Efficient Implementations for Orthogonal Matching Pursuit

Abstract

Based on the efficient inverse Cholesky factorization, we propose an implementation of OMP (called as version 0, i.e., v0) and its four memory-saving versions (i.e., the proposed v1, v2, v3 and v4). In the simulations, the proposed five versions and the existing OMP implementations have nearly the same numerical errors. Among all the OMP implementations, the proposed v0 needs the least computational complexity, and is the fastest in the simulations for almost all problem sizes. As a tradeoff between computational complexities/time and memory requirements, the proposed v1 seems to be better than all the existing ones when only considering the efficient OMP implementations storing G (i.e., the Gram matrix of the dictionary), the proposed v2 and v3 seem to be better than the only existing one when only considering the efficient implementations not storing G, and the proposed v4 seems to be better than the naive implementation that has the (known) minimum memory requirements. Moreover, all the proposed five versions only include parallelizable matrix-vector products in each iteration, and do not need any back-substitutions that are necessary in some existing efficient implementations (e.g., those utilizing the Cholesky factorization).

Real-time video super-resolution reconstruction using wavelet transforms and sparse representation

“…The OMP algorithm uses Cholesky decomposition and obtains a complexity of M D N D + M D k + 3 2 k 2 with a dictionary of size M D × N D and k number of atoms. 23 Therefore, these steps are parallelised over the matrix multiplications in both implementations, decreasing up to approximately 61%.…”

GNSS Signal Acquisition Algorithm Based on Two-Stage Compression of Code-Frequency Domain

“…The complexity of the proposed algorithm consists of three parts: frequency domain compression preprocessing, code domain compression, and signal reconstruction, of which the first and third are the main parts, and the second part can be ignored as the elements of the measurement matrix are −1 or 1. In this paper, we chose the orthogonal matching pursuit (OMP) algorithm for signal reconstruction, whose complexity is O(N • (log 2 (N)) 2 ) [30,31]. Table 1 gives the complexities of the serial acquisition algorithm, the PMF-FFT acquisition algorithm, the code-compression (CC) acquisition algorithm [26] and the proposed code-frequency compression (CFC) acquisition algorithm.…”

A review of optimisation and least-square problem methods on field programmable gate array-based orthogonal matching pursuit implementations

“…Nevertheless, the performance of parallel architectures designs still requires intensive exploration regarding output quality versus output performance of the reconstructed signal in the implementation of the OMP. There are a lot more of recent OMP implementation strategies, such as those presented in [51], which were only simulated using the MATLAB software but not on the hardware platform. Implementation in terms of hardware to accelerate the process of the new strategies will benefit the overall implementation in order to have an efficient real-time system.…”