We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional neural network. Recently, it has been argued that the distribution of natural images do not lie in a single manifold but rather lie in a union of several submanifolds. We propose a sparsity-driven latent space sampling (SDLSS) framework and develop a proximal meta-learning (PML) algorithm to enforce sparsity in the latent space. SDLSS allows the range-space of the generator to be considered as a union-of-submanifolds. We also derive the sample complexity bounds within the SDLSS framework for the linear measurement model. The results demonstrate that for a higher degree of compression, the SDLSS method is more efficient than the state-of-the-art method. We first consider a comparison between linear and nonlinear sensing mechanisms on Fashion-MNIST dataset and show that the learned nonlinear version is superior to the linear one. Subsequent comparisons with the deep compressive sensing (DCS) framework proposed in the literature are reported. We also consider the effect of the dimension of the latent space and the sparsity factor in validating the SDLSS framework. Performance quantification is carried out by employing three objective metrics: peak signal-to-noise ratio (PSNR), structural similarity index metric (SSIM), and reconstruction error (RE).

翻译：我们使用深层基因先前模型处理压缩遥感问题,并审议线性和学过的非线性非线性感测机制,非线性机制涉及完全连接的神经网络或进化神经网络。最近,有人争辩说,自然图像的分布不是单一的多元的,而是几个子元体的结合。我们提议了一个由宽度驱动的潜在空间取样框架(SDLSS),并开发了一种在潜空空间中实施宽度的模拟元学习(PML)算法。SDLSS允许将发电机的射程空间视为一个完全连接的神经网络或进化神经网络。我们还从SDLSS框架中得出线性测量模型的样本复杂性界限。结果显示,为了更高程度的压缩,SDLSS方法比最先进的方法更有效。我们首先考虑对FAship-MNISTS数据集的线性和非线性最高感测机制进行比较,并表明,所学过的非线性版比线性指数的线性比线性比线性比值之高一。我们报告的SDIM结构框架的后,还参照了SDIM的精确度(SDI 的精确度框架) 和SDIM 的精确度框架。我们所报告 的精确度框架的精确度的精确度(SDI) 和SDRI 的精确度的精确度的精确度的精确度的精确度(SDI) 的精确度(SDIBIFI) 的精确度框架。