  Given the prevalence of JPEG compressed images, optimizing image
reconstruction from the compressed format remains an important problem. Instead
of simply reconstructing a pixel block from the centers of indexed DCT
coefficient quantization bins (hard decoding), soft decoding reconstructs a
block by selecting appropriate coefficient values within the indexed bins with
the help of signal priors. The challenge thus lies in how to define suitable
priors and apply them effectively.
  In this paper, we combine three image priors---Laplacian prior for DCT
coefficients, sparsity prior and graph-signal smoothness prior for image
patches---to construct an efficient JPEG soft decoding algorithm. Specifically,
we first use the Laplacian prior to compute a minimum mean square error (MMSE)
initial solution for each code block. Next, we show that while the sparsity
prior can reduce block artifacts, limiting the size of the over-complete
dictionary (to lower computation) would lead to poor recovery of high DCT
frequencies. To alleviate this problem, we design a new graph-signal smoothness
prior (desired signal has mainly low graph frequencies) based on the left
eigenvectors of the random walk graph Laplacian matrix (LERaG). Compared to
previous graph-signal smoothness priors, LERaG has desirable image filtering
properties with low computation overhead. We demonstrate how LERaG can
facilitate recovery of high DCT frequencies of a piecewise smooth (PWS) signal
via an interpretation of low graph frequency components as relaxed solutions to
normalized cut in spectral clustering. Finally, we construct a soft decoding
algorithm using the three signal priors with appropriate prior weights.
Experimental results show that our proposal outperforms state-of-the-art soft
decoding algorithms in both objective and subjective evaluations noticeably.

Computer Vision and Pattern Recognition