Latent diffusion models (LDMs) have emerged as a prominent framework for image generation, consisting of a diffusion model$\mathcal{M}$and a VAE decoder$\mathcal{D}$. High-quality image generation models are large and computationally intensive. As a result, image generation is typically performed on cloud servers, with the generated images then transmitted to edge devices.

Remote sensing are widely used in applications including geoexploration, topographic mapping and weather forecasting, producing vast amounts of multi and hyper-spectral image data that need to be compressed [1]. The data acquisition process often leads to artifacts in the form of stripes with unpredictable positions and amplitudes [2]. The stripes deteriorate the smoonthless of the original image, causing challenges for high-ratio lossless compression. This motivates us to propose a split-and-compress framework. Rather than direct compression, we split (decompose) the image into a smooth part and a sparse remainder (capturing the stripes and artifacts alike) and compress the two parts separately. The decomposition is achieved using a fast, robust statistics based method with linear computational complexity on the number of pixels.

In the conventional range asymmetric numeral systems (rANS), state$x$becomes larger after encoding a symbol$s$. In contrast, the proposed scheme directly outputs an$n$-bit digit$cdf_{s}+x\ (\text{mod}\ f_{s})$for symbol$s$, and decrease$x$via$x\leftarrow\lfloor x/f_{s}\rfloor$, where$2^{n}$denotes the denominator of the quantized frequency distribution,$f_{s}$and$cdf_{s}= \sum\nolimits_{i=0}^{s-1}f_{i}$represent the frequency of symbol$s$and the cumulative frequency counts, respectively. Therefore,$x$will become too small after encoding several symbols. To solve this issue, our proposal forces the state$x$always at a specific interval$I= [2^{T-vn}, 2^{T})$, and$I_{s}:=\left[f_{s}\times 2^{T-vn}, 2^{T}\right)$indicates the interval corresponding to symbol$s$, where$T, v\in \mathbb{N}$. The specific algorithm can be implemented based on the deque. Precisely, for a symbol$s$to be encoded, if the current$x$is within$I_{s}$, we encode it to an$n$-bit digit$cdf_{s}+x\ (\text{mod}\ f_{s})$and push the digit to deque. Otherwise, we first pop data from the deque to enlarge$x$before encoding. Finally, the remaining data in the deque is the desired encoded bit sequence.