Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userUtilizing the Wavelet Transforms Structure in Compressed Sensing
56
0
0.0
(
0
)
Added by
Nicholas Dwork
Publication date
2020
fields
Electronic Engineering
and research's language is
English
Ask ChatGPT about the research
No Arabic abstract
Compressed sensing has empowered quality image reconstruction with fewer data samples than previously though possible. These techniques rely on a sparsifying linear transformation. The Daubechies wavelet transform is a common sparsifying transformation used for this purpose. In this work, we take advantage of the structure of this wavelet transform and identify an affine transformation that increases the sparsity of the result. After inclusion of this affine transformation, we modify the resulting optimization problem to comply with the form of the Basis Pursuit Denoising problem. Finally, we show theoretically that this yields a lower bound on the error of the reconstruction and present results where solving this modified problem yields images of higher quality for the same sampling patterns.
rate research
Read More
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it is a useful sparsifying transformation to be used with compressed sensing. Although the curvelet transform of a natural image is sparse, the low-frequency portion is not. This manuscript presents a method to modify the sparsifying transformation to take advantage of this fact. Instead of relying on sparsity for this low-frequency estimate, the Nyquist-Shannon theorem specifies a square region to be collected centered on the $0$ frequency. A Basis Pursuit Denoising problem is solved to determine the missing details after modifying the sparisfying transformation to take advantage of the known fully sampled region. Finally, by taking advantage of this structure with a redundant dictionary comprised of both the wavelet and curvelet transforms, additional gains in quality are achieved.
Compressed sensing fluorescence microscopy (CS-FM) proposes a scheme whereby less measurements are collected during sensing and reconstruction is performed to recover the image. Much work has gone into optimizing the sensing and reconstruction portions separately. We propose a method of jointly optimizing both sensing and reconstruction end-to-end under a total measurement constraint, enabling learning of the optimal sensing scheme concurrently with the parameters of a neural network-based reconstruction network. We train our model on a rich dataset of confocal, two-photon, and wide-field microscopy images comprising of a variety of biological samples. We show that our method outperforms several baseline sensing schemes and a regularized regression reconstruction algorithm.
We investigate a reconstruction limit of compressed sensing for a reconstruction scheme based on the L1-norm minimization utilizing a correlated compression matrix with a statistical mechanics method. We focus on the compression matrix modeled as the Kronecker-type random matrix studied in research on multi-input multi-output wireless communication systems. We found that strong one-dimensional correlations between expansion bases of original information slightly degrade reconstruction performance.
In applications of scanning probe microscopy, images are acquired by raster scanning a point probe across a sample. Viewed from the perspective of compressed sensing (CS), this pointwise sampling scheme is inefficient, especially when the target image is structured. While replacing point measurements with delocalized, incoherent measurements has the potential to yield order-of-magnitude improvements in scan time, implementing the delocalized measurements of CS theory is challenging. In this paper we study a partially delocalized probe construction, in which the point probe is replaced with a continuous line, creating a sensor which essentially acquires line integrals of the target image. We show through simulations, rudimentary theoretical analysis, and experiments, that these line measurements can image sparse samples far more efficiently than traditional point measurements, provided the local features in the sample are enough separated. Despite this promise, practical reconstruction from line measurements poses additional difficulties: the measurements are partially coherent, and real measurements exhibit nonidealities. We show how to overcome these limitations using natural strategies (reweighting to cope with coherence, blind calibration for nonidealities), culminating in an end-to-end demonstration.
Compressed sensing proposes to reconstruct more degrees of freedom in a signal than the number of values actually measured. Compressed sensing therefore risks introducing errors -- inserting spurious artifacts or masking the abnormalities that medical imaging seeks to discover. The present case study of estimating errors using the standard statistical tools of a jackknife and a bootstrap yields error bars in the form of full images that are remarkably representative of the actual errors (at least when evaluated and validated on data sets for which the ground truth and hence the actual error is available). These images show the structure of possible errors -- without recourse to measuring the entire ground truth directly -- and build confidence in regions of the images where the estimated errors are small.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
