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rajarshisaha95 authored Nov 4, 2023
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Expand Up @@ -11,18 +11,6 @@ Our algorithm first computes an approximate basis of the range space of $\mathbf
It then computes approximate projections of the columns of $\mathbf{A}$ onto this quantized basis.
The tradeoff between compression ratio and approximation accuracy allows for flexibility in choosing these parameters based on specific application requirements.

<p float="left">
<img src="artifacts/images/original.png" alt="Original image" width="19%">
<img src="artifacts/images/shepp-logan-rank-166_b1-4_b2-8_b0-2/nq.png" alt="Naïve quant." width="19%">
<img src="artifacts/images/shepp-logan-rank-166_b1-4_b2-8_b0-2/dsvd.png" alt="DSVD" width="19%">
<img src="artifacts/images/shepp-logan-rank-166_b1-4_b2-8_b0-2/lplr.png" alt="LPLR (ours)" width="19%">
<img src="artifacts/images/shepp-logan-rank-166_b1-4_b2-8_b0-2/lplr_svd.png" alt="LSVD (ours)" width="19%">
</p>

Original Image, Naive Quant, DSVD, LPLR, LSVD (in order)

Compression of Shepp-Logan phantom (a standard test image for medical image reconstruction). Naive quant. was done with $2$-bits per pixel of this $10^3 \times 10^3$ image. Quantizing the SVD factors ``directly" (i.e., DSVD) and (our) LPLR/LSVD algorithms factorize the image into a product of tall \& wide matrices reduces the total number of elements, allowing each entry to be represented using upto $8$-bits of precision per pixel. Despite the increase in precision per pixel, the total number of bits remains the same at $2 \cdot 10^6$.

### Algorithm

**LPLR: Randomized Low-Precision Low-Rank factorization**
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## 🚀 Trying out LPLR

## 💡 Tips
You can try out the image compression experiments from the paper using `example.ipynb` notebook

<!-- ## 💡 Tips -->

## 📊 Replicating experiments in paper

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