Introduction: L1 norm constrained reconstruction/compressed sensing techniques [1, 2] have recently been proposed to accelerate data acquisitions in MRI by acquiring fewer data in k-space. Image artifacts due to k-space undersampling are resolved by minimizing L1 norm of the sparse image estimate while preserving fidelity to the acquired data. Using an L1 norm constraint exploits implicit spars...

This paper gives new results on the recovery of sparse signals using l1-norm minimization. We introduce a two-stage l1 algorithm equivalent to the first two iterations of the alternating l1 relaxation introduced in [5] for an appropriate value of the Lagrange multiplier. The first step consists of the standard l1 relaxation. The second step consists of optimizing the l1 norm of a subvector whos...

Standard Principal-Component Analysis (PCA) is known to be very sensitive to outliers among the processed data. On the other hand, in has been recently shown that L1-norm-based PCA (L1-PCA) exhibits sturdy resistance against outliers, while it performs similar to standard PCA when applied to nominal or smoothly corrupted data. Exact calculation of the K L1-norm Principal Components (L1-PCs) of ...

This paper presents a novel L1-norm semisupervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm Laplacian regularization is defined directly over the eigenvectors of the normalized Laplacian matrix, we successfully formulate semi-supervised learning as a...

In this paper, a novel algorithm is presented for the design of sparse linear-phase FIR filters. Compared to traditional l1-optimization-based methods, the proposed algorithm minimizes l1 norm of a portion (instead of all) of nonzero coefficients. In this way, some nonzero coefficients at crucial positions are not affected by l1 norm utilized in the objective function. The proposed algorithm em...

Abstract. The main goal of the paper is to establish that the L1 norm of jumps of the normal derivative across element boundaries and the L1 norm of the Laplacian of a piecewise polynomial finite element function can be controlled by corresponding weighted discrete H2 norm on convex polyhedral domains. In the finite element literature such results are only available for piecewise linear element...

As far as we know, for most polynomially solvable network optimization problems, their inverse problems under l1 or l∞ norm have been studied, except the inverse maximum-weight matching problem in non-bipartite networks. In this paper we discuss the inverse problem of maximum-weight perfect matching in a non-bipartite network under l1 and l∞ norms. It has been proved that the inverse maximum-we...

We show that data assimilation using four-dimensional variation (4DVar) can be interpreted as a form of Tikhonov regularisation, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularisation recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularisation. We apply this idea to 4D...

Recognizing a face with significant lighting, disguise and occlusion variations is an interesting and challenging problem in pattern recognition. To address this problem, many regression based methods, represented by sparse representation classifier (SRC), are presented recently. SRC uses the L1-norm to characterize the pixel-level sparse noise but ignore the spatial information of noise. In th...

We propose a fast variant of the Gaussian algorithm for the reduction of two– dimensional lattices for the l1−, l2− and l∞−norm. The algorithm runs in at most O(nM(B) log B) bit operations for the l∞−norm and in O(n log n M(B) log B) bit operations for the l1− and l2−norm on input vectors a, b ∈ ZZ with norm at most 2 where M(B) is a time bound for B-bit integer multiplication. This generalizes...