NSCT

NSCT, short for Non-Subsampled Contourlet Transform, is a multi-scale, multi-directional image representation designed to provide a shift-invariant and redundant analysis of images. It extends the contourlet framework by avoiding downsampling in all stages, resulting in a highly redundant transform that preserves edge and texture information more reliably under translation.

The transform is built from two main components. The non-subsampled pyramid (NSP) decomposes the image into progressively coarser low-pass and high-pass bands without decimation, creating a multi-scale framework that captures image structure at different resolutions. The non-subsampled directional filter bank (NSDFB) then partitions the high-frequency content of each scale into a set of oriented subbands, providing rich directional information without sacrificing shift invariance. The combination yields a comprehensive, directionally selective representation suitable for a range of image analysis tasks.

Key properties of NSCT include shift invariance, redundancy, and strong directional selectivity. Because no subsampling occurs, small translations of the input do not significantly alter the transform coefficients, which improves robustness in tasks such as denoising and texture analysis. The representation is capable of capturing smooth regions, edges, and textures with high fidelity across multiple scales and orientations.

Common applications encompass image denoising, restoration, fusion, texture analysis, feature extraction, and compression experiments where robust, directionally rich representations are desirable. NSCT has influenced subsequent developments in image processing by providing a flexible, shift-invariant framework for sparse and stable image representation. See also contourlet transform and directional filter banks.