix would become unacceptably large to be stored in advance. To eliminate this defect, this paper proposes a maximum length sequence encoded Hadamard measurement paradigm that can be simply realized on chip without any usage of external memory, and proves this method can degenerate to a special permutation of the sequence ordered Walsh-Hadamard matrix so that the fast Walsh-Hadamard transform keeps feasible. Simulations show that compared with the conventional permuted Walsh-Hadamard matrix, the proposed one can emerge from the limit of external memory without losing much randomness performance in the measurement basis required by compressed sensing.