1. Ground Truth Signal
Original 32x32 spatial domain
2. Masked K-Space
Click / Drag to Paint Mask
3. L2 Least Squares
Aliased Zero-Filled Reconstruction
4. L1 ISTA (Tao Proof)
Compressed Sensing Recovery
Reconstruction Fidelity Proof Metrics
L1 Peak SNR (PSNR)
-- dB
L2 Peak SNR (PSNR)
-- dB
L1 Struct Similarity (SSIM)
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L2 Struct Similarity (SSIM)
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Active Samples / Total
256 / 1024
L1 Basis Sparsity Norm
--
Why Terence Tao's Theorem Holds:
Conventional Nyquist sampling requires taking 100% of spatial frequencies to avoid aliasing artifacts (shown in the L2 reconstruction). Tao and Candès proved that if an image is sparse in a transform basis (such as DCT or Wavelets), an L1-minimization solver (Iterative Soft-Thresholding Algorithm) converts undersampling interference into random incoherent noise and eliminates it, recovering identical crisp slice features from 25% or fewer Fourier measurements.