Graph-Based Depth Denoising & Dequantization for Point Cloud Enhancement.

A 3D point cloud is typically constructed from depth measurements acquired by sensors at one or more viewpoints. The measurements suffer from both quantization and noise corruption. To improve quality, previous works denoise a point cloud a posteriori after projecting the imperfect depth data onto 3D space. Instead, we enhance depth measurements directly on the sensed images a priori, before synthesizing a 3D point cloud. By enhancing near the physical sensing process, we tailor our optimization to our depth formation model before subsequent processing steps that obscure measurement errors. Specifically, we model depth formation as a combined process of signal-dependent noise addition and non-uniform log-based quantization. The designed model is validated (with parameters fitted) using collected empirical data from a representative depth sensor. To enhance each pixel row in a depth image, we first encode intra-view similarities between available row pixels as edge weights via feature graph learning. We next establish inter-view similarities with another rectified depth image via viewpoint mapping and sparse linear interpolation. This leads to a maximum a posteriori (MAP) graph filtering objective that is convex and differentiable. We minimize the objective efficiently using accelerated gradient descent (AGD), where the optimal step size is approximated via Gershgorin circle theorem (GCT). Experiments show that our method significantly outperformed recent point cloud denoising schemes and state-of-the-art image denoising schemes in two established point cloud quality metrics.

Iteratively reweighted ℓ1-ℓ2 norm minimization using wavelets in inverse scattering.

Recently, many techniques have been employed to solve inverse scattering problems by exploiting the sparsity of the scatterer in the wavelet basis. In this paper, we propose an iteratively reweighted $ {\ell _1} $ norm regularization scheme within the settings of the Born iterative method (BIM) to effectively leverage the sparsity of the wavelet coefficients. This "iteratively reweighted $ {\ell _1} $ minimization" method is then used along with $ {\ell _2} $ norm minimization in order to achieve solutions that are not over-smoothened at the discontinuities. The proposed method is an expansion of a well-known joint $ {\ell _1} {-} {\ell _2} $ norm minimization technique. The advantage offered by the algorithm is that the reconstruction is now independent of the initial choice of weights. This technique accounts for the fact that sparsity is concentrated more in the detail wavelet coefficients rather than their coarse counterpart. The effectiveness of the method is demonstrated using several 2D inverse scattering examples by employing it in each iteration of the BIM.

Iteratively reweighted ℓ1-ℓ2 norm minimization using wavelets in inverse scattering: publisher's note.

This publisher's note corrects the author list in J. Opt. Soc. Am. A37, 680 (2020).JOAOD60740-323210.1364/JOSAA.381365.