Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Compressed Sensing and Sparse Coding with the Difference Map   In compressed sensing, we wish to reconstruct a sparse signal $x$ from
observed data $y$. In sparse coding, on the other hand, we wish to find a
representation of an observed signal $y$ as a sparse linear combination, with
coefficients $x$, of elements from an overcomplete dictionary. While many
algorithms are competitive at both problems when $x$ is very sparse, it can be
challenging to recover $x$ when it is less sparse. We present the Difference
Map, which excels at sparse recovery when sparseness is lower and noise is
higher. The Difference Map out-performs the state of the art with
reconstruction from random measurements and natural image reconstruction via
sparse coding.

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The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc