Adaptive Compressed Sensing with Diffusion-Based Posterior Sampling

TL;DR

AdaSense tackles rapid image acquisition by marrying adaptive compressed sensing with diffusion-based posterior sampling. It uses a pre-trained diffusion model to sample from the posterior $p(\mathbf{x}|\mathbf{y})$ and to estimate the conditional covariance, guiding a greedy, sequential selection of the next measurement directions in $\mathbf{H}$. The method is training-free, domain-agnostic, and validated on CelebA-HQ face data as well as MRI and sparse-view CT, showing competitive performance with training-based approaches while enabling real-world acceleration. By leveraging zero-shot priors and efficient posterior sampling (e.g., DDRM with modest NFEs), AdaSense yields practical gains in reconstruction quality under limited measurements, with clear implications for faster MRI/CT workflows and broader adaptive sensing applications.

Abstract

Compressed Sensing (CS) facilitates rapid image acquisition by selecting a small subset of measurements sufficient for high-fidelity reconstruction. Adaptive CS seeks to further enhance this process by dynamically choosing future measurements based on information gleaned from data that is already acquired. However, many existing frameworks are often tailored to specific tasks and require intricate training procedures. We propose AdaSense, a novel Adaptive CS approach that leverages zero-shot posterior sampling with pre-trained diffusion models. By sequentially sampling from the posterior distribution, we can quantify the uncertainty of each possible future linear measurement throughout the acquisition process. AdaSense eliminates the need for additional training and boasts seamless adaptation to diverse domains with minimal tuning requirements. Our experiments demonstrate the effectiveness of AdaSense in reconstructing facial images from a small number of measurements. Furthermore, we apply AdaSense for active acquisition of medical images in the domains of magnetic resonance imaging (MRI) and computed tomography (CT), highlighting its potential for tangible real-world acceleration.

Figures (9)

• Figure 1: A diagram of AdaSense. In each acquisition step, the diffusion model generates conditional posterior samples, which are then used to estimate the posterior's covariance. The ground truth image (highlighted in blue) is measured using our newly-chosen sensing matrix, corresponding to the directions of highest uncertainty in the posterior distribution. This cycle continues until sufficient measurements are acquired. Finally, AdaSense leverages these measurements to restore the final image.
• Figure 2: Progressive restoration using AdaSense, demonstrating the increasing image reconstruction quality with the accumulation of additional measurements. The number of reconstruction steps is denoted below each image, each step adds 24 measurements.
• Figure 3: Face image restoration using AdaSense. We illustrate how our adaptive approach (bottom) is better for image reconstruction than block-downsampling or bicubic-downsampling (top), where measurements have 192 elements. Notably, AdaSense successfully preserves some finer details (circled in blue). Also, we compare AdaSense with the optimal non-adaptive approach, using PCA (\ref{['eq:pca']}) on the distribution of training images. The images are restored using DDRM.
• Figure 4: Graphs of the effect of adaptivity on restoration. AdaSense is used to restore the same set of images using the same total number of measurements $N\cdot r$, but with different numbers of iterations $N$ and measurements per iteration $r$. The image restoration improves considerably the more adaptive the algorithm.
• Figure 5: MRI active restoration using AdaSense. We compare various subsampling masks with AdaSense, restoring vertical subsampling with acceleration 10 and subsampling with acceleration 400. Images are reconstructed using DDRM kawar2022denoising. Each column of the figure shows, from left to right: the subsampling mask, the zero-filled measurements, the restored image, the ground-truth image, and the absolute error. The central 320×320 region is cropped and the image intensity is displayed.

Theorems & Definitions (2)

• proof
• proof