Phantom Denoising - A Compressed Sensing and Multiscale Transform Approach

Phantom_denoising is an image denoising method that integrates compressed sensing (CS) with multiscale transformations. The core methodology involves sparse representation and reconstruction optimization of noisy signals through two distinct transform domains: Non-Subsampled Contourlet Transform (NSCT) and Undecimated Wavelet Transform (UWT). In code implementation, this typically involves creating transform objects, applying forward transforms to decompose images, and implementing optimization algorithms for sparse recovery.

In the CS+UWT denoising approach, the algorithm first decomposes the image into multiscale spaces using undecimated wavelet transform. Subsequently, compressed sensing theory is applied to perform threshold processing on high-frequency noise coefficients while preserving valid signal components. This method requires careful selection of wavelet bases and is particularly suitable for handling noise with local characteristics. Code implementation would involve wavelet filter design, coefficient thresholding functions, and iterative reconstruction algorithms.

The CS+NSCT denoising method employs non-subsampled contourlet transform, which offers superior directional selectivity and can more accurately capture image edges and texture information. Through adaptive thresholding and sparse optimization, this approach effectively removes noise while better preserving image details. Implementation typically includes directional filter banks, multiscale decomposition routines, and adaptive threshold calculation functions based on coefficient statistics.

Both methods follow a "decomposition-thresholding-reconstruction" workflow, but the NSCT version demonstrates better performance on complex texture images, while the UWT version offers higher computational efficiency. In practical applications, developers need to balance computational cost against denoising accuracy requirements, often implementing both approaches with configurable parameters for different use cases.