Approximate Message Passing (AMP) type algorithms are widely used for signal recovery in high-dimensional noisy linear systems. Recently, a principle called Memory AMP (MAMP) was proposed. Leveraging this principle, the gradient descent MAMP (GD-MAMP) algorithm was designed, inheriting the strengths of AMP and OAMP/VAMP. In this paper, we first provide an overflow-avoiding GD-MAMP (OA-GD-MAMP) to address the overflow problem that arises from some intermediate variables exceeding the range of floating point numbers. Second, we develop a complexity-reduced GD-MAMP (CR-GD-MAMP) to reduce the number of matrix-vector products per iteration by 1/3 (from 3 to 2) with little to no impact on the convergence speed.

翻译：近似消息传递（AMP）类算法被广泛用于高维噪声线性系统中的信号恢复。最近，一种称为内存近似消息传递（MAMP）的原理被提出。基于该原理，梯度下降MAMP（GD-MAMP）算法被设计出来，继承了AMP和OAMP/VAMP的优势。本文首先提出一种避免溢出的GD-MAMP（OA-GD-MAMP），以解决因某些中间变量超出浮点数表示范围而导致的溢出问题。其次，我们开发了一种复杂度降低的GD-MAMP（CR-GD-MAMP），将每次迭代所需的矩阵-向量乘积次数减少三分之一（从3次降至2次），同时对收敛速度几乎没有影响。