Restoration by Compression

Yehuda Dar, Michael Elad, Alfred M. Bruckstein

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


In this paper, we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods were suggested only for the Gaussian denoising task, leaving more complicated restoration problems without a generally constructive approach. Here, we present practical methods for complexity-regularized restoration of signals, accommodating deteriorations caused by a known linear degradation operator of an arbitrary form. Our iterative procedure, obtained using the alternating direction method of multipliers (ADMM) approach, addresses the restoration task as a sequence of simpler problems involving \ell -2 -regularized estimations and rate-distortion optimizations (considering the squared-error criterion). We replace the rate-distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression. Additionally, we propose a shift-invariant complexity regularizer, measuring the bit-cost of all the shifted forms of the estimate, extending our method to use averaging of decompressed outputs gathered from compression of shifted signals. On the theoretical side, we present an analysis of complexity-regularized restoration of a cyclo-stationary Gaussian signal from deterioration by a linear shift-invariant operator and an additive white Gaussian noise. The theory shows that optimal complexity-regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter. These ideas are realized also in the proposed practical methods. Finally, we present experiments showing good results for image deblurring and inpainting using the JPEG2000 and HEVC compression standards.

Original languageEnglish
Article number8469083
Pages (from-to)5833-5847
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number22
StatePublished - 15 Nov 2018
Externally publishedYes


  • Complexity regularization
  • alternating direction method of multipliers (ADMM)
  • image deblurring
  • rate-distortion optimization
  • signal restoration

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


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