An Efficient Compression Method for Sign Information of DCT Coefficients via Sign Retrieval
Chihiro Tsutake, Keita Takahashi, Toshiaki Fujii
TL;DR
The paper tackles the intractable problem of compressing sign information for DCT coefficients in block-based image compression. It introduces sign retrieval (SR), a phase-retrieval–driven approach that recovers sign bits at the decoder from magnitude information, while sign bits are omitted from the encoder stream. The authors provide a non-convex SR formulation, a convex relaxation inspired by PhaseMax and compressive sampling, and a cascaded Fienup algorithm to solve it efficiently, including an $oldsymbol{\Psi}$-based sparsity-promoting regularization. Experimental results in a JPEG framework show lower sign-bit entropy and improved rate-distortion compared with prior methods, with cascading SR further enhancing performance; the method has potential applicability to standards like HEVC and VVC as a drop-in enhancement for sign compression.
Abstract
Compression of the sign information of discrete cosine transform coefficients is an intractable problem in image compression schemes due to the equiprobable occurrence of the sign bits. To overcome this difficulty, we propose an efficient compression method for such sign information based on phase retrieval, which is a classical signal restoration problem attempting to find the phase information of discrete Fourier transform coefficients from their magnitudes. In our compression strategy, the sign bits of all the AC components in the cosine domain are excluded from a bitstream at the encoder and are complemented at the decoder by solving a sign recovery problem, which we call sign retrieval. The experimental results demonstrate that the proposed method outperforms previous techniques for sign compression in terms of a rate-distortion criterion. Our method implemented in Python language is available from https://github.com/ctsutake/sr.