Rank Minimization for Snapshot Compressive Imaging

Abstract

Snapshot compressive imaging (SCI) refers to compressive imaging systems where multiple frames are mapped into a single measurement, with video compressive imaging and hyperspectral compressive imaging as two representative applications. Though exciting results of high-speed videos and hyperspectral images have been demonstrated, the poor reconstruction quality precludes SCI from wide applications. This paper aims to boost the reconstruction quality of SCI via exploiting the high-dimensional structure in the desired signal. We build a joint model to integrate the nonlocal self-similarity of video/hyperspectral frames and the rank minimization approach with the SCI sensing process. Following this, an alternating minimization algorithm is developed to solve this non-convex problem. We further investigate the special structure of the sampling process in SCI to tackle the computational workload and memory issues in SCI reconstruction. Both simulation and real data (captured by four different SCI cameras) results demonstrate that our proposed algorithm leads to significant improvements compared with current state-of-the-art algorithms. We hope our results will encourage the researchers and engineers to pursue further in compressive imaging for real applications.Index Terms-Compressive sensing, computational imaging, coded aperture, image processing, video processing, nuclear norm, rank minimization, low rank, hyperspectral images, coded aperture snapshot spectral imaging (CASSI), coded aperture compressive temporal imaging (CACTI).

Video from Stills: Lensless Imaging with Rolling Shutter

“…Another technique, proposed by Llull and Yuan et al, achieved high-speed video reconstruction (22 frames at 660 fps) from a single-shot coded-aperture image that is obtained by translating binary amplitude masks within the focal plane of a global shutter sensor [3], [4]. Koller et al later improved the mask design [5] and Liu et al proposed a reconstruction that exploits the low-rank structure of the underlying scene [6]. The commonality between these setups is that each pixel is temporally modulated during the exposure, and all require bulky and expensive hardware.…”

Snapshot Compressed Sensing: Performance Bounds and Algorithms

“…On the other hand, (θ t ij ) 2 and (θ t+1 ij ) 2 are bounded as (53), i.e., |θ t ij | 2 ≤ ρ 2 nBδ , |θ t+1 ij | 2 ≤ ρ 2 nBδ Therefore,…”

“…One drawback of the JPEG-based MPEG compression is that, since it relies on discrete Cosine transformation (DCT) of individual local patches, it does not exploit nonlocal similarities [50] (The most recent video Codec, e.g., H.265/266 considers the similarities between patches but the patches need to be connected, thus it is still local similarity). Using nonlocal similarities in images or videos can potentially improve the performance significantly and this has been observed in various applications [32], [51]- [53].…”

High-speed compressed-sensing fluorescence lifetime imaging microscopy of live cells

“…Here Ci,m,n-k Im,n-k,k (i = 1, 2) represents the complimentary-coded, sheared scene, and the inverse problem of equation 10can be solved using existing compressed-sensing algorithms 35,59,60 .…”