13 research outputs found
Compression-Based Compressed Sensing
Modern compression algorithms exploit complex structures that are present in
signals to describe them very efficiently. On the other hand, the field of
compressed sensing is built upon the observation that "structured" signals can
be recovered from their under-determined set of linear projections. Currently,
there is a large gap between the complexity of the structures studied in the
area of compressed sensing and those employed by the state-of-the-art
compression codes. Recent results in the literature on deterministic signals
aim at bridging this gap through devising compressed sensing decoders that
employ compression codes. This paper focuses on structured stochastic processes
and studies the application of rate-distortion codes to compressed sensing of
such signals. The performance of the formerly-proposed compressible signal
pursuit (CSP) algorithm is studied in this stochastic setting. It is proved
that in the very low distortion regime, as the blocklength grows to infinity,
the CSP algorithm reliably and robustly recovers instances of a stationary
process from random linear projections as long as their count is slightly more
than times the rate-distortion dimension (RDD) of the source. It is also
shown that under some regularity conditions, the RDD of a stationary process is
equal to its information dimension (ID). This connection establishes the
optimality of the CSP algorithm at least for memoryless stationary sources, for
which the fundamental limits are known. Finally, it is shown that the CSP
algorithm combined by a family of universal variable-length fixed-distortion
compression codes yields a family of universal compressed sensing recovery
algorithms
Reconstruction of compressed spectral imaging based on global structure and spectral correlation
In this paper, a convolution sparse coding method based on global structure
characteristics and spectral correlation is proposed for the reconstruction of
compressive spectral images. The proposed method uses the convolution kernel to
operate the global image, which can better preserve image structure information
in the spatial dimension. To take full exploration of the constraints between
spectra, the coefficients corresponding to the convolution kernel are
constrained by the norm to improve spectral accuracy. And, to solve the problem
that convolutional sparse coding is insensitive to low frequency, the global
total-variation (TV) constraint is added to estimate the low-frequency
components. It not only ensures the effective estimation of the low-frequency
but also transforms the convolutional sparse coding into a de-noising process,
which makes the reconstructing process simpler. Simulations show that compared
with the current mainstream optimization methods (DeSCI and Gap-TV), the
proposed method improves the reconstruction quality by up to 7 dB in PSNR and
10% in SSIM, and has a great improvement in the details of the reconstructed
image
Theoretical Analysis of Binary Masks in Snapshot Compressive Imaging Systems
Snapshot compressive imaging (SCI) systems have gained significant attention
in recent years. While previous theoretical studies have primarily focused on
the performance analysis of Gaussian masks, practical SCI systems often employ
binary-valued masks. Furthermore, recent research has demonstrated that
optimized binary masks can significantly enhance system performance. In this
paper, we present a comprehensive theoretical characterization of binary masks
and their impact on SCI system performance. Initially, we investigate the
scenario where the masks are binary and independently identically distributed
(iid), revealing a noteworthy finding that aligns with prior numerical results.
Specifically, we show that the optimal probability of non-zero elements in the
masks is smaller than 0.5. This result provides valuable insights into the
design and optimization of binary masks for SCI systems, facilitating further
advancements in the field. Additionally, we extend our analysis to characterize
the performance of SCI systems where the mask entries are not independent but
are generated based on a stationary first-order Markov process. Overall, our
theoretical framework offers a comprehensive understanding of the performance
implications associated with binary masks in SCI systems