Recently, low-rank matrix recovery theory has been emerging as a significant progress for various image processing problems. Meanwhile, the group sparse coding (GSC) theory has led to great successes in image restoration (IR) problem with each group contains low-rank property. In this paper, we...
Tensor robust principal component analysis via tensor nuclear norm (TNN) minimization has been recently proposed to recover the low-rank tensor corrupted with sparse noise/outliers. TNN is demonstrated to be a convex surrogate of rank. However, it tends to over-penalize large singular values and ...
Group sparse representation (GSR) based method has led to great successes in various image recovery tasks, which can be converted into a low-rank matrix minimization problem. As a widely used surrogate function of low-rank, the nuclear norm based convex surrogate usually leads to over-shrinking ...
The matrix completion (MC) problem is to recover a low-rank matrix from a small amount of observations:minX∈Rn1×n2{rank(X):AX=b}, where A is a linear operator and b∈Rn3. In general, we choose A as a componentwise projection [4], [9]. Due to the minimization of ℓ0-...
It is also more robust to data with outliers—for example, salt and pepper noise. Wright et al. [16] proposed the problem of low-rank restoration, which decomposes the original data as the sum of the low-rank matrix and sparse noise matrix. Candes et al. [17] accurately removed large ...
Figure 2. Time-frequency diagram: (a) periodic impulsive features; (b) noisy signal. 3. The Proposed Fault Information-Based Sparse Low-Rank Algorithm The sparsity and low-rank characteristics of the fault features are explored in Section 2. To abstract the STFT coefficient matrix X correspondi...
As illustrated in Section 2.1, natural images consist of rich self-repetitive structures suggesting that the image matrix rank should be relatively low. However, due to the influence of noise or blur, the information obtained by patch clustering algorithms is insufficient. As such, we employ low-...