Shuhang Gu

As a convex relaxation of the low rank matrix factorization problem, the nuclear norm minimization has been attracting significant research interest in recent years. The standard nuclear norm minimization regularizes each singular value equally to pursue the convexity of the objective function. However, this greatly restricts its capability and flexibility in dealing with many practical problems (e.g., denoising), where the singular values have clear physical meanings and should be treated differently. In this paper we study the weighted nuclear norm minimization (WNNM) problem, where the singular values are assigned different weights. The solutions of the WNNM problem are analyzed under different weighting conditions. We then apply the proposed WNNM algorithm to image denoising by exploiting the image nonlocal self-similarity. Experimental results clearly show that the proposed WNNM algorithm outperforms many state-of-the-art denoising algorithms such as BM3D in terms of both quantitative measure and visual perception quality.

Model-based optimization methods and discriminative learning methods have been the two dominant strategies for solving various inverse problems in low-level vision. Typically, those two kinds of methods have their respective merits and drawbacks, e.g., model-based optimization methods are flexible for handling different inverse problems but are usually time-consuming with sophisticated priors for the purpose of good performance, in the meanwhile, discriminative learning methods have fast testing speed but their application range is greatly restricted by the specialized task. Recent works have revealed that, with the aid of variable splitting techniques, denoiser prior can be plugged in as a modular part of model-based optimization methods to solve other inverse problems (e.g., deblurring). Such an integration induces considerable advantage when the denoiser is obtained via discriminative learning. However, the study of integration with fast discriminative denoiser prior is still lacking. To this end, this paper aims to train a set of fast and effective CNN (convolutional neural network) denoisers and integrate them into model-based optimization method to solve other inverse problems. Experimental results demonstrate that the learned set of denoisers can not only achieve promising Gaussian denoising results but also can be used as prior to deliver good performance for various low-level vision applications.

Due to the poor lighting condition and limited dynamic range of digital imaging devices, the recorded images are often under-/over-exposed and with low contrast. Most of previous single image contrast enhancement (SICE) methods adjust the tone curve to correct the contrast of an input image. Those methods, however, often fail in revealing image details because of the limited information in a single image. On the other hand, the SICE task can be better accomplished if we can learn extra information from appropriately collected training data. In this work, we propose to use the convolutional neural network (CNN) to train a SICE enhancer. One key issue is how to construct a training dataset of low-contrast and high-contrast image pairs for end-to-end CNN learning. To this end, we build a large-scale multi-exposure image dataset, which contains 589 elaborately selected high-resolution multi-exposure sequences with 4,413 images. Thirteen representative multi-exposure image fusion and stack-based high dynamic range imaging algorithms are employed to generate the contrast enhanced images for each sequence, and subjective experiments are conducted to screen the best quality one as the reference image of each scene. With the constructed dataset, a CNN can be easily trained as the SICE enhancer to improve the contrast of an under-/over-exposure image. Experimental results demonstrate the advantages of our method over existing SICE methods with a significant margin.

Lossy image compression is generally formulated as a joint rate-distortion optimization problem to learn encoder, quantizer, and decoder. Due to the non-differentiable quantizer and discrete entropy estimation, it is very challenging to develop a convolutional network (CNN)-based image compression system. In this paper, motivated by that the local information content is spatially variant in an image, we suggest that: (i) the bit rate of the different parts of the image is adapted to local content, and (ii) the content-aware bit rate is allocated under the guidance of a content-weighted importance map. The sum of the importance map can thus serve as a continuous alternative of discrete entropy estimation to control compression rate. The binarizer is adopted to quantize the output of encoder and a proxy function is introduced for approximating binary operation in backward propagation to make it differentiable. The encoder, decoder, binarizer and importance map can be jointly optimized in an end-to-end manner. And a convolutional entropy encoder is further presented for lossless compression of importance map and binary codes. In low bit rate image compression, experiments show that our system significantly outperforms JPEG and JPEG 2000 by structural similarity (SSIM) index, and can produce the much better visual result with sharp edges, rich textures, and fewer artifacts.