CS subverts the traditional signal sampling method. It uses the sparse representation of the signal to ensure the main structure of the original signal, and then uses the reconstruction algorithm to accurately reconstruct the original signal. Some papers about image denoising schemes have been proposed using the CS methods. [PERSON]. [13] introduced a family of entropy-based sparsity measures in the performance of the BP denoising algorithm. This paper offered a new deconvolution-based method for estimating unknown sparsity, which was more applicable and reliable. In [14], a new approach was proposed for level-set formulations, including basis pursuit denoising and residual-constrained low-rank formulations. Ref. [15] presented a mathematical reasoning for improvement using the Kronecker-based recovery over standard CS recovery procedure. Compared with the standard Kronecker-based recovery technique, this technique resulted in improvement in the quality of recovered measurements. This article adopts CS theory for signal denoising, restores the original ECG and completes the noise removal according to the advantages of basis pursuit (BP) [16; 17]. BP is a method in the field of sparse signal reconstruction [18]. The classic BP algorithm denoises the signal containing Gaussian white noise, so as to achieve the purpose of signal reconstruction [19]. It has a better denoising effect on Gaussian white noise. The classical BP model cannot fully adapt to the impulse noises mentioned above, so it needs improving [20]. In [21], a distributed algorithm is proposed to solve the optimization problem by BP. It solved BP on a distributed platform such as sensor networks and aimed to minimize the communication between nodes. It sought to obtain the sparsest representation of the signal from the set of complete functions, that is, to accurately represent the original signal with as few bases as possible, so as to obtain the intrinsic characteristics of the signal. The BP method uses the norm of the representation coefficient as a measure of signal sparsity, and defines the signal sparsity representation problem as a kind of constrained extreme value problem by minimizing the L1 norm, and then transforms it into a linear programming problem for solution. In contrast, the BP method has been little considered for ECG denoising. Alternating direction method of multipliers (ADMM) is a computational framework for solving separable convex optimization problems [22]. ADMM is a simple but powerful iterative regularization algorithm that can be regarded as an attempt to combine the advantages of augmented Lagrangian methods and dual decomposition for constraint optimization [23; 24]. Some research studies in [25], [PERSON]. [26] considered ADMM, which was well suited to the distributed computation model for optimizing a sum of convex objective functions corresponding to multiple agents. [PERSON]. [27] used the ADMM to reconstruct piecewise-smooth distributed parameters of elliptical partial differential equations from noisy and linear observations of the underlying field. The distributed parameters are estimated by solving an inverse problem with total variation regularization. The following paper [28] built an ADMM algorithm model to solve the inverse problem of ECG. It adopted the method of neural network training. [PERSON]. [29] has developed a learning scheme for signal denoising using ADMM in which a single shrinkage function is constrained to be antisymmetric, firmly non-expansive, and learning from data via a simple projected gradient descent to minimize reconstruction error. [PERSON] [30] proposed the Plug-and-Play ADMM algorithm. The papers mentioned above mainly deal with image processing. In this paper, the ECG signal denoising and reconstruction method is proposed according to the BP algorithm and ADMM optimization (BP-ADMM). ADMM is used to transform the multi-variable non-convex optimization problem into an optimization problem for sub-problems, which reduces the computational complexity and difficulties.