Real-valued Noiselet Transform for Image Compression Sensing

In image compressed sensing applications, employing the real-valued Noiselet transform as a measurement matrix enables efficient image compression with reduced storage requirements. This transform technique decomposes images into localized frequency components through computational algorithms that typically involve recursive matrix operations or fast transform implementations. The core implementation often utilizes recursive functions that apply specific weighting patterns to pixel neighborhoods, achieving significant data reduction while preserving visual quality. By maintaining critical image information through selective frequency domain representation, the real-valued Noiselet transform has become essential in image compression systems. It provides crucial solutions for efficient image storage and transmission, with practical implementations featuring O(n log n) computational complexity similar to fast Fourier transforms but with better sparse representation capabilities for natural images.