Affine rank minimization problem is the generalized version of low rank matrix completion problem where linear combinations of the entries of a low rank matrix are observed and the matrix is estimated from these measurements. We propose a trainable deep neural network by unrolling a popular iterative algorithm called the singular value thresholding (SVT) algorithm to perform this generalized matrix completion which we call Learned SVT (LSVT). We show that our proposed LSVT with fixed layers (say T) reconstructs the matrix with lesser mean squared error (MSE) compared with that incurred by SVT with fixed (same T) number of iterations and our method is much more robust to the parameters which need to be carefully chosen in SVT algorithm.

翻译：Affine排级最小化问题是低级矩阵完成问题的普遍版本,即观测到低级矩阵条目的线性组合,并从这些测量中估算出矩阵。我们建议通过释放一种称为单值阈值(SVT)算法的流行性迭代算法来进行这一通用矩阵完成(我们称之为Clearn SVT(LSVT) ) 。我们表明,我们提议的LSVT以固定层(Say T)重建矩阵时,与SVT的固定迭代数(同T)和我们的方法比,与SVT的固定迭代数(与T相同)产生的错误(MSE)相比,与SVT的错误(MSE)相比,与SVT中需要谨慎选择的参数相比,我们的方法要更牢固得多。