In compressed sensing, we wish to reconstruct a sparse signal $x$ fromobserved data $y$. In sparse coding, on the other hand, we wish to find arepresentation of an observed signal $y$ as a sparse linear combination, withcoefficients $x$, of elements from an overcomplete dictionary. While manyalgorithms are competitive at both problems when $x$ is very sparse, it can bechallenging to recover $x$ when it is less sparse. We present the DifferenceMap, which excels at sparse recovery when sparseness is lower and noise ishigher. The Difference Map out-performs the state of the art withreconstruction from random measurements and natural image reconstruction viasparse coding.
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机译：在压缩感测中，我们希望从观察到的数据$ y $重建稀疏信号$ x $。另一方面，在稀疏编码中，我们希望找到观察信号$ y $的表示形式，该信号是来自不完整字典的元素的稀疏线性组合，系数为xx $。当$ x $非常稀疏时，许多算法在两个问题上都具有竞争性，但是当$ x $稀疏时，它可以具有挑战性地恢复$ x $。我们提出了差分图，当稀疏度较低而噪声较高时，它在稀疏恢复方面表现出色。差异图在通过随机测量进行重建和通过稀疏编码进行自然图像重建方面表现优于现有技术。
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