PatchSVD: A Non-uniform SVD-based Image Compression Algorithm

TL;DR

PatchSVD addresses efficient image compression by non-uniformly allocating bits to image patches based on a delta from a rank-1 SVD. It computes $\Delta = A - k_{rank\_SVD}(A,1)$, scores patches via a standard deviation-based metric, and applies higher-rank SVD to the most complex patches while using lower-rank representations elsewhere. Across Kodak and CLIC datasets, PatchSVD improves SSIM, PSNR, and MSE relative to standard SVD and offers distinct, often preferable, artifacts to JPEG in text- and edge-rich regions. The method is training-free, scalable, and particularly promising for high-resolution or diagnostic images where local detail preservation is critical.

Abstract

Storing data is particularly a challenge when dealing with image data which often involves large file sizes due to the high resolution and complexity of images. Efficient image compression algorithms are crucial to better manage data storage costs. In this paper, we propose a novel region-based lossy image compression technique, called PatchSVD, based on the Singular Value Decomposition (SVD) algorithm. We show through experiments that PatchSVD outperforms SVD-based image compression with respect to three popular image compression metrics. Moreover, we compare PatchSVD compression artifacts with those of Joint Photographic Experts Group (JPEG) and SVD-based image compression and illustrate some cases where PatchSVD compression artifacts are preferable compared to JPEG and SVD artifacts.

Figures (6)

• Figure 1: JPEG produces more compression artifacts in images containing text compared to the proposed method. The sample is taken from the IAM Handwriting Database and the image has been zoomed in 30 times the original size to better visualize the compression artifacts.
• Figure 2: PatchSVD algorithm first applies low-rank SVD to the original image and subtracts the low-rank approximation from the original image (Figure \ref{['subfig:a']}) to obtain $\Delta$ (Figure \ref{['subfig:b']}). Then, by applying a score function, PatchSVD calculates the patches that contain more information according to $\Delta$ (\ref{['subfig:c']}) to create the final compressed image (see Figure \ref{['subfig:d']}).
• Figure 3: This figure shows the effect of patch size on the performance of the PatchSVD algorithm across CLIC (first row) and Kodak (second row) datasets.
• Figure 4: This figure compares SSIM, PSNR, and MSE metrics for PatchSVD, JPEG, and SVD image compression algorithms on the CLIC dataset with a patch size of 10 (top row) and the Kodak dataset with a patch size of 16 (bottom row).
• Figure 5: PatchSVD, JPEG, and SVD compression algorithms applied to two image samples from the Kodim dataset show the compression artifacts produced by each algorithm. As you can see, PatchSVD produces more sharp edges which results in perfectly legible text even after the image has been greatly compressed.