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Source code for 2D wavelets, wavelet packets (complete or overcomplete), complex wavelets, and complex wavelet packets:

[wavelet_code.zip] (after reading below you can click here to browse the source code through doxygen).
 

Overview: Wavelets and wavelet packets can be grown overcomplete (each overcomplete transform is invertible, etc.). Image boundaries are handled correctly. There is a test routine that implements a check for invertibility and another test routine that does denoising with hard-thresholding. The code is commented and should be easy to use and modify. Please report bugs and mistakes here. Please use the subject line "Regarding wavelet code". Thank you.
 

Notes:

• Adding new filters for wavelets is easy and can be done in wav_filters.h (see also choose_filter() in wav_trf.c). You have to make sure that the bank is properly aligned (see comments around filter_n_decimate() and upsample_n_filter() in wav_basic.c) and appropriate symmetry is chosen (periodic symmetry PS=1 for an orthonormal bank, PS=0 for symmetric banks). I always use unit energy filters so you may want to adjust your bank accordingly.

• The code compiles on linux, cygwin (Makefile included), and on Visual C++ (just include all source files in a project with either test_transforms.c or test_denoise.c). It should be portable to other major platforms without problems. This is research code, it is not intended to be fast or tight. It was intended to be easily modified (by me though, you are on your own:) I added the example code test_transforms.c and test_denoise.c, and thereby contributed further to the bug count.

• My implementation of complex wavelets is basically a port from a matlab file by Ivan Selesnick. Please check literature and Nick Kingsbury’s page to confirm that I am doing things correctly.

Manifest:

o wav_basic.c: basic filtering, decimation and upsampling routines.

o wav_basic.h: interface to wav_basic.c.

o wav_trf.c: transform routines.

o wav_trf.h: interface to wav_trf.c.

o wav_filters.h: where filter banks and their properties are defined.

o wav_filters_extern.h: interface to wav_filters.h.

o wav_gen.h: some parameters and min/max macros.

o macros.h: pointer check macro.

o test_transforms.c: main routine for testing transforms and invertibility.

o test_denoise.c: main routine for the example denoising applications.

o alloc.c: pointer allocation/deallocation.

o alloc.h: interface to alloc.c.

o Makefile

o peppers.raw: 512x512 grayscale test image.

Image Recovery Proof of Concept Demo using DCTs:

[recover.zip] : recovers a single missing block at an arbitrary location in the image, see more below

(after reading the instructions below you can click here to browse the source code through doxygen).

 

[recover_arbitrary.zip] :  recovers arbitrary shape missing regions.

This version overestimates T_0 and is slower for block recovery

(instructions for this version are in the archive).
 

General Note: There are many ways to make this code run much faster. One can do fast transforms, fast overcomplete transforms, increase dt, etc., to get orders of magnitude improvements (read factor of ~100). The demo code is a proof of concept implementation and does none of that. I will implement a fast version in the future (in the unlikely event that I have some free time :).

 

Overview: This code contains a proof of concept implementation of the ideas in:

1. Onur G. Guleryuz, "Nonlinear Approximation Based Image Recovery Using Adaptive Sparse Reconstructions and Iterated Denoising: Part I - Theory," IEEE Transactions on Image Processing, in review. [.pdf]

2. Onur G. Guleryuz, "Nonlinear Approximation Based Image Recovery Using Adaptive Sparse Reconstructions and Iterated Denoising: Part II - Adaptive Algorithms,"IEEE Transactions on Image Processing, in review. [.pdf]

 

Please try it on different types of image regions. Please report bugs and mistakes here. Please use the subject line "Regarding image recovery code". Thank you.
 

Notes:

• The code compiles on linux, cygwin (Makefile included), and on Visual C++ (just include all source files in a project). It should be portable to other major platforms without problems. This is research code, it is not intended to be fast, tight, or bulletproof.

1. First run, ./recover_demo, without any options  to see the usage info.

2. Then try, ./recover_demo lena.raw lena_filled.raw 512 512 167 110 16

3. Open lena_filled.raw in your favorite image viewer and go to row 167 and column 110 (start counting from 0 for both). The 16x16 region there has been erased and filled by the algorithm. Compare with the original. Also open mean_filled.raw in your favorite image viewer to compare with the image that has that block filled only by the surrounding mean. (On my linux machine I got: "Performed 458 iterations Recovered region, PSNR 26.526 dB").

4. If you want you can erase that portion in lena.raw yourself and then try again in case you do not trust the program. In that case the PSNRs reported by the program will be wrong and you will have to calculate PSNR on your own.

Manifest:

o dct_trf.c: code that handles forward/inverse dcts.

o dct_trf.h: interface to dct_trf.c.

o init_vals.c: calculates rudimentary statistics to intialize the algorithm.

o init_vals.h: interface to init_vals.c.

o layer.c: two ways of implementing my layer recovery iterations.

o layer.h: interface to  layer.h.

o recover.c: main routine.

o support_routines.c: pointer allocation/deallocation, etc.

o support_routines.h: interface to support_routines.c.

o threshold.c: simple hard-thresholding.

o threshold.h: interface to threshold.c.

o Makefile

o lena.raw, barbara.raw:512x512 grayscale test images.