A new algorithm is proposed for a) unsupervised learning of sparse
representations from subsampled measurements and b) estimating the parameters
required for linearly reconstructing signals from the sparse codes. We verify
that the new algorithm performs efficient data compression on par with the
recent method of compressive sampling. Further, we demonstrate that the
algorithm performs robustly when stacked in several stages or when applied in
undercomplete or overcomplete situations. The new algorithm can explain how
neural populations in the brain that receive subsampled input through fiber
bottlenecks are able to form coherent response properties.

提出了一种新算法，用于从子采样测量中无监督地学习稀疏表示并估计用于从稀疏编码线性重构信号的参数，进一步证明该算法在数据压缩方面效率与压缩采样的最近方法相当，同时演示在堆叠多层或在欠完备或过完备情况下应用时该算法的鲁棒性，该算法能够解释大脑中接收通过纤维瓶颈的子采样输入的神经群体如何形成连贯的响应特性。

自适应压缩采样：作为大脑通讯原则的子采样数据解密

Deciphering subsampled data: adaptive compressive sampling as a  principle of brain communication

Modeling data with linear combinations of a few elements from a learned
dictionary has been the focus of much recent research in machine learning,
neuroscience and signal processing. For signals such as natural images that
admit such sparse representations, it is now well established that these models
are well suited to restoration tasks. In this context, learning the dictionary
amounts to solving a large-scale matrix factorization problem, which can be
done efficiently with classical optimization tools. The same approach has also
been used for learning features from data for other purposes, e.g., image
classification, but tuning the dictionary in a supervised way for these tasks
has proven to be more difficult. In this paper, we present a general
formulation for supervised dictionary learning adapted to a wide variety of
tasks, and present an efficient algorithm for solving the corresponding
optimization problem. Experiments on handwritten digit classification, digital
art identification, nonlinear inverse image problems, and compressed sensing
demonstrate that our approach is effective in large-scale settings, and is well
suited to supervised and semi-supervised classification, as well as regression
tasks for data that admit sparse representations.

本文提出了一种通用的配合各种任务的有监督学习词典的方法，并介绍了一个解决相应优化问题的高效算法，实验证明这种方法适用于大规模的监督和半监督分类，以及对能够产生稀疏表示的数据的回归任务。