l_(1)-l_(2)最小化模型在不同噪声下的误差估计

Error Estimation of l_(1)-l_(2) Minimization Model Under Different Noises

压缩感知理论利用信号的稀疏性这一特点,通过较少的观测数据来高概率地重构出原始信号,从而降低了采样的频率,打破了传统奈奎斯特采样定理的局限性,同时也缓解了采样设备在硬件方面的局限性,减少了数据存储,处理及传输的成本.在l_(1)-l_(2)最小化模型的基础上,讨论了当测量矩阵的限制等距常数满足一定的条件,针对不同的噪声情形,l_(1)-l_(2)最小化模型求得的解与真实解之间的误差是可以被有效控制的,并且当信号是稀疏且无噪音干扰时,原始信号可以被精确恢复.

Compressed sensing theory uses the sparsity of the signal to reconstruct the original signal with a high probability through less observation data,thus reducing the sampling frequency,breaking the limitations of the traditional Nyquist sampling theorem,and easing the hardware limitations of the sampling equipment,and redu-cing the cost of data storage,processing and transmission.On the basis of the minimization model,this paper discusses that when the restricted isometric constant of the measurement matrix satisfies certain conditions,the error between the solution obtained by the minimization model and the real solution can be effectively controlled for different noise situations,and the original signal can be accurately restored when the signal is sparse and there is no noise interference.