We propose an unfolded accelerated projected-gradient descent procedure to estimate model and algorithmic parameters for image super-resolution and molecule localization problems in image microscopy. The variational lower-level constraint enforces sparsity of the solution and encodes different noise statistics (Gaussian, Poisson), while the upper-level cost assesses optimality w.r.t.~the task considered. In more detail, a standard $\ell_2$ cost is considered for image reconstruction (e.g., deconvolution/super-resolution, semi-blind deconvolution) problems, while a smoothed $\ell_1$ is employed to assess localization precision in some exemplary fluorescence microscopy problems exploiting single-molecule activation. Several numerical experiments are reported to validate the proposed approach on synthetic and realistic ISBI data.

翻译：我们提出一种展开加速投影梯度下降流程，用于在显微成像中估计图像超分辨与分子定位问题的模型及算法参数。变分下层约束强制解的稀疏性并编码不同噪声统计特性（高斯、泊松），而上层代价函数则针对所考虑任务评估最优性。具体而言，针对图像重建问题（如去卷积/超分辨、半盲去卷积）采用标准$\ell_2$代价函数，而利用单分子激活的典型荧光显微定位问题中，则采用平滑$\ell_1$代价评估定位精度。通过合成数据与真实ISBI数据的多组数值实验验证了所提方法的有效性。