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Compressed sensing recovery with unlearned neural networks
This report investigates methods for solving the problem of compressed sensing, in which the goal is to recover a signal from noisy, linear measurements. Compressed sensing techniques enable signal recovery with far fewer measurements than required by traditional methods such as Nyquist sampling. Signal recovery is an incredibly important area in application domains such as consumer electronics, medical imaging, and many others. While classical methods for compressed sensing recovery are well established, recent developments in machine learning have created wide opportunity for improvement. In this report I first discuss pre-existing approaches, both classical and modern. I then present my own contribution to this field: creating a method using untrained machine learning models. This approach has several advantages which enable its use in complex domains such as medical imagingElectrical and Computer Engineerin
The Power of Triply Complementary Priors for Image Compressive Sensing
Recent works that utilized deep models have achieved superior results in
various image restoration applications. Such approach is typically supervised
which requires a corpus of training images with distribution similar to the
images to be recovered. On the other hand, the shallow methods which are
usually unsupervised remain promising performance in many inverse problems,
\eg, image compressive sensing (CS), as they can effectively leverage non-local
self-similarity priors of natural images. However, most of such methods are
patch-based leading to the restored images with various ringing artifacts due
to naive patch aggregation. Using either approach alone usually limits
performance and generalizability in image restoration tasks. In this paper, we
propose a joint low-rank and deep (LRD) image model, which contains a pair of
triply complementary priors, namely \textit{external} and \textit{internal},
\textit{deep} and \textit{shallow}, and \textit{local} and \textit{non-local}
priors. We then propose a novel hybrid plug-and-play (H-PnP) framework based on
the LRD model for image CS. To make the optimization tractable, a simple yet
effective algorithm is proposed to solve the proposed H-PnP based image CS
problem. Extensive experimental results demonstrate that the proposed H-PnP
algorithm significantly outperforms the state-of-the-art techniques for image
CS recovery such as SCSNet and WNNM
Pixel Adaptive Deep Unfolding Transformer for Hyperspectral Image Reconstruction
Hyperspectral Image (HSI) reconstruction has made gratifying progress with
the deep unfolding framework by formulating the problem into a data module and
a prior module. Nevertheless, existing methods still face the problem of
insufficient matching with HSI data. The issues lie in three aspects: 1) fixed
gradient descent step in the data module while the degradation of HSI is
agnostic in the pixel-level. 2) inadequate prior module for 3D HSI cube. 3)
stage interaction ignoring the differences in features at different stages. To
address these issues, in this work, we propose a Pixel Adaptive Deep Unfolding
Transformer (PADUT) for HSI reconstruction. In the data module, a pixel
adaptive descent step is employed to focus on pixel-level agnostic degradation.
In the prior module, we introduce the Non-local Spectral Transformer (NST) to
emphasize the 3D characteristics of HSI for recovering. Moreover, inspired by
the diverse expression of features in different stages and depths, the stage
interaction is improved by the Fast Fourier Transform (FFT). Experimental
results on both simulated and real scenes exhibit the superior performance of
our method compared to state-of-the-art HSI reconstruction methods. The code is
released at: https://github.com/MyuLi/PADUT.Comment: ICCV 202
Linear Inverse Problems and Neural Networks
We investigate two ideas in this thesis. First, we analyze the results of adaptingrecovery algorithms from linear inverse problems to defend neural networks against adversarial attacks. Second, we analyze the results of substituting sparsity priors with neural network priors in linear inverse problems. For the former, we are able to extend the framework introduced in [1] to defend neural networks against ℓ0, ℓ2,and ℓ∞ norm attacks, and for the latter, we find that our method yields an improvement over reconstruction results of [2]
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