A Deep Learning Approach to Structured Signal Recovery

In this paper, we develop a new framework for sensing and recovering structured signals. In contrast to compressive sensing (CS) systems that employ linear measurements, sparse representations, and computationally complex convex/greedy algorithms, we introduce a deep learning framework that supports both linear and mildly nonlinear measurements, that learns a structured representation from training data, and that efficiently computes a signal estimate. In particular, we apply a stacked denoising autoencoder (SDA), as an unsupervised feature learner. SDA enables us to capture statistical dependencies between the different elements of certain signals and improve signal recovery performance as compared to the CS approach

Wavelet Integrated CNNs for Noise-Robust Image Classification

Convolutional Neural Networks (CNNs) are generally prone to noise interruptions, i.e., small image noise can cause drastic changes in the output. To suppress the noise effect to the final predication, we enhance CNNs by replacing max-pooling, strided-convolution, and average-pooling with Discrete Wavelet Transform (DWT). We present general DWT and Inverse DWT (IDWT) layers applicable to various wavelets like Haar, Daubechies, and Cohen, etc., and design wavelet integrated CNNs (WaveCNets) using these layers for image classification. In WaveCNets, feature maps are decomposed into the low-frequency and high-frequency components during the down-sampling. The low-frequency component stores main information including the basic object structures, which is transmitted into the subsequent layers to extract robust high-level features. The high-frequency components, containing most of the data noise, are dropped during inference to improve the noise-robustness of the WaveCNets. Our experimental results on ImageNet and ImageNet-C (the noisy version of ImageNet) show that WaveCNets, the wavelet integrated versions of VGG, ResNets, and DenseNet, achieve higher accuracy and better noise-robustness than their vanilla versions.Comment: CVPR accepted pape

Monte Carlo-based Noise Compensation in Coil Intensity Corrected Endorectal MRI

Background: Prostate cancer is one of the most common forms of cancer found in males making early diagnosis important. Magnetic resonance imaging (MRI) has been useful in visualizing and localizing tumor candidates and with the use of endorectal coils (ERC), the signal-to-noise ratio (SNR) can be improved. The coils introduce intensity inhomogeneities and the surface coil intensity correction built into MRI scanners is used to reduce these inhomogeneities. However, the correction typically performed at the MRI scanner level leads to noise amplification and noise level variations. Methods: In this study, we introduce a new Monte Carlo-based noise compensation approach for coil intensity corrected endorectal MRI which allows for effective noise compensation and preservation of details within the prostate. The approach accounts for the ERC SNR profile via a spatially-adaptive noise model for correcting non-stationary noise variations. Such a method is useful particularly for improving the image quality of coil intensity corrected endorectal MRI data performed at the MRI scanner level and when the original raw data is not available. Results: SNR and contrast-to-noise ratio (CNR) analysis in patient experiments demonstrate an average improvement of 11.7 dB and 11.2 dB respectively over uncorrected endorectal MRI, and provides strong performance when compared to existing approaches. Conclusions: A new noise compensation method was developed for the purpose of improving the quality of coil intensity corrected endorectal MRI data performed at the MRI scanner level. We illustrate that promising noise compensation performance can be achieved for the proposed approach, which is particularly important for processing coil intensity corrected endorectal MRI data performed at the MRI scanner level and when the original raw data is not available.Comment: 23 page

Compressive Imaging via Approximate Message Passing with Image Denoising

We consider compressive imaging problems, where images are reconstructed from a reduced number of linear measurements. Our objective is to improve over existing compressive imaging algorithms in terms of both reconstruction error and runtime. To pursue our objective, we propose compressive imaging algorithms that employ the approximate message passing (AMP) framework. AMP is an iterative signal reconstruction algorithm that performs scalar denoising at each iteration; in order for AMP to reconstruct the original input signal well, a good denoiser must be used. We apply two wavelet based image denoisers within AMP. The first denoiser is the "amplitude-scaleinvariant Bayes estimator" (ABE), and the second is an adaptive Wiener filter; we call our AMP based algorithms for compressive imaging AMP-ABE and AMP-Wiener. Numerical results show that both AMP-ABE and AMP-Wiener significantly improve over the state of the art in terms of runtime. In terms of reconstruction quality, AMP-Wiener offers lower mean square error (MSE) than existing compressive imaging algorithms. In contrast, AMP-ABE has higher MSE, because ABE does not denoise as well as the adaptive Wiener filter.Comment: 15 pages; 2 tables; 7 figures; to appear in IEEE Trans. Signal Proces